L ICE N T IAT E T H E S I S

Department of Business Administration, Technology and Social Sciences Division of Business Administration and Industrial Engineering

Luleå University of Technology 2013

Martin Holmbom Approaches to Improve Quality in Supply Chains

ISSN: 1402-1757 ISBN 978-91-7439-555-6

Approaches to Improve Quality in Supply Chains

Martin Holmbom

Licentiate Thesis

Approaches to Improve Quality in Supply Chains

Martin Holmbom

Luleå University of Technology Department of Business Administration, Technology & Social Science Industrial Logistics and Quality Technology & Management

Printed by Universitetstryckeriet, Luleå 2013 ISSN: 1402-1757 ISBN 978-91-7439-555-6 Luleå 2013 www.ltu.se

ACKNOWLEDGEMENT The research presented in this thesis was carried out at the Division of Business Administration and Industrial Engineering for the disciplines of Industrial Logistics and Quality Technology & Management, between April 2010 and December 2012. The research was financed by the Kolarctic project Barents Logistics 2, which is partly sponsored by the Swedish organisations: Länsstyrelsen Norrbotten, Region Västerbotten and Luleå kommun. Thank you for your support. Soon after I had completed my Master’s degree in the autumn of 2009, I was sharing a cup of coffee with my close friend Peder Lundkvist at his new work. Peder had just signed up for PhD studies at Quality Technology and Management, the discipline of our master’s degree, so we sat there and enjoyed our coffee with our former teachers. We laughed and cheered at the fact that Peder had actually applied to a PhD-program, something that we had both sworn never to do just a few months earlier. Little did I know that my laughter was about to get stuck in my throat, but after we had finished our coffee someone suddenly pushed me into Bjarne Bergquist’s office, the head of the division, and before I knew it, a voice from the corridor declared: “he’s the new PhD student”. Some weeks later I stepped into my own office in that very same corridor, intensively wondering what I was doing. I would like to express my appreciation to my supervisors: Anders Segerstedt, Erik Vanhatalo, Bjarne Bergquist and Kerstin Vännman. Anders – thank you for inspiring and encouraging me and for caring about how I feel. I admire your inventiveness and your ability to see opportunities. Erik – thank you for making me believe in my skills and for your constructive criticism that always hits right on target. You are a great role model. Bjarne – thank you for giving me the opportunity to become a PhD and for your insistent support in my writing. Kerstin – thank you for your kindness and guidance that made me feel safe from day one. A special thanks also to Dr. Behzad Ghodrati for very valuable feedback on a draft of this thesis. I am very grateful to all of you! I am also grateful to all of my colleagues, especially my student colleagues Peder Lundkvist, Helena Ranängen and Charlotte Malmgren. Without your constant smiling I would have quit my academic career by now, and I would probably be doing something completely different. Thank you for making me keep trying! Finally, but certainly not least, I am grateful to my mom and dad, my brother and sister, and my loving Jessica, for encouraging me and believing in me. Thank you for being there! I dedicate this thesis to my nephew Pelle. Martin Holmbom Luleå, December 2012

I

ABSTRACT The quality in a supply chain can be improved by enhancing the customer value of the end product or by reducing the total cost of the product. This thesis focuses on values and costs associated with logistical activities in the supply chain. Two approaches to improve supply chain quality are discussed. The first approach, known as performance-based logistics (PBL), is a business model that aims to improve the quality in industries with technically advanced products, in particular in the military and aviation industry. The second approach is a mathematical solution procedure for solving economic lot scheduling problems (ELSP). The purpose of this research is to describe and develop approaches to improve the quality in supply chains. More specifically, the aims of this research are (1) to summarize previously reported benefits and drawbacks of PBL and to explore critical aspects of implementation, and (2) to develop a solution procedure that finds a feasible minimum cost production schedule for a single machine producing several different products. The results are presented in two appended papers. Paper A provides a literature study on PBL. The literature study shows that PBL can: enhance the supplier’s freedom to decide how to produce and improve the performance of a product; generate better opportunities for the supplier to earn profit; improve the supplier’s long-term competitive position; enable the customer to focus on core activities; reduce the customer’s financial risks; reduce support costs; and increase product performance. However, PBL can also: increase the supplier’s financial risks; require organizational changes that induce the supplier’s business risks; and increase the customer’s dependency on the supplier. Some of the critical aspects of implementation are: designing contracts and payment models; deciding on how to measure performance; defining performance indicators; specifying system levels; and setting target values. Paper B presents a heuristic solution procedure intended to minimize setup cost and inventory holding cost in a machine that produces several products in lots. The solution procedure generates a production schedule that can be repeated in a cyclic pattern without shortages, and it uses an extended approximation for the inventory holding cost, since previous literature has shown that the traditional approximation underestimates the cost. Keywords: logistics, production, supply chain, quality, performance-based logistics, contracting, logistic support, order quantity, scheduling, cyclic planning, economic lot scheduling.

III

SWEDISH ABSTRACT Kvaliteten i en försörjningskedja kan förbättras genom att öka slutproduktens kundvärde eller genom att minska de totala kostnaderna för produkten. Denna avhandling fokuserar på värden och kostnader kopplade till logistiska aktiviteter i försörjningskedjan. Två angreppssätt för att förbättra kvaliteten i försörjningskedjan behandlas. Det första angreppssättet, känt som prestationsbaserad logistik (PBL), är en affärsmodell med målet att förbättra kvaliteten i industrier med tekniskt avancerade produkter, framförallt inom militär- och flygindustrin. Det andra angreppssättet är en matematisk lösningsmodell för att beräkna och planera ekonomiska orderkvantiteter. Syftet med denna forskning är att utveckla och beskriva angreppssätt för att förbättra kvaliteten i försörjningskedjor. Mer specifika mål är att (1) summera tidigare rapporterade fördelar och nackdelar med PBL samt att utforska kritiska aspekter för implementering, samt (2) utveckla en lösningsmodell som finner en produktionsplan som ger lägsta möjliga kostnad för en enskild maskin som producerar flera olika produkter. Resultaten presenteras i två bilagda artiklar. Artikel A presenterar en litteraturstudie om PBL. Litteraturstudien visar att PBL kan: öka leverantörens frihet att besluta över produktion och förbättringar av en produkts prestanda; generera bättre möjligheter för leverantören att göra vinster; förbättra leverantörens långsiktiga konkurrensmässiga position; göra det möjligt för kunden att fokusera på kärnaktiviteter; minska kundens finansiella risker; minska stödkostnader; och öka produktprestanda. Men PBL kan även innebära att: leverantörens finansiella risker ökar; leverantörens affärsmässiga risker ökar till följd av organisatoriska förändringar; och att kunden blir mer beroende av leverantören. Några av de kritiska aspekterna för implementering är: utformning av kontrakt och betalningsmodeller; mätning av prestanda; definiera prestandamått; specificera systemnivåer; och sätta målvärden. Artikel B presenterar en heuristisk lösningsmodell som syftar till att minimera ställkostnad och lagerhållningskostnad i en maskin som tillverkar flera produkter satsvis. Lösningsmodellen genererar en produktionsplan som kan repeteras i ett cykliskt mönster utan att brister uppstår, och den använder en vidareutvecklad approximation för lagerhållningskostnaden, eftersom tidigare litteratur har visat att den traditionella approximationen underskattar kostnaden. Nyckelord: logistik, produktion, försörjningskedja, kvalitet, prestationsbaserad logistik, kontrakt, logistiskt stöd, orderkvantitet, schemaläggning, cyklisk planering, planering av ekonomiska orderkvantiteter.

V

CONTENTS 1. INTRODUCTION ....................................................................................... 1 1.1 Logistics ..................................................................................................................1 1.2 Quality .....................................................................................................................7 1.3 Quality in supply chains ................................................................................... 11 1.4 Research purpose and aims .............................................................................. 16 1.5 Organisation of the research process ............................................................. 16 2. PERFORMANCE-BASED LOGISTICS ................................................. 19 2.1 Benefits ................................................................................................................. 19 2.2 Drawbacks ........................................................................................................... 20 2.3 Critical aspects of implementation ................................................................. 21 3. ECONOMIC LOT SCHEDULING PROBLEMS ................................... 27 3.1 Scheduling ........................................................................................................... 28 3.2 Inventory holding cost approximation ........................................................... 30 3.3 Solution procedure ............................................................................................. 33 4. FURTHER RESEARCH .......................................................................... 37 REFERENCES ............................................................................................. 39

VII

APPENDED PAPERS The thesis includes the following two papers. The papers, which are appended in full, are summarised and discussed in the thesis. A

Holmbom, M., Bergquist, B. and Vanhatalo, E. (2012). Performancebased logistics – An illusive panacea or a concept for the future? This paper is submitted for publication. A draft version of this paper was presented at the 14th QMOD conference on Quality and Service Sciences, San Sebastian, Spain, August 2011.

B

Holmbom, M., Segerstedt, A. and van der Sluis, E. (2012). A solution procedure for Economic Lot Scheduling Problems even in high utilisation facilities. This paper is accepted for publication in International Journal of Production Research. A draft version of this paper was presented at the 17th International Working Seminar on Production Economics, Innsbruck, Austria, February 2012.

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INTRODUCTION

1. INTRODUCTION This chapter provides an introduction and background to the research area. The purpose and aims of the research are presented and the research process is described.

1.1 Logistics Doing business is essentially about finding opportunities to produce some value that customers are willing to pay for. Regardless if the value is based upon products or services the producer must figure out a way to deliver this value to the customer in order to close the deal. However, delivering products and services can be an expensive and complicated task that includes far more activities than merely transports. For example, customers expect deliveries to be cost effective which calls for high capacity utilisation, low inventory levels, suitable production plans and optimized transport routes. Customers also expect on-time deliveries and short delivery times, which in turn require high inventory service levels, flexible production, accurate demand prognoses and short lead and throughput times. These and other closely related customer demands are normally compiled and dealt with under the term logistics. Logistics can be defined as “the management of the flow of resources between the point of origin and the point of destination in order to meet some requirements” (Wikipedia). The term logistics is considered to have originated in the military’s need to supply themselves with arms, ammunition and rations as they moved from their bases to forward positions (Ballou, 2004, p. 22). In fact, some still regard logistics to be a strictly military concern, for example the Oxford English Dictionary that describes logistics as “the branch of military science relating to procuring, maintaining and transporting material, personnel and facilities” (emphasis added). However, the need for logistics has grown in other contexts as well, and logistics is therefore commonly described in a broader sense. Ever since the industrial revolution in the late 18th century logistics has been important for manufacturing firms and for business in general (Nahmias, 1997, p. xi). The Council of Logistics Management defines logistics in a business context as “…the part of the supply chain process that plans, implements, and controls the efficient, effective forward and reverses flow and storage of goods, services and related information between the point of origin and the point of consumption in order to meet customers' requirements.” That definition is indeed a suitable starting-point of this thesis. The logistical challenge within a manufacturing firm is basically to achieve high delivery service, i.e. short delivery time and on-time delivery, to a

1

INTRODUCTION

low cost (Hopp and Spearman, 2008, p. 346, Stevenson et al., 2005, Starbek and Menart, 2000). However, in many production processes it is difficult to maximize delivery service and minimize cost concurrently, and thus manufacturing firms are often forced to find a balance between the objectives (Wiendahl and Breithaupt, 1999, Hopp and Spearman, 2008, p. 331). Modig and Åhlström (2011, p. 88) describe this as a balance between flow efficiency and resource efficiency. According to them, high flow efficiency means that a large portion of a product’s lead time corresponds to value-adding operation time, and high resource efficiency means that a large portion of the available production time in a machine is utilized for value-adding operations. Thus, flow efficient manufacturers focus on the product’s flow through the production processes, and resource efficient manufacturers focus on the utilisation of the production facilities, see Figure 1-1. Which kind of efficiency to focus on is a strategic question depending on, for example, customer demands and facility conditions (Modig and Åhlström, 2011, p. 94, Wiendahl and Breithaupt, 1999).

Figure 1-1. It can be difficult to achieve high flow efficiency and high resource efficiency concurrently. Therefore, manufacturers are often forced to find a balance between these objectives.

The conflict between flow efficiency and resource efficiency can be exemplified with the production process illustrated in Figure 1-2. The process consists of five machines and inventories in-between acting as buffers. The operation time in each machine is assumed to be normally distributed with the mean μ and the standard deviation ı.

Figure 1-2. An example of a production process with five machines and inventories in-between. The operation times in the machines are assumed to be observations from a normal distribution.

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INTRODUCTION

If the process belonged to a manufacturing firm aiming for high flow efficiency probably it would prefer small inventories which generates little work in progress and thus short lead time (Starbek and Menart, 2000, Towill, 1997), see Figure 1-3a. But small inventories means that the machines occasionally will starve or be blocked due to the variance of the operation time and hence that the throughput will be low (Dallery and Gershwin, 1992, Conway et al., 1988), see Figure 1-3b. Therefore, a manufacturing firm aiming for high resource efficiency probably would prefer larger inventories to maintain a high machine utilisation and throughput. However, Meissner (2010) and Conway et al. (1988) point out that even resource efficient manufacturers must be cautious not using too high levels of work in progress since work in progress equals tied up capital and inventory holding costs, see Figure 1-3c. To find the optimal inventory size, resource efficient manufacturers must balance between the facility cost per product, which depends on the throughput, and the inventory holding cost per product, which depends on the average work in progress. Thus, manufacturers must not only balance between flow efficiency and resource efficiency to find the best combination from a strategic viewpoint, but also between different costs in order to be cost effective.

Figure 1-3. The average lead time, the average throughput and the average inventory holding cost increases with more work in progress. The lead time increases slowly at first, but accelerates when the bottleneck is fully utilised. The throughput increases dramatically with more work in progress at first, but levels off as the risks for starvation and blocking diminish. (Silver et al., 1998, p. 696, Hopp and Spearman, 2008, p. 249, Dallery and Gershwin, 1992)

Another example of cost-to-cost balancing is the well-known problem of the economic order quantity, which is derived from production processes where products are produced in lots, or order quantities. The problem assumes that a setup is required before producing each lot and that the finished products are stored in an inventory that must cover the demand between replenishments, i.e.

3

INTRODUCTION

between the lots. Moreover, it is assumed that each setup generates a setup cost, and for each day a product is stored in the inventory it generates an inventory holding cost depending on the cost of the product and the interest rate. Thus, the setup cost per day decreases with larger order quantities but the inventory holding cost per day increases, since the time between replenishments is prolonged and a larger stock is required to cover the demand. Consequently, it is possible to find an order quantity that corresponds to the minimum sum of setup cost and inventory holding cost. The economic order quantity (EOQ) can be calculated from the famous equation derived by Harris (1913); 2 AD vr

EOQ

(1.1)

where A is the setup cost, D is the demand rate, v is the cost of the product and r is the interest rate. The economic order quantity is found in the minimum point of the total cost curve, which corresponds to the optimal balance between inventory holding cost and setup cost (Hopp and Spearman, 2008, p. 52), see Figure 1-4. Section 1.3 provides a more thorough discussion on economic order quantities and the relation to production scheduling.

Figure 1-4. The inventory holding cost/product increases and the setup cost/product decreases with larger order quantity. The economic order quantity corresponds to the minimum point of the total cost curve, which is where the inventory holding cost equals the setup cost.

The inbound logistical challenges that have been mentioned so far are important for firms to address since they affect both the efficiency and effectiveness, and in the end the firm’s profitability. However, the prosperity of a firm also depends on how well other firms in the same supply chain succeed in their mission to refine products and meet the end customers’ demands and 4

INTRODUCTION

requirements (Simchi-Levi et al. (2003, p. 5). A supply chain can be described as a logistics network that consist of retailers, wholesalers, manufacturers, suppliers and customers (Mattson, 2012, p. 16, Hopp, 2008, p. 5), as well as raw materials, work in progress inventory and finished products that flow between the processes (Simchi-Levi et al., 2003, p. 1), see Figure 1-5.

Figure 1-5. A supply chain is a network of processes and stock points necessary to transform materials and information to products and deliver them to customers. Adapted from Hopp (2008, p.6).

The revenue of all firms in a supply chain depends on the willingness of the customer to buy the finished product, since the customer contributes with external cash flow (Mattson, 2012, p. 55). Therefore, it should be in all firm’s interest to maximize the overall value and minimize the overall cost of the supply chain as a whole (Christopher, 1998, p. 16). Many firms have accordingly realized the importance of the supply chain, and the mind-set of competition has in many businesses shifted from firm-to-firm competition to supply chain-to-supply chain competition (Chandra et al., 2000, Lambert and Cooper, 2000). The optimization of an entire supply chain is a difficult and complex task that requires efficiency improvements and system-wide reduction of costs due to, for example, transportation and distribution, raw material inventories, work in progress, and finished products, (Simchi-Levi et al. (2003, p. 2), That kind of systemwide approach for improvements is known as supply chain management. According to Christopher (1998, p. 18), supply chain management is “the management of upstream and downstream relationships with suppliers and 5

INTRODUCTION

customers to deliver superior customer value at less cost to the supply chain as a whole.” Thus, supply chain management aims to achieve opportunities for cost or customer service improvements, and the means commonly focus on coordination and collaboration between the firms (Ballou, 2004, p. 5). Information technology is often regarded as a key issue for successful supply chain management, since information is crucial for the firms’ ability to take decisions that achieve performance at or near the overall optimum, see Chopra and Meindl (2010, p. 488), Meissner (2010) and Tummala et al. (2006). But decisions that gain the overall performance do not necessarily benefit the specific firm that is about to take the decision (Hopp, 2008, p. 179). Therefore, another key issue is the alignment of goals and incentives in order to neutralize conflicting objectives between the firms (Chopra and Meindl, 2010, p. 491, Simchi-Levi et al., 2003, p. 1). To achieve such alignments it is common that firms make contractual agreements that stipulate the sharing of economic risks, with the aim to make each individual firm benefit from decisions that benefit the whole supply chain (Hopp, 2008, p. 195). Such risk sharing contracts can for example stipulate: special prices for buying back unsold products from the buyer; sharing of revenue with the seller, in return for a discount on the wholesale price; or discounts on the wholesale price if the buyer (for example a retailer) manage to increase sales above a certain quantity (Chopra and Meindl, 2010, p. 427-437, Simchi-Levi et al. 2003, p. 53-55). Another way to align goals and incentives is through vertical integration. The implicit assumption is that if a single firm owns a larger part of the supply chain it can at least theoretically optimize it. In recent years such vertical integration has been common in the military equipment and aviation industry (Nowicki et al., 2010). The suppliers, which commonly are the manufacturers as well, integrate downstream and take over the responsibility for support and maintenance of the products from their customers. The expectation is that the suppliers can support and maintain the products more efficient than their customers, since they have access to competency and skills required to support the often technically advanced products (Doerr et al., 2004). Furthermore, if the firm that designs and manufactures the product is responsible for the support of the product during its life cycle, the firm has strong incentives to make designs that are reliable and easy to maintain (Spring and Araujo, 2009). This specific kind of vertical integration is further discussed in Section 1.3.

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INTRODUCTION

1.2 Quality Quality is commonly associated with desirable product attributes such as availability, reliability, maintainability, sustainability, safety, environmental friendliness etc. (Bisgaard, 2008a, Feigenbaum, 1951, p. 7). Notwithstanding, it is hard to point out the meaning of quality and its essence has shifted over time. One of the first to develop methods for controlling and improving quality was Walter A. Shewhart (1891-1967) (Bergman and Klefsjö, 2006, p. 78). Shewhart represented an early era of quality engineers that primarily associated quality with defect-free products. Shewhart is most known for his statistical methods to identify, correct and prevent defects in manufacturing, see for example Shewhart (1939), Shewhart (1938) and Shewhart (1928), which have had significant impact on the quality field (Montgomery, 2005, Oakland, 2003, Western Electrics, 1956). However, despite his main interest for defects Shewhart realized that manufacturers must work on more than defect preventions to succeed. According to Shewhart (1931, p. vii) “…the object of industry is to set up economic ways and means of satisfying human wants and in so doing to reduce everything possible to routines requiring a minimum amount of human effort”. Thus, manufacturers should aim to satisfy human wants (or customers’ wants) as cost effective as possible. Feigenbaum (1951, p. 7) agree with Shewhart and adds that only the customer can decide whether he or she is satisfied with the product and therefore he concludes that quality is a customer determination that can only be measured against the customer’s demands. Moreover, Juran and Gryna (1951) make two important proposals in line with Shewhart’s statement. First, they propose that it is insufficient to estimate the consequences of poor quality by calculating the cost of defects, since defects do not cover the total cost of poor quality (Juran and Gryna, 1951, p. 4.3). Instead they argue that it is better to measure the deficiencies, i.e. the delays, rework, repairs and scrap caused by the defects (ibid). Second, Juran and Gryna (1951, p. 2.2) propose that the customer’s perception of quality is based on the overall value that the product provides. Thus, firms that exclusively rely on defect prevention are exposed to the risk that competitors might develop innovations involving new features or entirely new products or services that provide better value to the customers. Based on these proposals, Juran and Gryna conclude that there are two separate dimensions of quality; features, which have to do with the design of the product i.e. what is intended to deliver, and freedom from deficiencies, which have to do with the actual delivery (Bisgaard, 2008a, Juran and Gryna,

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INTRODUCTION

1951, p. 2.2). Juran (1989, p. 15) describes these dimensions as the cornerstones of quality, which he defines as fitness for use, see Figure 1-6.

Figure 1-6. Quality defined as fitness for use and based on the two cornerstones features and freedom from deficiencies.

The idea of quality as something that the customer determines based on his or her demands and expectations gained much support during the 1950s. Quality engineers started to work in any project that either aimed to provide more value to the customers or enhance the firm’s efficiency (Bisgaard, 2008a). Various methods and tools that facilitated quality improvements were developed, for example the PDCA-cycle that was first invented by Shewhart but modified and promoted by William Edwards Deming, and the quality circle developed by Kauro Ishikawa, see Deming (1986, p. 88) and Ishikawa (1989, p. 78). Quality was also introduced as a management concept to increase customer satisfaction and make all employees involved in controlling and improving quality, see Crosby (1996), Juran (1995) and Deming (1982). This management concept, commonly known as “quality management”, was by many regarded as a critical component for strengthening organizational efficiency, effectiveness and competitive position (Hellsten and Klefsjö, 2000, Dalrymple et al., 1999). Juran’s and Gryna’s quality dimensions have been paraphrased several times and are known under different names, for example design and delivery quality (Bisgaard, 2008b), and outbound and inbound quality (Bergman and Klefsjö, 2006, p. 53). In this thesis the dimensions are called product quality and process quality. The product quality refers to the ability of the product or service to satisfy the customer’s demands, needs and expectations, i.e. create value for the customer. The process quality refers to the ability of the firm to produce and create value efficiently through their products or services. Hence, process quality improvements may be the reduction of any problem in the supply chain that makes the production, delivery or use of the product or service more efficient and cuts the total cost. Thus, a quality improvement can either be such

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INTRODUCTION

that the customer value is strengthened or that the total cost is reduced, see Figure 1-7.

Figure 1-7. The product quality is determined by the degree to which the product or service solves the customer’s problems, i.e. the customer value. The process quality is determined by the production efficiency, which depends on the total cost for production, delivery and use, i.e. the total cost.

The bottom line objective of a quality improvement is to increase the profitability either by increasing the value or reducing the total cost (Bisgaard and Freiesleben, 2004). Thus, a quality improvement is valid only if it proves to strengthen the economic results, or as Drucker (1973, p. 60) points out: “Profit is not the explanation, cause or rationale of business behaviour and business decisions, but the test of their validity.” Figure 1-8 illustrates some economic aspects of quality presented by Bisgaard (2008a) and Juran (1989, p. 16). Improving product quality sometimes increases the cost of producing the product or service, but it might also allow the firm to charge a premium price or help to increase the sales volume. On the other hand, improving process quality reduces the total costs as it leads to improved productivity and reduced deficiencies. Furthermore, improved process quality may also strengthen the firm’s market reputation and hence allow the firm to charge a premium price or increase market shares. The profit could for example be used for product developments, raised salaries or dividends.

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INTRODUCTION

Figure 1-8. Improved product quality potentially enables higher sales price, larger market share and more revenue. Improved process quality generates better productivity, reduced deficiencies and waste, and perhaps better reputation on the market. Adapted from Bisgaard (2008a).

The idea of quality as a means to increase profit by focusing on customer demands and costs was predominating until the late 1990s. However, in recent years that idea has received vast criticism for neglecting the demands and requirements of other stakeholders than customers and shareholders (Foley, 2005, p. 107). The critics mean that the idea inflicts societal problems and do not encourage good business ethics, see for example Agle et al. (2008) and Mitchell et al. (1997). They argue that economic interests and strive for increased profit does not support sustainable development of the firm or its surroundings, and that firms need to change mind-sets and adopt a so-called stakeholder perspective (Foley, 2005, p. 114, Mitchell et al. 1997). A stakeholder perspective is based on the idea that different interested parties (not only customers) can be stakeholders in a firm and that the firm therefore needs to satisfy other demands and requirements than merely the customer’s in order to survive, see Figure 1-9. Nevertheless, in most situations the customer is one of the stakeholders that the firm needs to satisfy (Foley, 2005, p. 145). This thesis mainly considers the customer’s demands, and therefore it focuses on approaches to improve quality in terms of customer value and total cost. It is however important to keep in mind that firms concurrently need to balance the interests of many stakeholders.

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INTRODUCTION

POWER

Dormant stakeholder

LEGITIMACY Dominant stakeholder

Definitive Dangerous stakeholder stakeholder

Discretionary stakeholder

Dependent stakeholder Demanding stakeholder

Nonstakeholder

URGENCY

Figure 1-9. A stakeholder model presented by Mitchell et al. (1997). A stakeholder must either have power, legitimacy or urgency.

1.3 Quality in supply chains The purpose of this research is to describe and develop approaches to improve the quality in supply chains. The research focus on values and cost associated with logistical activities, which some call logistical quality, see for example Wiendahl and Breithaupt (1999). The logistical quality can schematically be described as a subset of the total quality, since logistics is both value-creating and cost-driving. It creates values such as short delivery time and on-time deliveries and it drives costs such as transportation cost and inventory holding cost. However, a clear line between logistical quality and overall quality can hardly be drawn, especially since the meaning of logistics and logistical values vary between contexts. For example, logistical value within manufacturing firms is commonly described in terms of delivery time and delivery precision, but in some cases it can also be valid to include flexibility to customer demands (Stevenson et al., 2005) or information (Segerstedt, 2008, p. 108). Moreover, in military industry logistics commonly involves maintenance activities such as spare part providence, maintenance services and after-sales support (Nowicki et al., 2010, Keating and Huff, 2005), which clearly generates unconventional logistical values. Instead of just providing products in the right place at the right time, which is a traditional logistical approach, military industry logistics takes

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INTRODUCTION

it one step further and provides the availability, or performance, of the product, see Christopher (1998, p. 39). According to Hopp (2008, p. 7), Chopra and Meindl, (2010, p. 25) and Simchi-Levi et al. (2003, p. 2), it is important to facilitate efficiency on all levels in a supply chain in order to achieve high overall efficiency. Hence, quality improvements should be addressed at problems in processes and flows as well as in networking; from production planning and control in machines, to cooperation between firms in the supply chain network. The thesis focuses on two quite different approaches to improve supply chain quality. The first approach, called performance-based logistics (PBL), is a business model that via vertical integration aims to improve the quality in industries with technically advanced products, in particular in the military and aviation industry. The second approach is a mathematical solution procedure for economic lot scheduling problems (ELSP), which is an extension of the economic order quantity problem. The solution procedure aims to find the minimum setup and inventory holding cost in a machine that produce several products, i.e. improve process quality by optimizing a part of the production cost. Performance-based logistics (PBL) Today many manufacturing firms of large-scale, capital-intensive and technically advanced products offer more than the physical products – they sell the output of their products, i.e. the product performance. This is especially apparent among manufacturers of defense and aerospace equipment, which early became performance-orientated and now seem to have the most developed approach for selling performance. In the defense and aerospace industry context, this way of making business is known as performance-based logistics (PBL) (Hypko et al., 2010). The supplier in a PBL arrangement offers a combination of the product, which is often a technical system, and related support services, such as maintenance, repair, and logistics. The supplier is then awarded according to the level of system performance, for example, according to the availability of an aircraft instead of the aircraft itself, and thus the responsibility for the system performance is shifted from the customer to the supplier; see Figure 1-10. A pure PBL contract could be exemplified by a system owned by the supplier during its lifecycle and where the contract only stipulates the performance that should be reached and maintained.

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INTRODUCTION

Supplier

Supplier

Traditionally:

Use

Traditionally:

PBL: Product

Product

(aircraft)

(aircraft)

Output

Payment

Output

(flight hours)

(flight hours)

Payment

Use Customer

Customer

Figure 1-10. The difference between performance-based logistics (PBL) and the traditional way of making businesses.

PBL is commonly presented as beneficial for both the supplier and the customer compared to traditional business contracts for buying and supporting capitalintensive and complex systems, see for example Keating and Huff (2005), Beanum (2007), Sols et al. (2007), Dang et al. (2009), and Hypko et al. (2010). However, even from a shallow study of the PBL research literature it is evident that the PBL field is small and that the scientific evidence seems weak. The benefits of PBL are often taken for granted and few propose criticism against PBL or recognize the existence of any drawbacks. Moreover, the publications reveal limited information on important aspects to consider when implementing PBL, which means that practitioners are left with few practical guidelines. The amount of scientific publications is small given the significant financial and organizational implications of PBL and the fact that PBL-contracts have been used for several years. Thus, there is a need for a critical review that summarizes previously reported benefits and drawbacks of PBL and explores critical aspects of implementation, in order to bring clarity to practitioners and identify knowledge gaps. Economic lot scheduling problems (ELSP) In many situations firms cannot afford to have special machines and equipment for every product they produce. Therefore, it is common that multiple products or variants of a main product are manufactured in the same machine, see Figure 1-11. Moreover, in many industrial processes a setup must be done before changing the production from one product to another. The setup often requires time and drives costs due to for example expendable material or

13

INTRODUCTION

defective products during the warm up period (Hopp and Spearman, 2008, p. 50).

Figure 1-11. An example of a process where five products are manufactured in one machine. The products are manufactured in lots due to setup time and setup cost, and the finished products are stored in an inventory for instant delivery to the customer. Only one product can be manufactured at a time.

In cases when the setup cost or the setup time is significant relative to a single product it is necessary to employ lot-wise production to reduce the setup cost per product to a reasonable level and increase the throughput high enough to satisfy the demand (Silver et al., 1998, p. 151). As shown in Section 1.1 the production cost in processes with lot-wise production depends on the order quantities. Therefore, it might seem straightforward to use Equation (1.1) to calculate the economic order quantities even when multiple products are produced in the same machine. However, Equation (1.1) does not consider setup time, operation time or machine capacity and hence it cannot be guaranteed that a feasible production schedule can be developed from Equation (1.1), in the sense that it satisfies the demand of all products all the time. In fact, the determination of economic order quantities and their scheduling in processes with multiple products is far more complicated, and constitutes a separate research field. Such problems, called Economic Lot Scheduling Problems (ELSP), are common in many industrial processes, for example bottling, paper production, molding and stamping (Sox et al., 1999). The objective of ELSP-solutions is to determine a production schedule that (1) can be repeated in a cyclic pattern without shortages and (2) minimizes costs, traditionally the sum of the inventory holding costs and setup costs. To do that the inventory holding cost and setup cost should have as similar magnitude as possible for all items, which was shown in Figure 1-4. Several solution procedures have been developed in the attempt to find the minimum cost 14

INTRODUCTION

production schedule, for example Segerstedt (1999), Bourland and Yano (1997), Zipkin (1991), Axsäter (1987), Hsu (1983), Elmaghraby (1978), Goyal (1975), and Doll and Whybark (1973). Bomberger (1966) presented a 10-product problem that has been used extensively in the literature ever since. The solution procedures of Doll and Whybark (1973), Goyal (1975) and Segerstedt (1999) all find the best known solution to the Bomberger problem. Nilsson and Segerstedt (2008) compare these solution procedures. Moreover, they show that the approximation for the inventory holding cost, commonly used in earlier solution procedures, is not accurate. They show that the inventory holding cost often becomes larger than the common approximation, since the time between replenishments varies and hence some replenishment starts before the inventory is consumed to zero, see Figure 1-12. Even though Nilsson and Segerstedt (2008) do not present a procedure that can calculate the “real” inventory holding cost, they conclude that such procedure requires detailed scheduling of the production of all products.

Time

Figure 1-12. Sometimes the time between replenishment varies and therefore some replenishment starts before the inventory is consumed to zero. The common inventory holding cost approximation does not account for such “early starts” and therefore underestimates the inventory holding cost.

Since the existing solution procedures use an inventory holding cost approximation that often underestimates the inventory holding cost, the solutions obtained with these procedures may not be the best solutions in practice. The timing and the size of the order quantities will decide how efficient the processing will be; it determines the costs, the service to customers, and in the end the profitability of the manufacturing company. Thus, there is a need for a new solution procedure that can schedule the production in detail and compute the real inventory holding cost.

15

INTRODUCTION

1.4 Research purpose and aims The purpose of this research is to describe and develop approaches to improve the quality in supply chains. More specifically, the aims of this research are: 1. to summarize previously reported benefits and drawbacks of performancebased logistics and to explore critical aspects of implementation, and 2. to develop a solution procedure that finds a feasible minimum cost production schedule for a single machine producing several different products.

1.5 Organisation of the research process The research in this thesis has been conducted in two research projects, see Figure 1-13. My involvement in the first project, Enhanced Life Cycle Assessment for Performance-based Logistics, reached from April 2010 to May 2011. During that time I collected and studied literature on PBL and other related research fields. I summarised the literature in a conference paper that I presented at the 14th QMOD conference on Quality and Service Sciences in San Sebastian, Spain, in August 2011. The conference paper was further refined and submitted for publication in June 2012. The submitted version of the paper is appended in full (Paper A). In December 2011 I became involved in the second research project; Barents logistics 2. That project is still ongoing and my work until now has mainly covered ELSP and the writing of this thesis. During the spring of 2012 I studied solution procedures for ELSP and developed a new procedure. I summarized the early outcome of that work in a conference paper that I presented at the 17th International Working Seminar on Production Economics in Innsbruck, Austria, in February 2012. After the conference, I further developed the solution procedure and added complementary sections to the conference paper, and in December 2012 it was accepted for publication in the International Journal of Production Research. The accepted version of the paper is appended in full (Paper B).

16

INTRODUCTION

Figure 1-13. An overview of the main research activities during the research process. The research has been conducted in two research projects, and has resulted in two papers.

17

PERFORMANCE-BASED LOGISTICS

2. PERFORMANCE-BASED LOGISTICS This chapter presents the findings of a literature review on performance-based logistics. The findings concern benefits, drawbacks and critical aspects of implementation. The complete literature review is appended (Paper A).

2.1 Benefits In traditional deals with technically advanced systems the customer is responsible for all support services after the purchase. However, the original equipment manufacturer is often the only actor able to support and provide spare parts to complex systems, such as aircrafts (Keating and Huff, 2005, Nowicki et al., 2010). The complexity thus limits the possible alternatives for the customers and consequently the customer often becomes dependent of one supplier. This dependency may be advantageous for the supplier since spare parts and support services usually constitute a large part of the supplier’s revenues. However, the customer’s limited freedom to choose service and maintenance supplier alternatives leads to small incentives for the supplier to improve the system availability and lowering lifecycle costs, since failures are profitable from the supplier standpoint (Sols et al., 2007). In PBL, the supplier is free to decide how to produce and improve the performance of the product, for example, to improve the repair processes, logistics processes, and product reliability (Smith, 2004, Kim et al., 2007, Kumar et al., 2007), which would increase revenues as the performance increases. Such improvements would also likely improve the supplier’s longterm competitive position as the improvements may lead to technological enhancement (Baines et al., 2009a, Hypko et al., 2010) and likely strengthen customer loyalty (Hypko et al., 2010). Nowicki et al. (2010) claim that although the supplier’s financial risk increases in PBL, so does the opportunities to make profit. From a customer’s perspective, PBL implies an increased focus on core activities, such as maintaining a country’s defensive ability or defending a country (Martin, 1997), rather than supporting and maintaining the systems. The reduced responsibility for support will therefore likely reduce the customer’s financial risks (Dang et al., 2009). The customer will receive better performance if the supplier manages to improve the system and the support services during the system’s lifetime (Fino, 2006). Altogether, PBL aims to provide the customer with better performance to a fixed cost, or similarly, less cost to a fixed performance (Nowicki et al., 2010).

19

PERFORMANCE-BASED LOGISTICS

2.2 Drawbacks The transferal of responsibility for the system performance from the customer to the supplier increases the supplier’s financial risks due to low system performance (Jacopino, 2007, Hypko et al., 2010), or due to higher than expected costs to deliver the required performance (Kim et al., 2007, Nowicki et al., 2010). The size of the supplier’s risk therefore depends on its ability to predict costs and performance in the PBL contract bidding stage (Tukker, 2004, Erkoyuncu et al., 2011). The complexity of the systems and performance uncertainties makes predictions hard, and the long term contracting common in PBL aggravate the consequences of miscalculations (Smith, 2004). Furthermore, the responsibility of the performance of the system during use requires organizational changes and investments in infrastructure and the training that may be required when shifting from selling products toward delivering performance. These organizational changes also induce business risks (Baines et al., 2009a, Kuo et al., 2010). Other challenges include the need to improve the understanding of customer value, and managing close and long-term customer relations (Baines et al., 2009b, Martinez et al., 2010). Moreover, PBL usually requires that the supplier can perform maintenance and service swiftly to reach contracted goals. For military operations, this may lead to situations where a civilian supplier may be forced to support the system at war at unsafe locations (Doerr et al., 2004). Apart from the difficulties associated with delivering performance at war, the supplier also risk the employees’ well-being (Gansler and Lucyshyn, 2006). In PBL, the customer becomes more dependent on the supplier since the control over the support services is transferred to the supplier. Probably, as a consequence, the customer has dismantled its organization with the competence necessary to provide system support. Thus, the customer stands the risk of being locked to one supplier in a long-term contract that systematically delivers bad performance (Nowicki et al., 2010), and, as a consequence, not able to enhance system performance (Jacopino, 2007). Moreover, the customer will have difficulties to introduce a new supplier to support the system if the supplier breaks the contract, since both the customer and any new supplier likely lacks access to all vital system data (Kim et al., 2007, Dang et al., 2009). Full insights into military operations is a normal customer prerequisite, but such insights may become restricted if the supplier is responsible for the support services (Tegtmeier, 2010). Many report that PBL have resulted in reduced costs, see for example Phillips (2005), Keating and Huff (2005), Gansler and Lucyshyn (2006), Mahon

20

PERFORMANCE-BASED LOGISTICS

(2007) and Ott (2008). However, many reports are vague as to how savings have been measured and the published empirical support for the profitability hypothesis based on the above mentioned reports is weak. A few studies regarding profitability are more thorough. Two works from the U.S. Government Accountability Office (GAO) are inconclusive whether PBL reduces, have no effect, or even increases the customer’s costs (GAO, 2005; GAO, 2008). Another large study including 10 000 companies indicate that the company size also matters for PBL profitability, where small firms seem to gain the most from moving to PBL (Neely, 2009). The latter three more thorough studies thus provide mixed conclusions regarding the profitability of PBL and selling and buying performance. The profitability hypothesis thus needs more empirical support. An obvious risk is that the cost for mitigating the financial risks and rearranging organizations, equipment and attitudes from a traditional support structure exceeds the gains. Furthermore, assuming that PBL is effective, it is unclear how the cost reduction is shared between the customer and the supplier. It is possible that the supplier sets a higher price due to the increased financial risks and thus that the customer’s cost remains or even increases.

2.3 Critical aspects of implementation The risks in PBL-contracts force both the supplier and the customer to put extensive efforts on; designing contracts and payment models, deciding on how to measure performance, defining performance indicators, specifying system levels and setting target values. In this section the findings related to implementation of PBL are presented: commonly used contracts in PBL, the scope and the typical arrangement of PBL-contracts, performance measurements, and payment models. PBL-contracts The literature emphasizes that each PBL-contract has to be tailored (Sols et al., 2007, Nowicki et al., 2010), and the contract types thus differ. In fact, authors do not even agree on how to separate PBL contracts from traditional contracts. The same contract type seems to be considered traditional by one author and as a PBL-contract by another, see for example the different interpretations by Kim et al. (2007) and Nowicki et al. (2010). Two contract types are more frequently mentioned in PBL-literature: the firm fixed price contract and the cost plus award fee contract (Cunic, 2003, Kim et al., 2007, Sols et al., 2007, Nowicki et al., 2010).

21

PERFORMANCE-BASED LOGISTICS

In firm fixed price contracts the supplier agrees to deliver some level of performance (for example aircraft availability) based on some level of use (for example the amount of flying hours per month). The contract then states the level of remuneration, for example price per flying hour, and an award fee may be added to stimulate performance improvements (Kim et al., 2007, Nowicki et al., 2010); increasing payments if performance surpasses the contracted minimum level. The financial risks are thus concentrated to the supplier, whose income depends on the ability to deliver and improve performance. The risks are especially high for new systems, for which performance must be predicted based on little or no historical data (Smith, 2004, Kim et al., 2007, Erkoyuncu et al., 2011, Sols et al., 2008). In a cost plus award fee contract, the customer reimburses the supplier for their costs for the performed services, adding an award fee to stimulate performance improvements or cost reductions. Here, the financial risks are mainly held by the customer who is forced to pay the supplier despite the performance output (Cunic, 2003, Sols et al., 2007, Nowicki et al., 2010). Costplus award fee contracts are often used in a transition phase when a non-PBL contract is being converted to a firm fixed price with award fee (Kim et al., 2007, Nowicki et al., 2010, Liu et al., 2009). Scope of PBL-contracts PBL-contracts are applied to complete systems, subsystems, major components, or certain support services, for example spare parts provision (GAO, 2004, Sols et al., 2008, Dang et al., 2009). Moreover, PBL can be applied to a system’s lifecycle as well as to parts of the lifecycle (Sols et al., 2007). A disadvantage of implementing PBL partly can be that opportunities due to economies of scale may be lost (Nowicki et al., 2010). Furthermore, it can be difficult to find appropriate performance indicators if the supplier is only responsible for the performance of a subsystem, (Fino, 2006). Like any other contract, PBL-contracts vary in length. However, a common recommendation is that PBL-contracts should be long term, (Maples et al., 2000, Keating and Huff, 2005) and some authors even claim that PBLcontracts are long term by definition (Berkowitz et al., 2005, Nowicki et al., 2010). The literature describes two main benefits of long term contracting related to return on investments. First, setting up, negotiating and implementing PBL takes time and is costly while the benefits received are distributed over the contract period. The contracts have to be long enough for the benefits to exceed the costs (Berkowitz et al., 2005). Second, a long term contract increases motivation for the supplier to make larger investments in the system that can 22

PERFORMANCE-BASED LOGISTICS

improve system performance, even if the pay-off time is long (Nowicki et al., 2010). Such investments may be related to mitigating obsolescence and enhancing system reliability (Fino, 2006) which are especially important for systems with long product life cycles (Sols et al., 2007). For these reasons, it has been argued that a PBL-contract should not be shorter than about five years (Sols et al., 2007, Nowicki et al., 2010). Performance measurements Performance is a central part of PBL as performance reflects customer value and forms the basis for the supplier’s income. Consequently, it is important that the performance can be measured accurately (Devries, 2004, Sols et al., 2008, Hollick, 2009). The supplier and the customer must agree on: performance indicators, definitions of the indicators, target values and how to perform measurements and analyses (Forslund, 2009). The performance indicators should be specific, straightforward, measurable and relevant to the customer’s requirements (Fino, 2006, Dang et al., 2009). However, to select and define performance indicators that reflect customer value is often difficult, since the customer’s needs often are formulated in abstract terms (Tukker, 2004, Spring and Araujo, 2009). Typically, several performance indicators are measured in a PBL-contract, for example: availability, reliability, maintainability, supportability, logistics response time, logistic footprint and cost of use, see Fino (2006), Sols et al. (2007) and Nowicki et al. (2010). The indicators can be measured on different system levels and address different customer needs. For example, reliability can be related to a component (component reliability), a system (system reliability) or the system’s performance (mission reliability) (Dang et al., 2009). Although performance indicators often are objectively measured such as the up-time of the system, they can also be subjective, as for example customer satisfaction (Dang et al., 2009). The availability of, for example, an aircraft is a highly aggregated performance indicator, dependent on many lower level indicators. It is difficult to track problems and identify improvements by only observing the overall aircraft availability. Lower level performance indicators are therefore required (Fino, 2006, Sols et al., 2008, Hollick, 2009). Moreover, the supplier cannot be held responsible for the availability on an aggregated level if the supplier only is responsible for the availability of some sub-components (Hollick, 2009). Conversely, achieving performance goals on lower-level performance indicators does not, per se, guarantee good system performance. Defining performance indicators and corresponding measurements can be challenging, for example if the definition must respect a certain equipment 23

PERFORMANCE-BASED LOGISTICS

requirement. For example, whether a military aircraft should be considered available or not might depend on what kind of missions it is scheduled for. Such availability is commonly called operational availability or operational readiness (Dang et al., 2009, Hollick, 2009). Agreeing on a definition of an indicator can also be difficult. For example, the mean time between failures (MTBF) is commonly used to measure reliability, but MTBF requires a definition of a failure and determination of how many failures that are required to reach statistical significance (Richardson and Jacopino, 2006). Performance target values must represent the customer’s needs and form a realistic challenge for the supplier. A baseline constituting the “normal” performance of the system must thus be identified to set target values. If the system has been used, the baseline could be drawn from historical performance (Sols et al., 2008). However, identifying a baseline from historical values might be difficult, such as when the measurements have been done differently and not according to a new indicator definition, or if the use of the system has changed (Sols et al., 2008). For new systems, the baseline must be built on predictions of future performance exclusively (Kim et al., 2007), which is even harder. Payment models A model must be established to transform the measured performance into supplier fees when the performance indicators are set. A good model includes incentives for the supplier to produce high performance (Dang et al., 2009), whereas a poor model could impose unwanted supplier actions (Nowicki et al., 2008). Payment models must often consider many performance indicators and this makes them complex (Sols et al., 2007). A conflict between performance criteria appears when one performance indicator is over-performing and another is under-performing. Consequently, the payment model must balance the results of several performance indicators and convert the overall result to a fair payment (Sols et al., 2008). Nowicki et al. (2008) propose a payment model consisting of a minimum performance limit, a penalty zone, a dead zone and a reward zone, as illustrated in Figure 2-1.

24

PERFORMANCE-BASED LOGISTICS

Reward Zone Dead Zone Penalty Zone

Min

Normal

Max

Measured system performance Figure 2-1. A conceptual payment model. The supplier’s payment depends on the measured system performance.

The minimum performance limit determines the performance level under which the supplier does not receive payment. If the supplier delivers performance just above this limit, the supplier enters the penalty zone and is paid according to the achieved performance. However, in the penalty zone the payment is smaller than the cost of delivering the performance. If the performance is within the limits of the dead zone, around normal system performance (Sols et al., 2007), the payment is comparable to the cost of delivering the performance. The supplier earns marginal or no profit in the dead-zone, but if the system performance is in the reward zone, the supplier receives payment exceeding the production cost (Nowicki et al., 2008). The frequency of measurements and performance reviews is also discussed in the literature. Sols et al. (2007) suggest that performance should be assessed over short periods, with long periods over which the payments are calculated, to even out possible shifts in payments to the supplier.

25

ECONOMIC LOT SCHEDULING PROBLEMS

3. ECONOMIC LOT SCHEDULING PROBLEMS This chapter presents a brief overview of the previous research on economic lot scheduling problems. Previous scheduling approaches and the common inventory holding cost approximation are described. Moreover, the solution procedure developed in Paper B is explained. Elmaghraby (1978) presents an overview of early contributions to ELSP. He divides the contributions into two categories: I. II.

Analytical approaches that achieve the optimum of a restricted version of the problem. Heuristic approaches that achieve “good” solutions of the original problem.

The analytical approaches commonly use either dynamic programming (Axsäter, 1987, Bomberger, 1966) or integer nonlinear programming models (Davis, 1990). Yao and Elmaghraby (2001) state that the analytical solutions require long run time and therefore tend to be inappropriate in practice, especially if the problem includes many products. Thus, heuristic approaches can be advantageous, even though the quality of their solutions cannot be guaranteed. The approaches for ELSP can also be divided into those that assume deterministic processes (Segerstedt, 1999, Bomberger, 1966) and those that assume stochastic processes (SELSP) (Qiu and Loulou, 1995). According to Sox et al. (1999) solution procedures that assumes stochastic processes are preferred in practice, since the demand rate for goods and services is often not deterministic but instead it can vary greatly, which adds a great deal of complexity to the problem. However, Brander et al. (2005) show that deterministic procedures can be successfully used on practical applications where the demand is stationary stochastic, if the procedures are complemented with decision rules to determine which item to produce and when to produce it. In fact, their study indicates that such decision rules are of greater importance for the performance than the actual procedure itself.

27

ECONOMIC LOT SCHEDULING PROBLEMS

3.1 Scheduling The following assumptions are commonly made when dealing with deterministic ELSP (Doll and Whybark, 1973, Bomberger, 1966): x Only one product can be produced at a time x Setup costs and setup times are independent of production order x Product demand rates are deterministic and constant over time x Production times are deterministic and constant over time x Inventory holding costs are determined on the value of stocks hold x Backorders are not allowed There are three broad categories of problem formulations for ELSP: the common cycle approach, the basic period approach and the extended period approach. The common cycle approach was first developed, see Hanssmann (1962). In the common cycle approach the production schedule is made over a certain time period, a production cycle, in which all products are produced exactly once, see Figure 3-1. The production cycle is repeated over and over again to achieve a cyclic production schedule. Even though successful applications of the common cycle approach have been reported, see for example Galvin (1987), the approach has drawbacks due to imbalances in demand rates, production rates or costs between the products.

Figure 3-1. In the common cycle approach all products are produced once during a production cycle, which is repeated to achieve a cyclic production schedule.

Differences in demand, costs and production times motivate more frequent production of some products and less frequent production of others. Therefore, the basic period approach, which is an extension of the common cycle approach, allows the products to have different cycle times as long as the cycle times are integer multiples of a basic period. The basic period is constrained to be long enough to accommodate production of all products, but some products might only be produced in some periods (Bomberger, 1966). Thus, products of lower

28

ECONOMIC LOT SCHEDULING PROBLEMS

volume can be produced less frequently than products of high volume. For example, while high volume products are produced in every basic period, the low volume products can be produced in every second basic period, every fourth basic period, or every eight basic period etc., see Haessler and Hogue (1976). According to Yao and Elmaghraby (2001), to simplify the construction of a cyclic schedule the production frequency of each product, i.e. the number of times that the product is produced during a production cycle, should be a multiplier of two. The restrictive constraint that the basic period must be long enough to accommodate production of all products often leads to low utilisation and waste of capacity. Therefore, that constraint is removed in the extended basic period approach, which allows smaller basic periods. In the extended basic period approach, the period is instead constrained to be long enough to cover the average setup times and operation times of all products (Haessler, 1979, Doll and Whybark, 1973), see Figure 3-2.

Figure 3-2. In the extended basic period approach the periods must be long enough to cover the average setup times and operation times of all products.

The extended basic period approach is advantageous compared to the other approaches since it allows the products to be produced with different frequencies and with fairly little waste of capacity. However, some waste of capacity is often inevitable, due to the restriction that the periods must be of the same length. Therefore, Cooke et al. (2004) and Nilsson and Segerstedt (2008) present solution procedures without this constraint. Even though their procedures aim to schedule the production in a way that makes the periods as equal as possible, there is no such requirement. Figure 3-3 illustrates a production schedule made according to their principles.

29

ECONOMIC LOT SCHEDULING PROBLEMS

Figure 3-3. The solution procedures of Cooke et al. (2004) and Nilsson and Segerstedt (2008) allow the period length to vary. Therefore, the solutions do not include any idle time due to the scheduling. Idle time can however exist but only if it is required to achieve the optimal cost.

The scheduling principles of Cooke et al. (2004) and Nilsson and Segerstedt (2008) make it possible to construct production schedules with minimum idle time and capacity waste. However, since they allow the period length to vary, the time between production of some products might vary as well, and thus the production sometimes starts before the inventory is consumed to zero. That is problematic since the traditional inventory holding cost approximation assumes that no products are left in the inventory when the production starts. Thus, a modified inventory holding cost approximation must be used.

3.2 Inventory holding cost approximation The approximation for the inventory holding cost for all products i traditionally used for ELSP is; Cinventory

di T

¦ h 2 ˜ f (1  o d ) i

i

i

i

(3.1)

i

where hi is the inventory holding cost per day, di is the demand rate, T is the cycle time, fi is the production frequency, and oi is the operation time per product. The traditional approximation is correct when the time between replenishments is constant for all products, i.e. if all periods are equally long, see Figure 3-4a. However, in cases when the time between replenishments varies, see Figure 3-4b, the traditional approximation does not hold.

30

ECONOMIC LOT SCHEDULING PROBLEMS

Figure 3-4. A graphical illustration of the inventory level of product A. (a) The time between replenishments is constant, and the inventory is consumed to zero before each production start. (b) The time between replenishments varies, and the production sometimes starts before the inventory is consumed to zero.

Due to uneven period lengths the replenishment of some products in some periods start before the inventory is consumed to zero. Such “early starts” creates some extra inventory that the traditional approximation does not account for. Early starts are especially apparent when the machine is working close to its capacity limit and there is little idle time that can be used to even out the periods. The magnitude of an early start of product i in period j is denoted ti j. Then, the extra inventory due to an early start is a rhomboid with the area a ˜ b , where a d i ti j and b T f i , see Figure 3-5.

31

ECONOMIC LOT SCHEDULING PROBLEMS

b a Time

T fi

tij

T fi

Figure 3-5. When the time between replenishments varies the production in some periods starts before the inventory is consumed to zero. Such early starts lead to additional inventories (the rhomboid in the graph).

When an early start occurs, the replenishment begins with di ti j items left in the inventory. The extra inventory holding cost of item i during the production cycle T is: d i ti j T 1 1 hi ˜ ˜ a ˜ b hi ˜ ˜ ¦ T T j fi

hi ˜ ¦ j

d i ti

j

fi

(3.2)

Consequently, the true total inventory holding cost for all items is: ª §d T di ti j ·º ¸» Cinventory ¦ «hi ¨ i (1  oi di )  ¦ ¨ 2˜ f ¸» f i « j i i ¹¼ ¬ ©

(3.3)

Observe that for each i at least one t i j 0 , otherwise more items are produced than what is consumed during the production cycle.

32

ECONOMIC LOT SCHEDULING PROBLEMS

3.3 Solution procedure The solution procedure developed in Paper B is briefly described in this section. In line with the feasibility conditions for the extended basic period approach presented in Eilon (1962) and Haessler and Hogue (1976), the shortest time interval, due to the capacity, in which all products can be produced with specific frequencies, is; Tmin

¦i f i si 1  ¦i oi di

(3.4)

where si is the setup time for item i. If Tmin  0 there is no feasible solution since there is not enough capacity to produce the required demand. The total cost per time unit according to the frequency vector, f, that contains the frequencies of all products, and an arbitrary cycle time, T, is; inventory holding cost cost § setup

  · P ¨ f i Ai ¸ di T  hi (1  oi d i ) ¸ ¨ ¦ T 2 ˜ fi i 1 ¨ ¸ © ¹ N

C (f , T )

(3.5)

where Ai is the cost per setup. Note that Equation 3.5 is based on the common inventory holding cost approximation and therefore does not account for any extra inventory due to early starts. The lowest total cost according to T can be found by differentiating the cost function, C (f ,T ) , with respect to T. Thus, the lowest total cost per time unit according to T is:

C0



C f ,T

; where T *

­° ½° ¦i fi Ai max® , Tmin ¾ °¯ ¦i hi (1  oi di )di /(2 fi ) °¿

(3.6)

The solution procedure begins with the frequency fi 1 for all products (i.e. solving the problem according to the common cycle approach). T * is calculated according to Equation (3.6). A ratio between the setup cost per time unit and the inventory holding cost per time unit is calculated for all products and according to T * : Ri (f )

f i Ai / T * hi (1  oi d i ) d i T * /( 2 f i )

33

i

(3.7)

ECONOMIC LOT SCHEDULING PROBLEMS

The frequency of the product k with the maximum ratio or inverted ratio, max ( Ri ,1 / Ri ) , is changed one step. If Rk  1 then f k is increase one step, and if Rk ! 1 then f k is reduced one step. The expectation is that the total cost per time unit will decrease if Ri approach 1 for all products. If the frequency is increased the setup cost per time unit will increase and the inventory holding cost per time unit will decrease. The opposite holds if the frequency is reduced. After changing f k , T * is calculated for the new frequency, f, according to Equation (3.6). To compute the total cost per time unit for the new frequency, the production must be scheduled so that the extra inventory due to early starts can be calculated. The production cycle is divided into max ( fi ) periods. The products are scheduled in descending order according to (1) frequency, fi , and (2) production time, pi , where pi is: operation time

  P o d T* si  i i fi

setup time

pi

(3.8)

The product(s) with highest frequency is scheduled in every period, and the other products are scheduled according to their frequency every second period, every fourth period etc. The scheduling aims to make the production time in all periods as even as possible to avoid early starts. If there is any idle time to schedule, that idle time is scheduled last with the aim to distribute it over the periods to make them even. After scheduling, the total cost per time unit can be calculated: C (f , T )

N

ª f i Ai

i 1

«¬

¦« T

*

fi dt § d T  hi ¨ i (1  oi d i )  ¦ i i j fi j 1 © 2 ˜ fi

·º ¸» ¹ »¼

(3.9)

where ti j is the early start of product i in period j. If the total cost per time unit after scheduling is less than the total cost per time unit before changing the frequency, then the new solution is better than the previous solution. If so, Ri (f ) is recalculated according to the new frequency, and the frequency is changed once again to with the aim to find an even better solution. However, if the total cost per time unit after scheduling end up to be higher than the total cost per time unit before changing the frequency, the previous frequency change is rejected and a new f k is identified, but this time with k corresponding to the product with the second highest ratio or inverted ratio. 34

ECONOMIC LOT SCHEDULING PROBLEMS

The procedure of calculating the optimal cycle time according to the frequency, changing the frequency depending on the setup and inventory holding cost per time unit, and scheduling the production to calculate the total cost per time unit, is repeated iteratively until the procedure cannot find any better solution. Finally, the order quantities for the best solution found are computed from: qi

di T fi

35

i

(3.10)

FURTHER RESEARCH

4. FURTHER RESEARCH This chapter presents suggestions for further research. A natural continuation of the research on ELSP could be to extend the solution procedure presented in Paper B to compute the economic order quantities and their scheduling for any number of products. That would make it possible to validate the performance of the procedure, for example by solving the wellknown Bomberger problem, which includes 10 products, and compare the results with those from previous solution procedures. The performance of the solution procedure could also be validated by testing it on a real case. Another possible extension of the ELSP research is to investigate the effect of prolonging the cycle time slightly, which sometimes may ease the scheduling, reduce the early starts and perhaps in some cases even lead to lower total cost. On a theoretical level that may be interesting even though the practical implications probably are small. Considering the research on PBL, a possible continuation is to investigate the effects of the servitization level on cost and delivered performance, that is, to investigate whether or not it is beneficial to buy and sell outcome rather than output. That is an interesting research question, but to answer it probably requires a large amount of empirical data which can be hard to find. This thesis covers possible quality improvements through PBLarrangements and ELSP-solutions. However, there are many other logistical research fields and methods that can contribute to the quality of supply chains, for example, route planning, inventory management and demand prognoses. Optimized transport routes and sound inventory management are important components for firms to be cost effective and achieve a high delivery service level, and good predictions of future demands is sometimes essential for firms in order to balance resources and demands.

37

REFERENCES

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PAPER A Performance-based logistics An illusive panacea or a concept for the future? Holmbom, M., Bergquist, B. and Vanhatalo, E. (2012)

Submitted for publication

Performance-based logistics An illusive panacea or a concept for the future? Martin Holmbom1, Bjarne Bergquist2 and Erik Vanhatalo2 1

Industrial Logistics Quality Technology & Management 1,2 Luleå University of Technology, SE-971 87, Luleå, Sweden 2

A business concept known as performance-based logistics (PBL) is currently changing the aerospace and defense industry. PBL means that manufacturers are responsible and paid for the delivered performance of their products. For example, an aircraft manufacturer delivers flying hours to a customer and is paid according to the availability of the aircraft. Purpose – to review PBL in the broader context of product service systems (PSS), servitization and performance contracting, with the aim to summarize previously reported benefits and drawbacks of PBL, to explore critical aspects of implementation, and identify knowledge gaps. Design/methodology/approach – This is a literature review based on 78 articles. The reviewed articles are relevant to PBL in particular, but also to performance contracting, product-service systems and servitization in general. The research method involved database searches, filtering results and reviewing publications. Findings – PBL is a business concept that aims to reduce the customer’s total costs for capital-intensive products and increase the supplier’s profit. The design of the contract, performance measurements and payment models are critical aspects for successful implementation. However, we find a reason for concern to be the lack of empirical evidence of the profitability of PBL for the customer and the supplier. Originality/value – This literature review of PBL also includes publications from the related research areas: performance contracting, product-service systems and servitization. Developing PBL can benefit from results in these research areas. Keywords – Performance-based logistics, Performance contracting, Product service systems, Servitization Article type – Literature review We are grateful for the financial support provided by the Swedish Governmental Agency for Innovation Systems (Vinnova). We are also grateful to our colleagues Dr. Rickard Garvare, Helena Ranängen and Peder Lundkvist for their constructive criticism and creative ideas that have improved this article. Thank you.

1

1. INTRODUCTION Today many manufacturing firms’ offers contain more than physical products – they sell the output of their products, i.e. the product performance. This is especially apparent among manufacturers of defense and aerospace equipment where the products are largescale, capital-intensive technical systems; in this article referred to as ’systems’. Manufacturers within the defense and aerospace industries early became performanceorientated and now seem to have the most developed approach for selling performance. In the defense and aerospace industry context, these contracts are known as performancebased logistics (PBL) (Hypko et al., 2010). The supplier in a PBL arrangement offers a combination of the system and related support services, such as maintenance, repair, and logistics. The supplier is then awarded according to the level of system performance, e.g. the availability of an aircraft instead of the aircraft itself, and thus the responsibility for the system performance is shifted from the customer to the supplier; see Figure 1. A pure PBL contract could be exemplified by a system owned by the supplier during its lifecycle and where the contract only stipulates the performance that should be reached and maintained. The implicit assumption of PBL is that when the producer is given the responsibility to produce a certain performance level and the freedom to design the product and production process accordingly, the total cost will decrease. A more efficient process will result in advantages shared by supplier and customer.

Figure 1: The difference between performance-based logistics (PBL) and the traditional way of making businesses.

PBL originated in the United States military in 2001 (Devries, 2004, GAO, 2004, Berkowitz et al., 2005), but the history of selling and contracting for performance is longer. Research relevant to PBL can be found under different labels, such as performance contracting, product-service systems (PSS) and servitization. Performance contracting has a broad meaning, describing many aspects of buying and selling performance in a large spectrum of industries (Cunic, 2003). PSS can be described as an integrated product and service offering that delivers value in use (Baines et al., 2007). Similar to PBL, the essence of PSS is selling and buying performance instead of products. PSS originated in the industrial ecology research field, because of the expectation that materials consumption could be reduced if the product ownership stayed with the supplier (Tukker, 2004, Baines et al., 2007, Spring and Araujo, 2009). PSS has

2

also been considered to improve product performance (Tukker, 2004). PBL can be viewed as a form of PSS with a large service component, implying that the supplier is free to decide how to produce the performance, see Tukker (2004) and Neely (2009). PBL is mainly implemented on systems, and thus the product complexity is typically high. Servitization is the occurrence of adding a service to a product, i.e. moving from selling a product to selling a PSS, see Vandermerwe and Rada (1988). The interdependence between PBL, PSS, servitization and performance contracting is described in Figure 2.

Product complexity

Performance contracting PBL P R O D U C T

PSS

S E R V I C E

Servitization level

Figure 2: Performance-based logistics (PBL) is a product-service system (PSS) with a complex product and a large service component. Servitization is the transformation of products to PSS:s by adding services. Moreover, all these research areas deal with performance contracting.

A conclusion from even a shallow study of the PBL research literature is that the PBL field is less developed than PSS, performance contracting and servitization, and consequently, PBL researchers may benefit from work presented under other labels. The purpose of this article is to review PBL in the broader context of PSS, servitization and performance contracting, with the aim to summarize previously reported benefits and drawbacks of PBL, explore critical aspects of implementation, and identify knowledge gaps. Section 2 outlines the method and explains how the literature review was performed. Section 3 presents the findings, focusing on benefits and drawbacks of PBL and critical aspects of implementation. In Section 4 we present our conclusions, identify knowledge gaps and give suggestions for future research.

3

2. METHODOLOGY This article is based on a review of literature about PBL, PSS, servitization and performance contracting. The search was conducted in Web of Science and Scopus. These databases were selected since they cover technical and management journals as well as conference proceedings where the research on servitization and related concepts primarily has been published. Initially, all articles having “performance-based logistics”, “product-service system”, “servitization” or “performance contract” in the title, abstract or keywords were selected. In total, 434 articles were identified through the search in the first step. Each article was classified as “relevant” or “not relevant” based on reviews of the abstracts. Relevant articles focused on PBL, or a topic closely related such as performance contracts, leaving 65 articles. In the second step, these articles were studied in more detail. Additional publications were found through the reference lists of selected articles, and these new articles were also added. In this step another 13 articles were added for a sum of 78 (Table 1).

3. FINDINGS 3.1 Benefits and drawbacks of PBL Switching to PBL is commonly presented as beneficial for both the supplier and the customer compared to traditional business contracts for buying and supporting capitalintensive and complex systems, see e.g. Keating and Huff (2005), Beanum (2007), Sols et al. (2007), Dang et al. (2009), and Hypko et al. (2010). Traditionally, the customer is responsible for all support services after the purchase. However, the original equipment manufacturer is often the only actor able to support and provide spare parts to complex systems, such as aircrafts (Keating and Huff, 2005, Nowicki et al., 2010). The complexity thus limits the possible alternatives for the customers and consequently the customer often becomes dependent of one supplier. This dependency may be advantageous for the supplier since spare parts and support services usually constitute a large part of the supplier’s revenues. However, the customer’s limited freedom to choose service and maintenance supplier alternatives leads to small incentives for the supplier to improve the system availability and lowering lifecycle costs, since failures are profitable from the supplier standpoint (Sols et al., 2007).

PBL from the supplier’s perspective In PBL, the supplier is free to decide how to produce and improve the performance of the product e.g. to improve the repair processes, logistics processes, and product reliability (Smith, 2004, Kim et al., 2007, Kumar et al., 2007), which would increase revenues as the performance increases. Such improvements would also likely improve the supplier’s long-term competitive position as the improvements may lead to technological enhancement (Baines et al., 2009b, Hypko et al., 2010) and likely strengthen customer

4

Table 1: The reviewed literature in chronological order. Number of publications by period Nr 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78

Author(s) Vandermerwe and Rada Martin Frost and Lithgow Mahoney and Thompson Maples et al. Cunic Devries Doerr et al. GAO Howard Smith Yik and Lee Tukker Barrie Berkowitz et al. GAO Keating and Huff Phillips Komoto et al. Fino Gansler and Lucyshyn Richardson and Jacopino Smith et al. Zhao et al. Aurich et al. Beanum Giannotti et al. Jacopino Kim Kumar et al. Lowenstein Mahon Sols et al. Baines et al. Cortez et al. GAO Nowicki et al. Ott Sols et al. Johnson and Mena Dang et al. Holllik Forslund Aurich et al. Bianchi Brad Liu et al. Pawar et al. Yang Yang and Li Baines et al. Baines et al. Baines et al. Neely Park and Lee Schmenner Spring and Araujo Nowicki et al. Mao et al. Tegtmeier Hypko et al. Abramovici et al. Aurich et al. Hong and Huo Kuo et al. Li and Li Li and Liu Yang et al. Yang et al. Baines et al. Lyul and Fu Martinez et al. Wang and Fu Lycette and Lowenstein Erkoyuncu et al. Johansson Meier et al. Greenough and Grubic

Year 1988 1997 1998 1998 2000 2003 2004 2004 2004 2004 2004 2004 2004 2005 2005 2005 2005 2005 2005 2006 2006 2006 2006 2006 2006 2007 2007 2007 2007 2007 2007 2007 2007 2007 2008 2008 2008 2008 2008 2008 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2009 2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 2010 2011 2011 2011 2011 2011

Origin Switzerland Netherlands Australia USA USA USA USA USA USA USA USA China Netherlands USA USA USA USA USA Netherlands USA USA Australia USA USA Germany USA USA Australia USA India, USA UK USA Spain, USA UK USA USA USA USA Spain, USA UK China Canada Sweden Germany Italy, UK Romania China UK China China UK UK UK UK Korea USA UK USA China USA Germany Germany Germany China China China China Australia Australia UK Taiwan UK China USA UK Sweden, UK Germany UK

Topic Servitization Performance contracting Performance contracting Performance contracting Performance contracting Performance contracting PBL PBL PBL PBL PBL Performance contracting PSS PBL PBL PBL PBL PBL PSS PBL PBL PBL PBL Performance contracting PSS PBL PBL PBL PBL PBL PBL PBL PBL PSS PBL PBL PBL PBL PBL Servitization PBL PBL Performance contracting PSS PSS PSS PSS PSS PSS PSS Servitization Servitization Servitization Servitization Servitization Servitization Servitization PBL PBL PBL Performance contracting PSS PSS PSS PSS PSS PSS PSS PSS Servitization Servitization Servitization Servitization PBL PSS PSS PSS Servitization

5

1988-1999 2000-2002 2003-2005 2006-2008 2009-2011

4 1

14

21

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loyalty (Hypko et al., 2010). Nowicki et al. (2010) claim that although the supplier’s financial risk increases in PBL, so does the opportunities to make profit. The transferal of responsibility for the system performance from the customer to the supplier increases the supplier’s financial risks due to low system performance (Jacopino, 2007, Hypko et al., 2010), or due to higher than expected costs to deliver the required performance (Kim et al., 2007, Nowicki et al., 2010). The size of the supplier’s risk therefore depends on its ability to predict costs and performance in the PBL contract bidding stage (Tukker, 2004, Erkoyuncu et al., 2011). The complexity of the systems and performance uncertainties makes predictions hard, and the long term contracting common in PBL aggravate the consequences of miscalculations (Smith, 2004). Furthermore, the responsibility of the performance of the system during use requires organizational changes and investments in infrastructure and the training that may be required when shifting from selling products toward delivering performance. These organizational changes also induce business risks (Baines et al., 2009b, Kuo et al., 2010). Other challenges include need to improve the understanding of customer value, and managing close and long-term customer relations (Baines et al., 2009c, Martinez et al., 2010). The military connection common in PBL contracts also need consideration. PBL usually requires that he supplier can perform maintenance and service swiftly to reach contracted goals. For military operations, this may lead to situations where a civilian supplier may be forced to support the system at war at unsafe locations (Doerr et al., 2004). Apart from the difficulties associated with delivering performance at war, the supplier also risk the employees’ well-being (Gansler and Lucyshyn, 2006).

PBL from the customer’s perspective From a customer’s perspective, PBL implies an increased focus on core activities, such as maintaining a country’s defensive ability or defending a country (Martin, 1997), rather than supporting and maintaining the systems. The reduced responsibility for support will therefore likely reduce the customer’s financial risks (Dang et al., 2009). The customer will receive better performance if the supplier manages to improve the system and the support services during the system’s lifetime (Fino, 2006). Altogether, PBL aims to provide the customer with better performance to a fixed cost, or similarly, less cost to a fixed performance (Nowicki et al., 2010). However, the customer stands the risk of being locked to one supplier in a long-term contract that systematically delivers bad performance (Nowicki et al., 2010), and, as a consequence, not able to enhance system performance (Jacopino, 2007). Moreover, the customer will have difficulties to introduce a new supplier to support the system if the supplier breaks the contract, since both the customer and any new supplier likely lacks access to all vital system data (Kim et al., 2007, Dang et al., 2009). Full insights into military operations is a normal customer prerequisite, but such insights may become restricted if the supplier is responsible for the support services (Tegtmeier, 2010).

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Cost and profitability If both parties are to benefit from PBL, the customer and the supplier must share the benefits of a more efficient value chain due to PBL as illustrated in Figure 3.

Figure 3: The intention of performance-based logistics (PBL) is to reduce the customer’s cost and increase the supplier’s profit.

Many also report that PBL have resulted in reduced costs, see for example Phillips (2005), Keating and Huff (2005), Gansler and Lucyshyn (2006), Mahon (2007) and Ott (2008). However, most reports are vague as to how savings have been measured and the published empirical support for the profitability hypothesis based on the above mentioned reports is weak. A few studies regarding profitability are more thorough. Two works from the U.S. Government Accountability Office (GAO) are inconclusive whether PBL reduces, have no effect, or even increases the customer’s costs (GAO, 2005; GAO, 2008). Another large study including 10 000 companies indicate that the company size also matters for PBL profitability, where small firms seem to gain the most from moving to PBL (Neely, 2009). The latter three more thorough studies thus provide mixed conclusions regarding the profitability of PBL and PSS. The profitability hypothesis thus needs more empirical support.

3.2 Critical aspects of implementation Here we present the findings related to implementation of PBL: commonly used contracts in PBL, the scope and the typical arrangement of PBL-contracts, performance measurements, and payment models.

PBL-contracts The literature emphasizes that each PBL-contract has to be tailored (Sols et al., 2007, Nowicki et al., 2010), and the contract types thus differ. In fact, authors do not even agree on how to separate PBL contracts from traditional contracts. The same contract type seems to be considered traditional by one author and as a PBL-contract by another, see e.g. the different interpretations by Kim et al. (2007) and Nowicki et al. (2010). Two contract types are more frequently mentioned in PBL-literature: the firm fixed price contract and the cost plus award fee contract (Cunic, 2003, Kim et al., 2007, Sols et al., 2007, Nowicki et al., 2010). In firm fixed price contracts the supplier agrees to deliver some level of performance (e.g. aircraft availability) based on some level of use (e.g. the amount of flying hours per month). The contract then states the level of remuneration, e.g. price per flying hour, and 7

an award fee may be added to stimulate performance improvements (Kim et al., 2007, Nowicki et al., 2010); increasing payments if performance surpasses the contracted minimum level. The financial risks are thus concentrated to the supplier, whose income depends on the ability to deliver and improve performance. The risks are especially high for new systems, for which performance must be predicted based on little or no historical data (Smith, 2004, Kim et al., 2007, Erkoyuncu et al., 2011, Sols et al., 2008). In a cost plus award fee contract, the customer reimburses the supplier for their costs for the performed services, adding an award fee to stimulate performance improvements or cost reductions. Here, the financial risks are mainly held by the customer who is forced to pay the supplier despite the performance output (Cunic, 2003, Sols et al., 2007, Nowicki et al., 2010). Cost-plus award fee contracts are often used in a transition phase when a non-PBL contract is being converted to a firm fixed price with award fee (Kim et al., 2007, Nowicki et al., 2010, Liu et al., 2009).

Scope of PBL-contracts PBL-contracts are applied to complete systems, subsystems, major components, or certain support services, e.g. spare parts provision (GAO, 2004, Sols et al., 2008, Dang et al., 2009). Moreover, PBL can be applied to a system’s lifecycle as well as to parts of the lifecycle (Sols et al., 2007). A disadvantage of implementing PBL partly can be that opportunities due to economies of scale may be lost (Nowicki et al., 2010). Furthermore, it can be difficult to find appropriate performance indicators if the supplier is only responsible for the performance of a subsystem, (Fino, 2006). Like any other contract, PBL-contracts vary in length. However, a common recommendation is that PBL-contracts should be long term, (Maples et al., 2000, Keating and Huff, 2005) and some authors even claim that PBL-contracts are long term by definition (Berkowitz et al., 2005, Nowicki et al., 2010). The literature describes two main benefits of long term contracting related to return on investments. First, setting up, negotiating and implementing PBL takes time and is costly while the benefits received are distributed over the contract period. The contracts have to be long enough for the benefits to exceed the costs (Berkowitz et al., 2005). Second, a long term contract increases motivation for the supplier to make larger investments in the system that can improve system performance, even if the pay-off time is long (Nowicki et al., 2010). Such investments may be related to mitigating obsolescence and enhancing system reliability (Fino, 2006) which are especially important for systems with long product life cycles (Sols et al., 2007). For these reasons, it has been argued that a PBL-contract should not be shorter than about five years (Sols et al., 2007, Nowicki et al., 2010).

Performance measurements Performance is a central part of PBL as performance reflects customer value and forms the basis for the supplier’s income. Consequently, it is important that the performance can be measured accurately (Devries, 2004, Sols et al., 2008, Hollick, 2009). The supplier and the customer must agree on: performance indicators, definitions of the indicators, target values and how to perform measurements and analyses (Forslund, 2009). The performance indicators should be specific, straightforward, measurable and relevant to the customer’s requirements (Fino, 2006, Dang et al., 2009). However, to

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select performance indicators that reflect customer value is often difficult, since the customer’s needs often are formulated in abstract terms (Tukker, 2004, Spring and Araujo, 2009). Typically, several performance indicators are measured in a PBL-contract, for example: availability, reliability, maintainability, supportability, logistics response time, logistic footprint and cost of use, see Fino (2006), Sols et al. (2007) and Nowicki et al. (2010). The indicators can be measured on different system levels and address different customer needs. For example, reliability can be related to a component (component reliability), a system (system reliability) or the system’s performance (mission reliability) (Dang et al., 2009). Although performance indicators often are objectively measured such as the up-time of the system, they can also be subjective, e.g. customer satisfaction (Dang et al., 2009). The availability of, for example, an aircraft is a highly aggregated performance indicator, dependent on many lower level indicators. It is difficult to track problems and identify improvements by only observing the overall aircraft availability. Lower level performance indicators are therefore required (Fino, 2006, Sols et al., 2008, Hollick, 2009). Moreover, the supplier cannot be held responsible for the availability on an aggregated level if the supplier only is responsible for the availability of some subcomponents (Hollick, 2009). Conversely, achieving performance goals on lower-level performance indicators does not, per se, guarantee good system performance. Defining performance indicators and corresponding measurements can be challenging, e.g. if the definition must respect a certain equipment requirement. For example, whether a military aircraft should be considered available or not might depend on what kind of missions it is scheduled for. Such availability is commonly called operational availability or operational readiness (Dang et al., 2009, Hollick, 2009). Agreeing on a definition of an indicator can also be difficult. For example, the mean time between failures (MTBF) is commonly used to measure reliability, but MTBF requires a definition of a failure and determination of how many failures that are required to reach statistical significance (Richardson and Jacopino, 2006). Performance target values must represent the customer’s needs and form a realistic challenge for the supplier. A baseline constituting the “normal” performance of the system must thus be identified to set target values. If the system has been used, the baseline could be drawn from historical performance (Sols et al., 2008). However, identifying a baseline from historical values might be difficult, such as when the measurements have been done differently and not according to a new indicator definition, or if the use of the system has changed (Sols et al., 2008). For new systems, the baseline must be built on predictions of future performance exclusively (Kim et al., 2007), which is even harder.

Payment models A model must be established to transform the measured performance into supplier fees when the performance indicators are set. A good model includes incentives for the supplier to produce high performance (Dang et al., 2009), whereas a poor model could impose unwanted supplier actions (Nowicki et al., 2008). Payment models must often consider many performance indicators and this makes them complex (Sols et al., 2007). A conflict between performance criteria appears when one performance indicator is over-performing and another is under-performing.

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Consequently, the payment model must balance the results of several performance indicators and convert the overall result to a fair payment (Sols et al., 2008). Nowicki et al. (2008) propose a payment model consisting of a minimum performance limit, a penalty zone, a dead zone and a reward zone, as illustrated in Figure 4.

Reward Zone Dead Zone Penalty Zone

Min

Normal

Max

System performance Figure 4: Payment model. The supplier’s payment depends on system performance.

The minimum performance limit determines the performance level under which the supplier does not receive payment. If the supplier delivers performance just above this limit, the supplier enters the penalty zone and is paid according to the achieved performance. However, in the penalty zone the payment is smaller than the cost of delivering the performance. If the performance is within the limits of the dead zone, around normal system performance (Sols et al., 2007), the payment is comparable to the cost of delivering the performance. The supplier earns marginal or no profit in the deadzone, but if the system performance is in the reward zone, the supplier receives payment exceeding the production cost (Nowicki et al., 2008). The frequency of measurements and performance reviews is also discussed in the literature. Sols et al. (2007) suggest that performance should be assessed over short periods, with long periods over which the payments are calculated, to even out possible shifts in payments to the supplier.

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4. CONCLUSIONS AND DISCUSSIONS The view of PBL as a business concept that creates value more efficient with less waste seems to be widely accepted. PBL transfers the service responsibility for a system from the customer to the supplier, i.e. the system manufacturer. This transfer is expected to increase the driving forces for improving the efficiency of the value chain, i.e. reduce the cost for delivering a certain performance level, and the reduced costs are to be split between supplier and customer. PBL has the potential to create this win-win situation, but the transfer of responsibilities is not without risk. The supplier is exposed to increased financial risks since the supplier carries the cost if the cost to deliver the required system performance is underestimated. Therefore, predicting cost and performance in the bidding stage of a PBL-contract is important for the supplier. However, such predictions are often difficult due to the complexity of the systems and the long-term contracts. The customer becomes more dependent on the supplier since the control over the support services is transferred to the supplier. Probably, as a consequence, the customer has dismantled its organization with the competence necessary to provide system support. Should the supplier fail, another supplier might be difficult to find. The risks force both parties to put extensive efforts on; designing contracts and payment models, decide on how to measure performance, define performance indicators, specify system levels and set target values. Given the significant financial and organizational implications of PBL we expected to find the financial effect of PBL a well-researched area, but the literature is scarce and few publications are scientific, containing little or no empirical evidence. Therefore, we believe that the profitability of PBL is an important knowledge gap to bridge. An obvious risk is that the cost for mitigating the financial risks and rearranging organizations, equipment and attitudes from a traditional support structure exceeds the gains. Furthermore, assuming that PBL is effective, it is unclear how the cost reduction is shared between the customer and the supplier. It is possible that the supplier set a higher price due to the increased financial risks and thus that the customer’s cost remains or even increases. More empirical research is also needed here. We believe that the servitization level, i.e. the degree to which the system is owned by the supplier, can impact the opportunities to achieve cost reductions and effectiveness from a PBL-agreement. Moreover, we suggest that a PBL-agreement with a high servitization level is more likely to result in cost reductions. As previous literature state, one of the main obstacles of the traditional business model is that the customer of a complex system often depends on the original system manufacturer to provide support services. We suggest that the customer’s position cannot be empowered as long as the ownership of the system, and perhaps even the utilization, stays with the customer. Thus, we propose that trading the outcome of the system rather than the output is advantageous, see Figure 5. Our proposition implies that the supplier is fully responsible for the system and the customer strictly purchases a service. The customer would neither own nor operate the system, but simply concentrate on specifying requirements and following up results of the delivered service.

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We see three possible advantages from trading the outcome: 1. The customer’s bargaining power is improved and competition is facilitated. It is easier for the customer to switch supplier which strengthens the customer’s position in negotiations concerning performance and cost. 2. The interface between the customer’s and the supplier’s responsibilities is distinct. Thus, the cost for specifying and follow up contracts, conduct measurement and ensure fair payments is reduced. 3. Customers with limited financial strength are able to take part of the outcome of complex systems. For example, a customer unable to buy the whole system could choose to buy the outcome of the system over a limited time period.

Figure 5: Trading the outcome makes it easier for the customer to switch supplier. The customer’s bargaining power is therefore improved.

However, it should be noted that delivering outcome in some cases is difficult. For example, delivering the outcome of a military system is in many cases equivalent to ‘delivering death’. Trading such an outcome definitely requires a change in mindsets not just for the supplier but for countries, governments and people in general. Certainly, it might be a development that changes the prerequisites of war in a way that does not serve humanity well. This literature review has been limited to articles in the PBL research area and topics closely related to PBL. For further studies on PBL we recommend that more literature from other research areas is included, possibly covering topics and results relevant for PBL but not yet considered in the PBL research area. Such approach would enable results and insights to be spread between PBL and other research areas.

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PAPER B A solution procedure for Economic Lot Scheduling Problems even in high utilisation facilities Holmbom, M., Segerstedt, A. and van der Sluis, E. (2012)

Accepted for publication: International Journal of Production Research

A solution procedure for Economic Lot Scheduling Problems even in high utilisation facilities Martin Holmbom1, Anders Segerstedt1, Erik van der Sluis2 1

Industrial Logistics, Luleå University of Technology, SE-971 87, Luleå, Sweden 2 Amsterdam University of Applied Science, School of Technology P.O. Box 1025, Amsterdam, The Netherlands (Martin Holmbom: E-mail: [email protected]) (Anders Segerstedt: E-mail: [email protected])

Abstract Economic Lot Scheduling Problem (ELSP) handles the problem of deciding what order quantities to use when different products/items are produced in the same capacity constrained production facility. It has previously been shown, and it is shown in this article, that it is possible to find a feasible solution fulfilling true feasibility conditions. However, if the utilisation of the production facility is high the production often has to start before the inventory reaches zero to avoid future shortages. Such “early starts” creates an extra inventory holding cost that the traditional approximation for the inventory holding cost does not account for. This article presents an iterative solution procedure that computes the true inventory holding cost and minimises the total costs. Contrary to previous solution procedures, this procedure requires that the production is scheduled in detail. The heuristic solution procedure is illustrated by a numerical example, it is programmed in MATLAB and variants of the problem are presented. Keywords: Economic Lot Scheduling Problem, ELSP, Cyclic planning, Production cycle, Production schedule, Production plan, Single machine, Capacity constrain

1. Introduction It is often too costly for a company to have special machines and equipment for every product they produce. Therefore, it is common that several products or variants of a main product are manufactured in one machine or production facility. The determination of production quantities and their scheduling is called the Economic Lot Scheduling Problem (ELSP). It sounds like a simple problem, but it is a complicated theoretical problem classified as NPhard in the strong sense (cf. Gallego and Shaw (1997)). Moreover, it is a common practical problem existing in several types of industries, e.g. paper mills and milling machines, reaching from process industries with more or less continuous flow to work shops. When the production must be finished before the customer order arrives a forecasted constant demand rate, which is adjusted in intervals, is a common assumption for the scheduling of the production facility. The timing and the size of the order quantities will decide how efficient the processing will be; it determines the costs, the service to customers, and in the end the profitability of the manufacturing company. Which order quantity to use for this item? – That is a question that must be answered several times per day in a manufacturing company. The objective of the ELSP is to determine a production schedule that minimizes costs, traditionally the sum of inventory holding costs and setup costs. However, constructing sensible and realistic schedules is difficult and several methods have been developed to find the minimum cost production schedule. A schedule where each item is produced exactly once during a cycle is called a common cycle solution. Such solution is an upper bound on the optimum cost that has capacity for the setup and the production of every item (showed by Hanssmann (1962)). Due to differences in demand rate, product cost or setup cost the common cycle approach will often not present an optimal solution to the original problem 1

even though there are reported cases when the approach is successful, e.g. Galvin (1987) investigating metal work applications. Differences in demand, costs and production times motivate more frequent production of some items and less frequent production of others. In the popular basic period approach the items are allowed to have different cycle times, as long as the cycle times are integer multiples of a basic period. High volume items are produced in every basic period and lower volume items are produced less frequently (every second basic period, or every fourth basic period etc.). Bomberger (1966) introduced the restrictive constraint that all items must be produced in at least one basic period. Therefore, the sum of the setup time and operations time of all items must be less than or equal to the basic period. However, this constraint is relaxed in the extended basic period approach, stating that the basic period must be long enough to cover the average setup times and processing times for all items. Bomberger (1966) presented a 10-item ELSP-problem which has been used extensively in the literature. Doll and Whybark (1973) present an iterative procedure, which reaches the best known solution to the Bomberger problem. Elmaghraby (1978) presented an overview of earlier research and own contribution to the problem. Goyal (1973) (1975), Hsu (1983), Axsäter (1987), Zipkin (1991), Bourland and Yano (1997) are all well-known references to this problem. Lopez and Kingsman (1991) make a review and compare different solution methods. They argue that the “power-of-two”, of the basic period, is a requirement for achieving schedule feasibility in practice. Yao and Elmaghraby (2001) also mean that power-of-two solutions seem to be a way to derive easy and effective heuristics. Segerstedt (1999) presented a heuristic method for this problem that has no explicit common basic period, but during a common cycle (time period) the different items are produced with different frequencies restricted to “power-of-two”. The heuristic consists of an iterative procedure and the main idea is to find a balance between the setup costs (i.e. the replenishment costs) and the inventory holding costs. Similarly to the economic order quantity model (EOQ) the solution becomes better as the ratios between the setup costs and the inventory holding costs approach one. Segerstedt (2004) shows that this heuristic is possible to extend to several machines and multi-level production. Nilsson and Segerstedt (2008) compare the heuristic from Segerstedt (1999), but first modified and improved, with the heuristic techniques of Doll and Whybark (1973) and Goyal (1975). All these heuristics find the best known solution to the Bomberger problem, 32.07; a solution that many methods do not find. Nilsson and Segerstedt (2008) show that feasible solutions can be found, both with their method and others, where the production can be scheduled during a time interval, the initial inventory level is the same as the final and the schedule can be repeated in a cyclic pattern without shortages. However, Nilsson and Segerstedt (2008) show that the common approximation for the inventory holding costs does not fit. Therefore their definition of feasibility differs from the traditional. The “real” inventory holding cost often becomes larger than the common approximation, because the replenishment of some items starts before the inventory is consumed to zero. Thus, the inventory holding costs depend on the production schedule. In many companies production cost is almost constant per hour regardless if the facility is idle, under setup, or under production. The cost per time unit of both production and setup in the production facility depend on the availability of the facility. Each hour of production is connected to a cost due to for example direct labour costs, indirect manufacturing costs, consumption of electricity and energy, and costs for tools, maintenance and necessities. The facility cost affects the time (hours, shifts) that the facility should be operating from an 2

economical point of view. Thus, the facility cost affects the scheduling and lot sizing. The scheduling and lot sizing in its turn will affect how many hours per working day the facility must produce to satisfy current demand. Therefore, Brander and Segerstedt (2009) treat the ELSP with an untraditional cost model: a cost per time unit of production and setup, traditional inventory holding costs, and an out-of pocket cost for the setup independent of the setup time. (They assume that the demand must be satisfied. Therefore, the setup cost does not include any lost sales or opportunity costs, but only expenditures created by the setup.) Brander and Segerstedt (2009) modify the heuristic procedure in Nilsson and Segerstedt (2008) to determine cyclic schedules. The examples in Brander and Segerstedt (2009) show that even a small cost per time unit of production and setup, makes solutions with high utilisation and little idle time economically beneficial. The main idea behind the heuristics of Nilsson and Segerstedt (2008) and Brander and Segerstedt (2009) is to find a balance between the setup costs and the inventory holding costs that will minimize the total cost. These costs should have as similar magnitudes as possible for all items. The principle has been applied to other problems than ELSP with good results, for example the Joint Replenishment Problem (Nilsson et al (2007)) and the One Warehouse N-retailer Problem (Abdul-Jalbar et al (2010)). This article presents an iterative solution procedure that finds the true inventory holding cost to the ELSP even in high utilisation facilities. The article shows that it is possible to find a feasible solution (fulfilling feasibility conditions from Eilon (1962), Goyal (1975) and Segerstedt (1999)), but the real inventory holding cost is larger than the commonly used approximation. The solution procedure schedules the production in detail (including frequencies, sequences, start times etc.) to compute the additional inventory holding cost dependent on the production schedule. The article has the following outlay: Section 2 presents the assumptions and notations used in the article. Section 3 shows that the inventory holding cost is underestimated by the traditional approximation and provides an equation for the true inventory holding cost. Section 4 explains the solution procedure in detail. Section 5 presents a step-by-step solution to a numerical example, and Section 6 provides a discussion about the findings. 2. Assumptions and notations The following assumptions are made for the solution procedure presented in this article: ƒ ƒ ƒ ƒ ƒ ƒ

Only one product can be produced at a time Product setup costs and setup times are independent of production order Product demand rates are deterministic and constant over time Production times are deterministic and constant over time Inventory holding costs are determined on the value of stocks hold Backorders are not allowed

We consider N different items which are produced in a capacity constrained machine and introduce the notations in Table 1.

3

di

Demand rate for item i, in units per day; i 1, 2,!, N

si

Setup time of item i, in days per production lot

oi

Operation time of item i, in days per unit

Ai

Setup cost for item i, in Swedish krona (SEK) per production lot

hi

Inventory holding cost of item i, in SEK per unit and day Production cycle time, in days (time interval in which all items are produced at least once)

T fi

Frequency, the number of times that item i is produced during a production cycle T

fic

Preliminary frequency; the frequency that is being tested

fˆ

The highest frequency among the items i; max( f i )

Tmin qi

The shortest possible production cycle time in days, in which all items can be produced with the chosen frequencies fi

pi

Order quantity for replenishment of item i, in units Production time; setup time and operation time for qi

Ri

Ratio; setup cost per day for item i divided by inventory holding cost per day for item i

4K

A subset of K items from the total set of items ^1, 2,!, N `

C f , T Total cost per day, in SEK (depending on chosen frequencies and time interval) S i, j

Scheduling matrix; production time for item i in period j, in days; j 1, 2, ! , max ^ f i `

T jc

Start time of period j if all periods would be of equal length

Tj

Real start time of period j

ti j

Adjusted early start of item i in period j, in days

Ij

Scheduled idle time in period j Table 1. The notations used in this article.

3. The true inventory holding cost The approximation for the total inventory holding cost traditionally used for ELSP is: Cinventory

¦ hi i

di T (1  oi d i ) 2 ˜ fi

(1)

The traditional approximation is correct when the time between replenishments is constant, i.e. if all production periods are equally long, see Figure 1. When the time between replenishments is constant equation (2) to (5) is ascertained (cf. Segerstedt, 1999): Maximum inventory =

di T (1  oi d i ) fi

4

(2)

Area of one triangle =

di T T 1 (1  oi d i ) ˜ ˜ fi 2 fi

Total area of all triangles = f i ˜

Average inventory =

(3)

di T T 1 (1  oi d i ) ˜ ˜ fi fi 2

1 dT T 1 ˜ f i ˜ i (1  oi d i ) ˜ ˜ T fi fi 2

di T (1  oi d i ) 2 ˜ fi

(4)

(5)

T fi

T fi

Figure 1. Inventory level when the time between replenishments is constant.

However, sometimes the time between replenishments varies. That is especially apparent when the machine is working close to its capacity limit and the idle time is too short to even out the production periods. When the time between replenishments varies the production of some items i in some periods j must start ti j time units earlier to prevent future shortages. Due to such “early starts” an additional inventory is created, see Figure 2. The additional inventory is a rhomboid with the area a ˜ b , where a di ti j and b T f i . Thus, if the time between replenishments varies the production in some periods has to start with di ti j items left in the inventory. Observe that for each i at least one ti

j

0 , otherwise more items are produced

Inventory

than what is consumed during the production cycle ( f i ˜ qi ! d i ˜ T ) .

b a

tij Figure 2. When the time between replenishments varies the production in some periods must start ti j time units earlier than normally. Such early starts cause additional inventories (the rhomboid in the graph).

5

The additional inventory holding cost for item i is: hi ˜

d i ti j T 1 ˜¦ T j fi

hi ˜ ¦ j

d i ti

j

(6)

fi

Consequently, the true total inventory holding cost for all items is:

ª §d T d i ti j · º ¸» Cinventory ¦ «hi ¨ i (1  oi di )  ¦ ¨ 2˜ f ¸» f i « j i i © ¹¼ ¬

(7)

4. Solution procedure The solution procedure is based on three steps. In STEP 0 a start solution is obtained. In STEP 1 an iterative procedure searches for solutions with lower total cost. The iterative procedure includes scheduling. When the solution procedure cannot find any better solution the order quantities are calculated in STEP 2. STEP 0 In STEP 0 a start solution with the frequency f i common cycle solution). Set f i

1 for all items is computed (known as the

1 i .

Determine the shortest time interval, due to the capacity, in which all items can be produced with the chosen frequencies (derived in Segerstedt (1999) and in line with the feasibility conditions for the extended basic period approach presented in Eilon (1962) and Haessler and Hogue (1976)): Tmin

¦i f i si 1  ¦i oi di

(8)

If Tmin  0 there is no feasible solution since the capacity does not cover the required demand. Thus; If Tmin  0 : Go to STOP. The total cost per time unit according to the frequencies, f, and an arbitrary production cycle time, T, is: inventory holding cost cost § setup

  · P ¨ fi Ai ¸ di T (1  oi di ) ¸  hi ¨ ¦ 2 ˜ fi T i 1¨ ¸ © ¹ N

C (f , T )

(9)

The lowest total cost according to T can be found by differentiating the cost function, C (f , T ) , with respect to T. Compute the lowest total cost according to T:

6

C0





C f , T ; where T *

­° ½° ¦ i f i Ai max ® , Tmin ¾ °¯ ¦ i hi (1  oi d i ) d i /( 2 f i ) °¿

(10)

Compute the ratio between the setup cost per time unit and inventory holding cost per time unit, for all items: R i (f )

f i Ai / T * hi (1  oi d i ) d i T * /( 2 f i )

i

(11)

Let K m N . STEP 1 In STEP 1 an iterative procedure tests solutions with different frequencies to find the solution with lowest total cost. Find the item with the maximum ratio or inverted ratio:

k m arg max ( Ri ,1 / Ri )

(12)

i4 K

If Rk ! 1 then f kc m f k / 2 else f kc m 2 ˜ f k . The smallest allowed frequency in a solution that is feasible in practice is f ic 1 , therefore; f ic m



f ic min( f ic)

(13)



If C f c, T t C 0 then ( 4 K 1 m 4 K \ ^k` and K m K  1 , If K t 1 Go to STEP 1 else Go to STEP 2). /Scheduling part/ A new order of the items is established. In descending order the items are rearranged according to (1) frequency, f ic , and (2) production time, pi , where; operation time

  P o d T i i si  fic

setup time

pi

(14)

Consequently, item 1 has max ^ f ic` fˆ and longest pi of the items with f ic has min ^ f ic` 1 and shortest pi of the items with f ic 1 .

fˆ , and item N

Item 1 is scheduled to be produced every period i.e. S 1, j m p1  j 1, 2, ! , fˆ .

7

i ­° i fˆ °½ If ¦ S m, k min ® ¦ ¦ S m, n ¾ then item i+1 is scheduled such that, S i  1, k m pi 1 , n °m 1 n 1 °¿ m 1 ¯ fˆ fˆ for the periods l: S i  1, l m pi 1 where l k  n n 0, 1, 2, ! , f ic . If l k  n ! fˆ f ic f ic fˆ then l k  n  fˆ . This procedure is repeated until all N items are scheduled. f ic When all N items are scheduled the idle time can be scheduled. The total idle time is:

I

N

T  ¦ si f ic  oi d i T

(15)

i 1

I is scheduled such that S N  1, j m I j and

fˆ

fˆ

j 1

j 1

¦ S N  1, j ¦ I j I . Moreover, I is

­N

½ first scheduled in the period min ® ¦ S i, j ¾ until the length of period j is equal to the length j ¯i 1 ¿ of the second shortest period. Then I is scheduled in both period j and the second shortest period until the length of these periods is equal to the length of the third shortest period etc. The ambition is to achieve: N 1

N 1

i 1

i 1

¦ S i, j ¦ S i, k  j , k

(16)

For each period j a point in time, Tjc , is calculated:

T jc

 j  1 Tˆ f

j 1, 2,!, fˆ

(17)

T jc corresponds to the starting point of period j that would have been if eq. (16) would have

been satisfied. The actual starting point of period j, T j , is: j 1N 1

T1

¦ ¦ S i, k j 2, 3,!, fˆ .

0 , Tj

(18)

k 1i 1

For all items with production in period j such that S i, j z 0 , a preliminary early start, tic j , is set: tic j m T jc  T j

The assumption T1

(19)

0 might cause that all tic j ! 0 for some i, or that some tic j  0 . Therefore

an adjustment is done. The adjusted early start of item i in period j is: 8

^ `

ti j m tic j  min tic j j

i

(20)

The total cost with the true inventory holding cost is calculated: C (f c, T )

N

ª f cA i i

¦«

T*

i 1¬ «

f ic d t § d T i ij  hi ¨ i (1  oi d i )  ¦ ¨ 2˜ f c j 1 f ic i ©

·º ¸» ¸» ¹¼

(21)

Return to original order and original index of items. /Exit scheduling part/





If C (f c, T )  C 0 then ( C0 m C f c, T , f m f c , K m N , Compute Ri (f )  i ) else ( 4 K 1 m 4 K \ ^k` , K m K  1 ) If K t 1 Go to STEP 1.

STEP 2 In STEP 2 the order quantity corresponding to the best solution that was found is calculated. Compute the order quantity: qi

di T fi

i

(22)

STOP. 5. Numerical example In this section the solution procedure is applied on a numerical example presented in Nilsson and Segerstedt (2008). Five items A, B, C, D and E are produced in a machine. The items have individual demand rate, operation time, setup time, setup cost and inventory holding cost, see Table 2. Production data: Variable Demand rate, d i Operation time, o i Setup time, s i Setup cost, A i Inv. holding cost, h i

Unit units/day days/unit days/setup SEK/setup SEK/(unit·day)

A 3.5 0.005 0.167 300 0.192

B 41 0.006 0.054 300 0.615

C 11 0.024 0.071 300 0.769

D 9.4 0.013 0.107 600 0.462

E 29 0.011 0.071 300 0.269

Table 2. The items A, B, C, D and E have individual demand rate, operation time, setup time, setup cost and inventory holding cost.

The start solution is obtained according to STEP 0 in the solution procedure. The frequency is set to f i 1 for all items i. The shortest possible cycle time Tmin is computed from equation (8). The optimal cycle time, T*, and the smallest total cost per day, C0 , is computed from equation (10), the ratio, Ri (f ) , is computed from equation (11) and the idle time is computed from equation (15). The start solution is presented in Table 3.

9

1st solution: Unit setups/cycle

A 1

B 1

Item C 1

D 1

E 1

Total 5

Setup time/cycle Operation time/cycle Production time/cycle Order quantity (q i )

days days days units

0.167 0.213 0.379 39.7

0.054 2.766 2.820 464.7

0.071 2.969 3.040 124.7

0.107 1.395 1.502 106.5

0.071 3.522 3.593 328.7

0.470 10.864 11.334

Setup cost/day Inv.holding cost/day Ratio (R i ) Inverted ratio (1/R i )

SEK SEK

26.47 3.74 7.07 0.14

26.47 108.09 0.24 4.08

26.47 35.39 0.75 1.34

52.94 21.56 2.46 0.41

26.47 30.50 0.87 1.15

158.81 199.29

Min cycle time (T min ) * Cycle time (T ) * Idle time/cycle (I )

days days days

11.334 11.334 0.000

Total cost/day (C 0 )

SEK

358.10

Variable Frequency (f i )

Table 3. In the start solution fi = 1 for all items i. The shortest possible cycle time, Tmin, the optimal cycle time, T*, and the smallest total cost per day, C0, have been computed according to STEP 0 in the solution procedure. To make the solution easier to understand the table also presents setup time, operation time, production time, order quantity, setup cost and inventory holding cost for each item.

After the start solution has been obtained the solution procedure starts searching for other solutions with lower cost (STEP 1). In the start solution item A has the maximum value among the ratios and inverted ratios (i.e. item A = k in equation (12)). Moreover, it is reasonable to expect that the total cost can be reduced by adjusting the frequency so that item A is produced less frequently than the other items, since the setup cost per day of item A is larger than the inventory holding cost per day ( RA ! 1 ). Thus, according to equation (13) the frequency is changed to f Ac 1 and f ic 2 for i = B, C, D, and E. From this frequency the second solution is computed, see Table 4. 2nd solution: Unit setups/cycle

A 1

B 2

Item C 2

D 2

E 2

Total 9

Setup time/cycle Operation time/cycle Production time/cycle Order quantity (q i )

days days days units

0.167 0.360 0.527 67.2

0.107 4.685 4.792 393.5

0.143 5.027 5.170 105.6

0.214 2.363 2.577 90.2

0.143 5.964 6.107 278.3

0.774 18.399 19.172

Setup cost/day Inv.holding cost/day Ratio (R i ) Inverted ratio (1/R i )

SEK SEK

15.63 6.34 2.47 0.41

31.26 91.53 0.34 2.93

31.26 29.97 1.04 0.96

62.52 18.26 3.42 0.29

31.26 25.83 1.21 0.83

171.92 171.92

Min cycle time (T min )

days

18.651

days

19.195

Idle time/cycle (I )

days

0.023

Total cost/day (C 0 )

SEK

343.84

Variable Frequency (f i )

*

Cycle time (T ) *

Table 4.In the second solution the frequencies are f Ac 1 and f ic 2 for i = B,C,D, and E. The calculated total cost per day is 343.84 SEK, which is less than 358.10 SEK in the start solution.

10

The second solution seems to generate a smaller total cost than the first solution. However, to find the true total cost the solution must be scheduled, see Table 5. The schedule is made according to the “scheduling part” in STEP 1. T jc and T j , are calculated from equation (17) and (18) and the early start, tic j and ti j , are calculated from equation (19) and (20). The true total cost per day in the second solution is 349.61 SEK according to equation (21). Item i E C B D A Idle

Period1 Earlystart Prod.time Sij t' i j tij 3.054 0 0.252 2.585 0 0.252 2.396 0 0.252 1.289 0 0.252 0.527 0 0 0

Item i E C B D A Idle

0 0

T' j Tj

Total cost/day (C 0 )

T' j Tj SEK

Period2 Earlystart Prod.time Sij t' i j tij 3.054 -0.252 0 2.585 -0.252 0 2.396 -0.252 0 1.289 -0.252 0 0 0.023 9.598 9.850

349.61

Table 5. Production schedule for the second solution. The cycle time, T*, has been divided into two periods. All items except item A are produced in both periods. The idle time is scheduled last in the second period. The true total cost per day in the second solution is 349.61 SEK.

The true total cost in the second solution is less than the total cost in the first solution. Therefore, the solution procedure moves on with the second solution at STEP 1, this time searching for a solution with lower cost than 349.61 SEK. In Table 4 item D has the maximum value among the ratios and inverted ratios. Moreover, RD ! 1 which implies that the frequency of item D should be reduced in the next solution. The third solution is presented in Table 6. 3rd solution: Unit setups/cycle

A 1

B 2

Item C 2

D 1

E 2

Total 8

Setup time/cycle Operation time/cycle Production time/cycle Order quantity (q i )

days days days units

0.167 0.310 0.476 57.8

0.107 4.029 4.136 338.4

0.143 4.324 4.466 90.8

0.107 2.032 2.139 155.2

0.143 5.129 5.272 239.4

0.667 15.823 16.490

Setup cost/day Inv.holding cost/day Ratio (R i ) Inverted ratio (1/R i )

SEK SEK

18.17 5.45 3.33 0.30

36.35 78.72 0.46 2.17

36.35 25.78 1.41 0.71

36.35 31.40 1.16 0.86

36.35 22.21 1.64 0.61

163.56 163.56

Min cycle time (T min )

days

16.069

days

16.508

Idle time/cycle (I )

days

0.018

Total cost/day (C 0 )

SEK

327.11

Variable Frequency (f i )

*

Cycle time (T ) *

Table 6. In the third solution the calculated total cost per day is 327.11 SEK, which is less than 349.61 SEK in the second solution.

11

The calculated total cost in the third solution is less than the total cost of the second solution. Therefore, the third solution is scheduled, see Table 7. Item i E C B D A Idle T' j Tj

Period 1 Early start Prod.time Sij t' i j tij 2.636 0 0.822 2.233 0 0.822 2.068 0 0.822 2.139 0 0 0 0

Item i E C B D A Idle

0 0

Total cost/day (C 0 )

T' j Tj SEK

Period 2 Early start Prod.time Sij t' i j tij 2.636 -0.822 0 2.233 -0.822 0 2.068 -0.822 0 0 0.476 -0.822 0 0.018 8.254 9.076

344.18

Table 7. Production schedule for the third solution. The true total cost per day is 344.18 SEK, which is less than 349.61 SEK in the second solution.

The true total cost in the third solution is less than the total cost in the second solution. Thus, the solution procedure moves on with the third solution at STEP 1. According to Table 6 item A has the maximum value among the ratios and inverted ratios. Moreover, R A ! 1 which implies that the frequency of item A should be reduced in the fourth solution. The fourth, fifth and sixth solution are presented in short format in Table 8. Results Frequency (f i ) Cycle time (T * ) Idle time/cycle (I * ) 4th solution 5th solution 6th solution

(1,4,4,2,4) (1,4,2,1,2) (1,8,4,2,4)

31.564 20.944 40.054

0.143 0.095 0.281

Total cost/day (C 0 ) (before scheduling) 323.15 315.13 314.57

Total cost/day (C 0 ) (after scheduling) 346.80 343.90 349.26

Table 8. The results of the fourth, fifth and sixth solution.

The calculated total cost in the fourth solution is less than the total cost in the third solution. However, after scheduling it is discovered that the true total cost in the fourth solution is higher than the total cost in the third solution. Therefore, the fourth solution is rejected and the solution procedure once again moves on with the third solution at STEP 1, this time identifying the item k corresponding to the second highest value among the ratios and inverted ratios, which turns out to be item B. The frequency of item B is increased in the fifth solution since RB  1 . The fifth solution is accepted since the true total cost in the fifth solution is less than the total cost in the third solution. Thus, the solution procedure moves on with the fifth solution at STEP 1. In the fifth solution item A has the maximum value among the ratios and inverted ratios and since R A ! 1 the frequency of item A should be reduced. After scheduling it is discovered that the true total cost of the sixth solution is higher than the total cost in the fifth solution. Therefore, the sixth solution is rejected and the solution procedure once again moves on with the fifth solution at STEP 1, this time identifying the item k corresponding to the second highest value among the ratios and inverted ratios, which turns out to be item D. The frequency of item D is increased in the seventh solution since RD  1 . The seventh solution is presented in Table 9.

12

7th solution: Unit setups/cycle

A 1

B 4

Item C 2

D 2

E 2

Total 11

Setup time/cycle Operation time/cycle Production time/cycle Order quantity (q i )

days days days units

0.167 0.457 0.623 85.3

0.214 5.945 6.159 249.7

0.143 6.380 6.523 134.0

0.214 2.999 3.213 114.5

0.143 7.569 7.712 353.2

0.881 23.349 24.230

Setup cost/day Inv.holding cost/day Ratio (R i ) Inverted ratio (1/R i )

SEK SEK

12.32 8.04 1.53 0.65

49.26 58.08 0.85 1.18

24.63 38.03 0.65 1.54

49.26 23.17 2.13 0.47

24.63 32.77 0.75 1.33

160.10 160.10

Min cycle time (T min )

days

21.234

days

24.360

Idle time/cycle (I )

days

0.130

Total cost/day (C 0 )

SEK

320.20

Variable Frequency (f i )

*

Cycle time (T ) *

Table 9. In the seventh solution the calculated total cost per day is 320.20 SEK, which is less than 343.90 SEK in the fifth solution.

The calculated total cost in the seventh solution is less than the total cost in the fifth solution. Therefore the seventh solution is scheduled, see Table 10. Item i B E C D A Idle T' j Tj

Item i B E C D A Idle T' j Tj

Period1 Earlystart Prod.time Sij t' i j tij 1.540 0 0.247 3.856 0 0.247 0 0 0.623 0 0 0

Item i B E C D A Idle

0 0

T' j Tj

Period3 Earlystart Prod.time t' i j tij Sij 1.540 -0.247 0 3.856 -0.247 0 0 0 0 0.130

Item i B E C D A Idle

12.180 12.427

Total cost/day (C 0 )

T' j Tj SEK

Period2 Earlystart Prod.time Sij t' i j tij 1.540 0.071 0.318 0 3.261 0.071 0 1.606 0.071 0 0 0 6.090 6.019 Period4 Earlystart Prod.time Sij t' i j tij 1.540 0.318 0.565 0 3.261 0.318 0.247 1.606 0.318 0.247 0 0 18.270 17.952

329.86

Table 10. Production schedule for the seventh solution. The true total cost per day is 329.86 SEK, which is less than 343.90 SEK in the fifth solution.

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The true total cost in the seventh solution is 329.86 SEK. This is the best solution that can be found by the current solution procedure. Changing the frequencies one at a time in the seventh solution does not generate any solutions with lower total cost. In the last step of the solution procedure the order quantities are calculated from equation (22). These are presented in Table 9. We have programmed the solution procedure in Matlab to easily generate solutions to various production settings. The settings and results of 10 different examples are presented in Table 11 and Table 12. The examples are variants of the example presented in Table 2. In each example one variable has been modified and the others are identical with the original settings. In Table 11 only the modified variable is presented. Settings Demand rate, d i Operation time, o i Setup time, s i Setup cost, A i Inv. holding cost, h i Example 1 Demand rate, d i Example 2 Demand rate, d i Example 3 Operation time, o i Example 4 Operation time, o i Example 5 Setup time, s i Example 6 Setup time, s i Example 7 Setup cost, A i Example 8 Setup cost, A i Example 9 Inv. holding cost, h i Example 10 Inv. holding cost, h i Original settings:

A 3.5 0.005 0.167 300 0.192 2 2 0.005 0.095 0.476 0.476 2000 100 0.038 0.038

B 41 0.006 0.054 300 0.615 30 115 0.006 0.006 0.476 0.476 2000 500 0.192 0.192

Item C 11 0.024 0.071 300 0.769 5 5 0.048 0.012 0.476 0.012 20000 150 0.058 0.058

D 9.4 0.013 0.107 600 0.462 33 9.4 0.013 0.013 0.107 0.107 2000 200

0.769 0.008

E 29 0.011 0.071 300 0.269 20 2 0.002 0.002 0.107 0.107 4000 300 0.115 0.115

Table 11. The examples are based on the original settings. One variable has been modified at a time. Only the modified variable in each example is presented.

Results Example 1 Example 2 Example 3 Example 4 Example 5 Example 6 Example 7 Example 8 Example 9 Example 10

Frequency (f i ) Cycle time (T * ) Min cycle time (T min ) (1,4,2,2,2) 25.177 19.474 (1,4,2,2,1) 26.719 19.653 (1,4,4,2,2) 48.179 48.179 (1,2,1,1,1) 12.158 5.263 (1,2,1,1,2) 53.659 53.659 (1,2,4,2,2) 45.911 45.911 (1,4,2,4,2) 104.046 26.399 (1,2,1,1,1) 12.626 12.626 (1,4,2,4,2) 47.116 26.399 (1,8,2,2,4) 81.420 29.942

*

Idle time/cycle (I ) 0.258 0.291 0 0.727 0 0 6.182 0 0.860 5.496

Total cost/day (C 0 ) 315.70 278.78 400.84 345.44 712.46 477.96 1268.70 304.44 218.13 153.54

Table 12. The final solutions to each example. The frequency is presented in the order A,B,C,D,E.

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6. Discussion, Conclusions and Extensions We have also tried to find a more guaranteed optimal solution by a mixed integer programming formulation and solution (similar to Cooke et al (2004)); but even for this small problem presented the time of computation is very long. Therefore we believe such a solution is very difficult to apply in any practical application; a heuristic solution like what we suggest here is necessary. We have also made some experiments by changing the chosen production sequence not according to our search procedure; e. g. disobeying “longest operation times first” etc. Sometimes with a sequence different to our solution procedure a lower cost solution is found, but in most cases our suggested solution procedure finds the best and low cost solution. van den Broecke et al (2005, 2008) report of successful practical applications of a variant of the calculation method of Doll and Whybark (1973). Brander et al (2005) also demonstrate by simulation it is possible to use a deterministic model, like this presented model, to calculate order quantities even if the demand and the reality are stochastic. However, the calculated order quantities should be combined with complementary decision rules when to produce a quantity of a special item and when not. Levén and Segerstedt (2007) suggest and discuss such rules in detail. In a practical situation with high utilisation and similar magnitudes for the different parameters; demand rates, setup times, operation times, setup costs etc and also stochastic variations; the best solution in many cases may be the common cycle solution. Then combined with a decision rule such that if for an item there is a large enough inventory on hand compared to the expected demand rate the production of this item is skipped and postponed to the next cycle. However, we do not undervalue the contribution of our recursion procedure to find differentiated production frequencies, such should be investigated when there are irregular and dispersed demand rates, setup times etc. In our small example we found a costs decrease of almost 8%, other cases with increased number of items will probably present more. That will create significant cost improvements, which will make the company more successful and competitive. We could have included also a time varying facility cost in this presented solution procedure; but Brander and Segerstedt (2009) show that this cost does not influence the chosen frequencies. It only increases the utilisation; and it influences what Tmin to start from. Even a small time variable cost makes high usage economically beneficial; if in a practical application the production facility has a small Tmin for the common cycle solution ( d 1 ) it may be questionable and a sign of over capacity. An increase of idle time creates costs. An increase of idle time means that instead of one shift (7-8 hours working time per day); we have to increase to two shifts (14-16 hours working time per day), this may cost too much and is therefore not a sensible solution. Here we have treated the time interval from step 1, T , as fixed. If we have prolonged T the setup cost would decrease, and the inventory holding cost increase more than the setup cost decrease, and if the working hours per day increase costs for that also increase. However, a prolonged T may also sometimes ease the scheduling so the early starts of production before the inventory reaches zero decrease and therefore the inventory holding costs decrease instead of increase. This may be a possible theoretical extension to investigate further, but probably it has small practical implications. Variants of the procedure are left for further studies. Ideas for other possible extensions may be found in related research outside the pure ELSPliterature: e. g. Quadt and Kuhn (2008) present a review about capacitated lot-sizing,

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Bollapragada et al (2011) study non-identical production lines and Haksöz and Pinedo (2011) study recourses in parallel.

7.

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