Proceedings of 8th International Conference on Supply Chain Management and Information Systems (SCMIS 2010) Hong Kong, China - 6-8 October 2010

Supply Chain Performance in the case of Decentralized Planning Maxime OGIER, Van-Dat CUNG, Fabien MANGIONE

Julien BOISSIERE LISTIC Polytech’Savoie, Université de Savoie Annecy Le Vieux, FRANCE

Laboratory G-SCOP CNRS UMR 5272/Grenoble INP/UJF Grenoble, FRANCE

[email protected]

{maxime.ogier, van-dat.cung, fabien.mangione}@grenoble-inp.fr

Abstract—Evaluating the performances of a Supply Chain is a hard task due to its decentralized structure and when one tries to take into account sustainable development issues. As a first step towards a realistic evaluation tool, in this paper, we provide a two-echelon supply chain model - a manufacturer and a 3PL provider - inspired from Jung, Chen & Jeong [4] which optimizes the economic criterion (costs) under a decentralized vision of the supply chain planning. We extended this model with a rolling planning horizon. The coordination between the actors is based on a negotiation process which exchanges the minimum information, i.e. the quantities needed. We evaluated this model with a cost structure inspired from the literature, several deterministic and stochastic demands and different rolling horizons. Results showed that decentralized planning is better than the centralized one in small rolling horizons. Sustainable considerations such as gas emission and securing resources will be discussed to extend this model.

constraints of the two others. A comparison between the planning is then performed, considering 2 rules: all that is produced and not transported is lost, and what is being transported but cannot be stored is lost as well. Three cases were studied: •

Demand, costs and capacities change in each period.

•

Only demand evolves over time. Costs and capacities are constant.

•

The same conditions as the previous case hold. In addition, the carrier is limited in capacity. Its carrying capacity is the same as the capacity of the factory. It is a case where pieces of information are exchanged between the factory and the carrier.

Tables I, II, III show the results obtained:

Keywords-supply chain performance; decentralized planning; coordination; optimization.

I.

INTRODUCTION

Supply chain management is an important issue in today’s business. To evaluate and optimize commodity flows, it is preferable to consider global supply chain than sequential supply chain [1]. It is then possible to define an optimal planning for the whole supply chain using lot sizing models. Although this centralized vision gives good results it is not realistic [3]. Indeed, it requires that a single decision-maker owns information from all the companies/actors of the supply chain which is difficult to gather especially when dealing with sensitive information such as capacities or costs. Another difficulty is how to make the global decisions accepted and applied by all the different actors. A decentralized approach in supply chain management seems to be more realistic, but it can lead to very bad results if there is not coordination between the actors. To show that, let us consider a “decentralized” supply chain composed of three actors: a factory manager, a carrier and an inventory manager. They all know the exact customers’ demands for each period on the entire planning horizon. The factory and the carrier cannot store products. The factory has a limited production capacity. For transportation, each vehicle has a limited capacity, but the number of vehicles is not limited. The central inventory has limitation in capacity. Each actor has setup costs and per unit costs. Each actor optimizes locally its own planning on the entire horizon without taking into account the

ISBN: 978-962-367-697-7

TABLE I.

RESULTS OF THE FIRST CASE.

Manufactured products not carried

68.38 %

Transported products not stored

29.50 %

Lost sales

77.71 %

TABLE II.

RESULTS OF THE SECOND CASE.

Manufactured products not carried

83.05 %

Transported products not stored

35.87 %

Lost sales

89.13% TABLE III.

RESULTS OF THE THIRD CASE.

Manufactured products not carried

15.31 %

Transported products not stored

24.62 %

Lost sales

36.16 %

It appears that a strong desynchronization between the actors of the supply chain happens and leads to very bad results. Notice that the case is very restrictive. There is no way to make storage, and the carrier in the first two cases has no capacity limitation, so it tends to propose very different plannings to those of the manufacturer. When it has no capacity limitation, the carrier plans to transport huge quantities when the cost is low and nothing when the cost is higher.

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This simple case shows the importance to coordinate actors in the supply chain to achieve better performance. To get this, the coordination process of [4] based on negotiation is used in this paper. However, we do not only consider a negotiation on all periods. When modeling or simulating the behavior of a supply chain on a large number of periods, it is unrealistic to assume that demand is perfectly known in advance for all periods. In the context of evaluating a supply chain, it is more relevant to consider that demand is known only on a small number of periods. Hence, the planning should be redone regularly. This supply chain model should be able to integrate sustainable aspects, like optimization of gas emissions. In this context, the work proposed here can be considered as a first aspect of sustainability. Indeed, coordination is important to have good results on the global supply chain, and rolling planning allows studying long-term effects. This paper is organized as follows. Section 2 presents a review of the literature. Section 3 describes the problem, the model considered and the cases studied. Results and analyses of the models are presented in Section 4. Section 5 shows the impact of planning horizon length. A conclusion and research prospects are drawn in Section 6. II.

LITERATURE REVIEW

To our knowledge, there has been no significant research on the decentralized planning of a supply chain. More specifically, we did not find articles that include both the distributed optimization of the supply chain and long-term simulation of the supply chain. However, some works have been made separately. There are a number of articles dealing with the distributed simulation of supply chains. In a lot of papers, the tool used is the multi-agent system. Some articles use a multi-agent system to study which information to exchange and how to share it. In this paper [5], four methods of sharing information have been tested and the performances of the supply chain in each case are compared. In [2], a more detailed study of how agents are coordinated is presented. These articles have an interest in terms of information sharing and reaction of the agents to the information they receive. However, these articles do not address the optimization of internal planning for each agent. Other articles are more interested in optimization. The supply chain is optimized using ILP (Integer Linear Programming) as in [6]. But they consider the supply chain globally, which is not realistic as mentioned earlier. Other articles present models in which each actor makes a local optimization, but they do not propose to simulate the supply chain. Article [4] is specially interesting because it suggests coordinating planning with minimal-information sharing. However, there is a lack concerning the evaluation of the supply chain on a rolling planning horizon basis. III.

PRESENTATION OF THE PROBLEM

This section describes the problem, the model and the various studied cases.

ISBN: 978-962-367-697-7

A. Description of the problem The major aim of this paper is to simulate the optimization of the decentralized planning of a supply chain. To do this, we use a negotiation process to coordinate the supply chain actors. The goals for a given instance are as follows: •

To evaluate the additional cost when the supply chain planning is decentralized w.r.t. the centralized case.

•

To highlight a possible imbalance in the sharing of costs between the actors.

•

To study the impact of the rolling planning horizon on commodity flows and costs.

•

To compare the importance of the effects of the rolling planning horizon and the decentralization of the actors on the costs.

B. Studied model This work is inspired from the one presented by Jung, Chen & Jeong [4]. 1) The supply chain The original model from Jung et al. [4] considers a supply chain with two actors: the manufacturer actor (MA) and the logistician actor (LA) who is a 3PL logistics provider (Fig. 7). The production is multi-products and multi-factories. The distribution is multi-inventories and multi-customers. The aim is to coordinate the two actors. Coordination is achieved when the deliverable quantities by the manufacturer in each period are equal to the quantities carried by the 3PL logistics provider. The information they share are the quantities required transmitted by LA to MA and the quantities available transmitted by MA to LA. Each actor optimizes its production plan using an ILP by taking into account the information received. The parameters are as follows: F = D = C = N = P = V = Dkct =

rkft = tkijvt = hkft = h̃kdt = l̃kct = Hft = H̃dt = sk =

set of production facilities set of distribution centers set of customer zones set of all locations, N = D ∪ F ∪ C set of products set of vehicles demand for product k( ∈ P ) in customer zone c( ∈ C ) at period t unit production cost of product k in production facility f( ∈ F ) at period t cost of transporting one unit of product k from location i( ∈ N ) to location j( ∈ N ) via vehicle v( ∈ V ) at period t unit inventory holding cost of product k in production facility f at period t unit inventory holding cost of product k in distribution center d( ∈ D ) at period t unit lost sales penalty cost of product k in customer zone c at period t inventory capacity in production facility f at period t inventory capacity in distribution center d at period t storage space required for one unit of product k

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Proceedings of 8th International Conference on Supply Chain Management and Information Systems (SCMIS 2010) Hong Kong, China - 6-8 October 2010

Mft = production capacity in production facility f at period t mkf = production capacity required to produce one unit of product k in production facility f Tijt = transportation capacity from location i to location j at period t The decision variables are the followings: xkft = production volume of product k in production facility f at period t ykijvt = transportation volume of product k from location i to location j via vehicle v at period t z̃kct = lost sales volume of product k in customer zone c at period t Ikft = inventory level of product k in production facility f at period t Ĩkdt = inventory level of product k in distribution center d at period t

Decision variables: zkft = production shortage volume of product k in production facility f to customer zone c at period t ykfct = transportation volume of product k from production facility f to customer zone c at period t The production planning problem for LA is formulated as follows:

∑

+

∑

k ∈K , f ∈F , t

Subject to Ikft = Ikft-1 + xkft −

∑ ∑ ∑

(l̃kctz̃kct)

(1)

Subject to Ikft = Ikft-1 + xkft −

∑

ykfdvt ∀ k, f, t

d ∈D , v∈V

Ĩkdt = Ĩkdt-1 +

∑

ykfdvt −

f ∈F , v∈V

∑

ykdcvt ∀ k, d, t

(2)

ykdcvt = Dkct − z̃kct ∀ k, c, t

(4)

k ∈K

∑

k∈K

(6)

∑ s Ĩ ≤ H̃ ∀ d, t ∑ s y ≤ T ∀ i, j, t

(7)

dt

k ∈K

(8)

ijt

k ∈K , v∈V

xkft, Ikft, Ĩkdt, ykijvt, z̃kct ≥ 0 ∀ k, f, d, c, i, j, v, t

(9)

Basically, the objective function (1) seeks to minimize the total costs of supply chain, constraints (2)-(4) ensure the flow conservation, constraints (5)-(8) are capacity restriction and (9) is decision variables constraint. In the decentralized case, for the agent-based decentralized supply chain planning (ADSCP), there are two optimization problems coming from the previous in the centralized case. For MA, new parameters and decision variables are defined as follows: Parameters: lkft = unit production shortage penalty cost of product k in production facility f at period t Skft = the requested supply quantity of product k in production facility f at period t

ISBN: 978-962-367-697-7

(12)

mkfxkft ≤ Mft ∀ f, t

(13)

skIkft ≤ Hft ∀ f, t

(14) (15)

The objective function (10) seeks to minimize the costs of MA. Constraints (11) ensure flow conservation for the production. Constraints (12) result from the negotiation process. Constraints (13) and (14) are capacity restriction. And (15) are constraints of the decision variables. For LA, there is one new parameter: S̃kft = the available supply quantity of product k in production facility f at period t.

(5)

skIkft ≤ Hft ∀ f, t

k kijvt

ykfct = Skft − zkft ∀ k, f, t

And the logistic planning problem for LA is as follows:

mkfxkft ≤ Mft ∀ f, t

k kdt

(11)

xkft, Ikft, ykfct, zkft ≥ 0 ∀ k, f, c, t

d ∈D , v∈V

∑

ykfct ∀ k, f, t

k ∈K

(3)

c∈C , v∈V

∑

c∈C

k ∈K

(tkijvtykijvt)

k ∈K , c∈C , t

(10)

c∈C

k ∈K , i∈ N , j∈ N , v∈V , t

∑

(h̃kdtĨkdt) +

k ∈ K , d ∈D , t

∑

∑

(rkftxkft + hkftIkft) +

(rkftxkft + hkftIkft + lkftzkft)

k ∈K , f ∈F , t

As presented in [4] the optimization problem for the centralized supply chain planning (CSCP) is given as follows: Min

∑

Min

∑

Min +

∑

(tkijvtykijvt)

+

k ∈K , i∈ N , j∈ N , v∈V , t

∑

(h̃kdtĨkdt)

k ∈ K , d ∈D , t

(l̃kctz̃kct)

(16)

k ∈K , c∈C , t

Subject to

∑

ykfdvt ≤ S̃kft ∀ k, f, t

d ∈D , v∈V

Ĩkdt = Ĩkdt-1 +

∑

ykfdvt −

f ∈F , v∈V

∑

∑

(17) ykdcvt ∀ k, d, t

(18)

c∈C , v∈V

ykdcvt = Dkct − z̃kct ∀ k, c, t

(19)

d ∈D , v∈V

∑ s Ĩ ≤ H̃ ∀ d, t ∑ s y ≤ T ∀ i, j, t k kdt

dt

(20)

k ∈K

k kijvt

ijt

(21)

k ∈K , v∈V

Ĩkdt, ykijvt, z̃kct ≥ 0 ∀ k, d, c, i, j, v, t

(22)

The objective function (16) seeks to minimize the costs of LA. Constraints (17) result from the negotiation process. Constraints (18) and (19) ensure flow conservation for the production. Constraints (20) and (21) are capacity restriction. And (22) are constraints of the decision variables.

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Proceedings of 8th International Conference on Supply Chain Management and Information Systems (SCMIS 2010) Hong Kong, China - 6-8 October 2010

Notice that MA and LA are linked by constraints (12) and (17) with respectively the variables Skft and S̃kft. This paper considers a simplified version of the model with a single product, a single factory, a central inventory and one customer. This will permit to better observe what occurs in the model, such as the convergence of the negotiation process and the financial impacts for each actor. 2) The negotiation process The two actors in this chain must negotiate to reach an agreement on a joint planning. It is necessary that at the end, the quantities sent by MA (ykfct) and the quantities transported by LA (ykfdvt) are equal. For this, they exchange pieces of information that are the quantities they plan to carry (Skft) or they plan to ship (S̃kft). Everyone considers this information in order not to provide more than what the other is willing to ship/transport.

LA starts the process by optimizing its production planning according to the demand. MA tries to satisfy as much as possible the forecast quantities of LA: there is a per-unit cost to pay if MA provides a quantity less than that requested by LA. The process stops when LA and MA agree on the quantities, thus MA does not pay a penalty at the end of the process. It should be noticed that this negotiation process never allows actors to increase forecast quantities. The fact of lowering the quantities during the negotiation process makes possible to demonstrate the convergence of the process [4]. Moreover, this process advantages LA because it starts the negotiation. This can be justified if we consider that commodity flows are pulled by demand. 3) Instances Instances are selected from those presented in [4]. U (a, b) means the uniform distribution between the values a and b. The instances on which our tests are based are presented in Table IV. TABLE IV. Demand

Capacities

Unit costs

The storage cost for MA represents half of the production cost. So, it is always more interesting to produce just in time, if the capacity allows it. The total cost of storage and transportation for LA is equivalent to the production cost for MA. For LA, the transport cost is equivalent to the storage cost. Hence, for LA, it is always more interesting to transport products between the factory and the inventory just in time. Lost sales have a cost much higher than other costs, which will encourage LA and MA to avoid lost sales. Remember that at the end of the negotiation process, MA has no penalties to pay because the quantities required by LA are equal to those it sends. LA will support shortage penalties on its own. Thus, its costs can increase dramatically in case of lost sales. The models are developed in Java and for the ILP the interface Concert Technology is used to run with CPLEX. C. Various cases of planning Three planning cases are presented here:

•

A global plan on all periods. This was the cases presented in [4]. But this is not very realistic because it is rare to know exact demands on a large number of periods.

•

A rolling planning horizon where at each period a new plan is recomputed for a given number of periods. For example if one plans for three periods each time and 20 periods in total, in period 1, periods 1, 2 and 3 are planned, and in period 2, periods 2, 3 and 4 are planned. In this case, a given level of inventory must be reached at the end of the last period in the planning. If there was no storage required for the last planning period, the least expensive inventory would be zero. However, it is clear that it is necessary to hold little inventory to anticipate the following periods. This also corresponds to reality because companies generally take inventory policies with a minimum threshold. This is the deterministic planning case.

•

A rolling planning horizon in which demands will no longer be certain. The demand for the initial planning period is known with certainty, and then there is an uncertainty that increases as shown in Table V. Let us recall that 40% is the variation in demand. An uncertainty of 2.5% means that demand is estimated at ± 2.5% of the real demand. This is the stochastic planning case.

Dt = U (1500 ; 3500) Dt

Mt = U ( 0.8;1.2 )

Storage MA

Ht = U ( 0.8;1.2 )

Transport Factory – Inventory

Tfdt = U ( 0.8;1.2 )

Storage LA

H̃t = U ( 0.8;1.2 )

Transport Inventory – Client

Tdct = U ( 0.8;1.0 )

Production

rt = ct + dt ct = U (45 ; 55) dt = U (0 ; 5)

Storage MA

ht = 12 rt . U (0.9 ; 1.1)

Transport Factory – Inventory

tfdt = 14 rt . U (0.9 ; 1.1)

Storage LA

h̃t = 12 rt . U (0.9 ; 1.1)

Transport Inventory – Client

tdct = 14 rt . U (0.9 ; 1.1)

lt = l̃t = 10000

With these instances, demand is fairly fluctuating (± 40%). The transport capacity between the inventory and the customer is closed to the demand quantity. Unlike other capacities, it always exceeds demand. Indeed, it is not interesting if this capacity is below the demand because it means that there is necessarily lost sales. Other capacities are such that they are close to the demand, but may be higher or lower. That is why it will be necessary to make storage at certain periods.

THE INSTANCES.

Production

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Lost sales penalties

Dt

Dt

Dt

Dt

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Proceedings of 8th International Conference on Supply Chain Management and Information Systems (SCMIS 2010) Hong Kong, China - 6-8 October 2010

TABLE V. Period

EVOLUTION OF UNCERTAINTY DEPENDING ON THE PERIOD. t+0

Uncertainty 0%

t+1

t+2

2.5%

5%

IV.

t+3

t+4

7.5% 10%

t+5

t+6

t+7

t+8 and more

15%

20%

30%

40%

inventory, the additional cost is higher with the global planning than with a rolling horizon. Moreover, in the version with no final inventory, there is a very large cost difference between the CSCP and ADSCP models. As suggested previously, we consider that this case is less relevant. Let us compare now, in Table VII, results concerning additional costs for MA and LA from centralized to decentralized model.

COMPARISON OF THE MODELS

The results obtained by tests on several instances are presented in this section and intuitive clues for understanding them are given. In this section the rolling planning horizon is three periods.

TABLE VII.

COMPARISON OF THE EVOLUTION OF THE COSTS.

Planning

A. Interpretation of the results The following tests have been performed:

•

•

Over 50 periods by making an average on 30 instances randomly generated according to what has been defined previously. Over 20 periods by making an average on 50 instances.

For the 20 period instances, two possibilities for the rolling planning horizons have been explored: •

A minimum inventory level to respect at the end of each planning horizon (average inventory level found in the global model).

•

No constraint on the final inventory level (and thus to minimize cost, the inventory is zero in the last period).

In what follows, we call CSCP the centralized model and ADSCP the distributed model in which we set up the negotiation process between MA and LA. Table VI presents the major differences between the two planning models: the number of iterations of the negotiation process and the gap between the costs of the centralized model and the decentralized model. TABLE VI.

50 periods with final inventory

DIFFERENCES BETWEEN MODELS.

Planning

Number of iterations for the negotiation process

Evolution of the total cost between CSCP and ADSCP

Global

1.833

3.132 %

Rolling horizon

1.506

0.446 %

20 periods with final inventory

Global

1.76

1.688 %

Rolling horizon

1.513

0.675 %

20 periods without final inventory

Global

1.76

0.043 %

Rolling horizon

1.486

9.631 %

Notice that there is more iteration on average in the global version than with the rolling planning version. This can be explained by the fact that the rolling planning horizons considers fewer periods each time, so it is easier to converge to a solution. The total cost is more important in the decentralized model than in the centralized model. In cases with forced final

ISBN: 978-962-367-697-7

50 periods with final inventory

Evolution of costs Evolution of costs for LA in the for MA in the ADSCP model ADSCP model compared to compared to CSCP CSCP

Global

0.746 %

4.243 %

Rolling horizons

0.393 %

0.476 %

20 periods with final inventory

Global

0.509 %

4.307 %

Rolling horizons

0.237 %

0.833 %

20 periods without final inventory

Global

0.437 %

- 0.166 %

Rolling horizons

- 0.878 %

11.266 %

With the global planning, the increase in costs is very badly distributed between the two actors. When there is a final inventory constraint, the rolling planning horizons model can rebalance the losses made by each actor relative to the centralized model. The evolution of costs between the global planning and the rolling planning horizon are shown in Table VIII. TABLE VIII.

EVOLUTION OF COSTS FROM GLOBAL PLANNING TO ROLLING HORIZONS PLANNING. Total Total Cost MA Cost LA Cost MA Cost LA costs costs CSCP CSCP ADSCP ADSCP CSCP ADSCP

50 periods with final inventory 20 periods with final inventory 20 periods without final inventory

88 %

- 8.3 %

117 %

84 %

- 8.6 %

111 %

40 %

- 3.6 %

48 %

40 %

- 3.9 %

48 %

44 %

- 4.2 %

53 %

44 %

-9%

68 %

Concerning costs, one can notice that both models are very different. The total cost is higher with the rolling planning horizons model, but distribution of this surplus is very uneven, with slightly lower costs for MA and therefore all of the increase is attributed to LA. This is explained by the fact that the planning horizon is smaller, so it is more difficult to anticipate, so there are more lost sales. But these losses are fully supported by LA, and as the quantity produced is lower, MA has lower costs. Moreover, over 50 periods, the effect is even stronger. Table IX presents lost sales in the centralized and decentralized supply chain models for each case of planning. It

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Proceedings of 8th International Conference on Supply Chain Management and Information Systems (SCMIS 2010) Hong Kong, China - 6-8 October 2010

suggests that the percentage of lost sales by model evolves in the same way as the costs. Lost sales are a little higher in the decentralized than in the centralized model, and much more with the rolling planning than with the global planning. TABLE IX.

50 periods with final inventory 20 periods with final inventory 20 periods without final inventory

COMPARISON OF LOST SALES.

Planning

Lost sales CSCP

Lost sales ADSCP

Global

1.57 %

1.64 %

Rolling horizons

3.79 %

3.81 %

Global

2.485 %

2.5 %

Rolling horizons

3.839 %

3.851 %

Global

2.604 %

2.606 %

Rolling horizons

4.151 %

4.569 %

All these results tend to show that in the studied case, the rolling planning horizon, that is to say the lack of information on demand, has more impact than the decentralized aspect of the supply chain. B. Explaining the increase in costs in the distributed version We show through this small example why costs are greater when the supply chain planning is decentralized. Here the overcost is not due to lost sales. Let us look at what occurs over one period in a global planning. The values are presented in Fig. 1. MA

LA

D = 2869

Production x = 3181

y = 3390 2869

Storage

Storage

t-1 : 209 t:0

t-1 : 0 t : 521

Figure 1. Planning CSCP.

In the centralized case, the demand is 2869 units, MA products 3181 units; it had 209 on hand that adds to the production units up to 3390 units. Then LA stores 521 units and sends the customer the 2869 units. Fig. 2 shows the quantities in the distributed version. Notice that the quantities are different from those obtained in the centralized case (CSCP). At the beginning of the process, LA computes the quantities it needs, according to its own costs. For this period it wants only 3245 units and it plans to store 376, whereas in the centralized version 3390 units are transported and 521 units are stored by LA. Then, MA receives the quantity LA is willing to transport, and it can not claim to carry more because of the constraint (12) y = S - z. MA produces as much as in the centralized version, sends 3245 units and stores the difference.

ISBN: 978-962-367-697-7

MA

S = 3245

LA

D = 2869

Production x = 3181

y = 3245

Storage

t : 12.701 t+1 : 12.134

t-1 : 209 t : 145

2869 Storage

t-1 : 0 t : 376

25.888

21.673

y=S-z Quantities down compared to CSCP Quantities up compared to CSCP Costs

Figure 2. Planning ADSCP.

Thus, the difference here lies in who holds the inventory. But the transport and storage by LA, in the period t costs 34.373 per unit, while storage by MA in the period t and transportation in the period t+1 costs 38.022 per unit. So the fact that LA takes an initial decision by taking into account only its costs and that MA cannot increase the quantity desired by LA results in increased costs. Moreover, the fact that LA does not know the capacity of MA, and that MA can not increase the quantities required by LA can lead in certain cases to additional lost sales. V.

IMPORTANCE OF PLANNING HORIZON LENGTH

This section discusses the effect of the planning horizon on the total cost of the supply chain. Recall that the rolling horizon has been set to three periods in the previous section. For planning with a rolling horizon, it was already mentioned that it is better to specify an inventory level for the last period. Here, this inventory level is adapted to the demand and its fluctuations. The final inventory is considered according to the average of the demand on the rolling planning horizon. It is set equal to 45% of the average demand. However, the maximum storage capacity should be respected (if the demand average is too important). This inventory is set to a level which is expected to achieve the continuity of the service and the satisfaction of the demand. Indeed, planning is done on a small number of periods, and ignores what may happen afterwards. The results presented here represent averages over 50 instances. Each instance covers 50 periods. The supply chain in its centralized (CSCP) and decentralized (ADSCP) version are studied along with the deterministic and stochastic demand cases and the rolling planning horizon. Results are presented in Fig. 3, Fig. 4, Fig. 5, and Fig. 6.

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Proceedings of 8th International Conference on Supply Chain Management and Information Systems (SCMIS 2010) Hong Kong, China - 6-8 October 2010

These graphs allow us to highlight interesting results. Remember that these results are considered specific to the instances and the final inventory specified. Notice that if there are reliable data about demand, it is better to plan on the longest possible horizon which is obvious. Indeed, in the deterministic case, costs clearly decrease when rolling planning horizon length increases.

Figure 3.

Figure 4.

Figure 5.

Evolution of the CSCP total cost, deterministic planning.

Evolution of the CSCP total cost, stochastic planning.

Evolution of the ADSCP total cost, deterministic planning.

If the data are not reliable, planning on a large number of periods is not very good. Thus, according to the different instances, the length of planning which gives the best results is of great interest. For the instances presented, in the case of stochastic planning, the best results are for a 7 periods planning horizon in the centralized case, and for a 4 periods planning horizon in the decentralized case. When planning for a small rolling horizon, it seems better to consider the decentralized version of the supply chain. This is true in the stochastic and deterministic cases. This result is remarkable because when computing a global planning the centralized case is always cheaper. Costs become lower in the centralized version from planning over 10 periods in the deterministic case, and from planning over 7 periods in the stochastic case. When planning for a small horizon, decentralized version is better because LA starts the negotiation process, and it wants to satisfy the demand and to reach its final inventory level. So it is important for LA to store as soon as it is possible, not worry about lowering the cost of the overall supply chain. In the centralized version, the central planner knows all the costs, and it makes the storage where it costs less. Sometimes, it is less expensive for MA to store in period t, so LA has no inventory. At period t+1, the transport capacity between LA and MA is below the demand, and MA holds inventory, so there are lost sales. In fact, when there is a limited vision of the demand, bad decisions are taken in the centralized case because costs are minimized without taking into account that LA is closer to the customer, so it needs to have a small inventory. Moreover, note that the effect of the distributed supply chain becomes more important than the effect of rolling planning horizon when planning for more than 24 periods. That is to say the cost of the rolling planning in the centralized case falls below the cost of the global planning in the decentralized case. VI.

Figure 6.

Evolution of the ADSCP total cost, stochastic planning.

ISBN: 978-962-367-697-7

CONCLUSION AND PROSPECTS

This paper has proposed an enriched model of coordination in a supply chain with a producer and a logistician. Although it is still limited to a two-echelon supply chain and analyzed under the assumption of a single product flow, it helps to better understand the impacts of the negotiation based coordination process and the decentralized planning on the performance of a supply chain. Instead of considering a global planning, a more realistic case is studied, in which decentralized planning is done for a limited number of periods. At each period, actors in the supply chain start again the negotiation over the periods to come. With a detailed analysis based on an instance of the problem it is suggested that the effect of the planning horizon is more important than the effect of the decentralization of the supply chain over the performance of the entire chain. Between

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Proceedings of 8th International Conference on Supply Chain Management and Information Systems (SCMIS 2010) Hong Kong, China - 6-8 October 2010

the two models, consequences in terms of costs are not the same for the producer and the logistician. The producer can reduce its costs by using the planning process that is proposed in this paper. Instead, the logistician undergoes a strong increase in costs. Furthermore, this model allows long-term monitoring, thanks to rolling planning horizon. Besides, coordination between the actors of the supply chain is also important for sustainable development because there are good results in terms of costs, which is one aspect of the sustainable development, and companies do not need to exchange a lot of information. Our major perspective in the future is to improve this model. On the one hand, investigations can be done on what contract could be implemented so that each of the two actors in the supply chain has an economic incentive to use this negotiation process. On the other hand, to avoid having too many lost sales, it could be interesting to study the possibility of actors to propose an increase in traded quantities during the negotiation process. Moreover to validate or not the results presented, tests on other costs structure can be made. Finally, two other prospects are considered. Firstly, new aspects of sustainability could be taken into account. Clearly, some aspects such as carbon cost can easily be integrated if they are financially expressed. Other aspects like securing resources, i.e. the limitation of the gap between forecast and achievement can also be integrated because only new

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P. Chandra and M.L. Fisher, “Coordination of production and distribution planning,” European Journal of Operational Research, vol. 72, 1994, p. 503–517. M.S. Fox, M. Barbuceanu, and R. Teigen, “Agent-oriented supply-chain management,” International Journal of Flexible Manufacturing Systems, vol. 12, 2000, p. 165–188. I. Giannoccaro and P. Pontrandolfo, “Supply chain coordination by revenue sharing contracts,” International Journal of Production Economics, vol. 89, 2004, p. 131–139. H. Jung, F. Frank Chen, and B. Jeong, “Decentralized supply chain planning framework for third party logistics partnership,” Computers & Industrial Engineering, vol. 55, 2008, p. 348–364. J.S. Lau, G.Q. Huang, and K.L. Mak, “Impacts of sharing production information on supply chain dynamics: a multi-agent simulation study,” Proceedings of 30th International Conference of Computers and Industrial Engineering, 2002, p. 27–30. Y. Pochet and L.A. Wolsey, “Production Planning by Mixed Integer Programming,” Springer, 2006.

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constraints are added in the model. A multi-objective adaptation of the model is also a major stake to integrate all these aspects. The second perspective is to extend the supply chain to more than two actors and two-echelon supply chains using multi-agent system. For instance, the negotiation based coordination process based can be used at two levels of a threeechelon supply chain.

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Figure 7. The supply chain model considered.

ISBN: 978-962-367-697-7

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