Produktion und Logistik Herausgegeben von B. Fleischmann, Augsburg, Deutschland M. Grunow, München, Deutschland H.-O. Günther, Berlin, Deutschland S. Helber, Hannover, Deutschland K. Inderfurth, Magdeburg, Deutschland H. Kopfer, Bremen, Deutschland H. Meyr, Hohenheim, Deutschland Th. S. Spengler, Braunschweig, Deutschland H. Stadtler, Hamburg, Deutschland H. Tempelmeier, Köln, Deutschland G. Wäscher, Magdeburg, Deutschland

Diese Reihe dient der Veröffentlichung neuer Forschungsergebnisse auf den Gebieten der Produktion und Logistik. Aufgenommen werden vor allem herausragende quantitativ orientierte Dissertationen und Habilitationsschriften. Die Publikationen vermitteln innovative Beiträge zur Lösung praktischer Anwendungsprobleme der Produktion und Logistik unter Einsatz quantitativer Methoden und moderner Informationstechnologie.

Herausgegeben von Professor Dr. Bernhard Fleischmann Universität Augsburg

Professor Dr. Herbert Meyr Universität Hohenheim

Professor Dr. Martin Grunow Technische Universität München

Professor Dr. Thomas S. Spengler Technische Universität Braunschweig

Professor Dr. Hans-Otto Günther Technische Universität Berlin

Professor Dr. Hartmut Stadtler Universität Hamburg

Professor Dr. Stefan Helber Universität Hannover

Professor Dr. Horst Tempelmeier Universität Köln

Professor Dr. Karl Inderfurth Universität Magdeburg

Professor Dr. Gerhard Wäscher Universität Magdeburg

Professor Dr. Herbert Kopfer Universität Bremen

Kontakt Professor Dr. Hans-Otto Günther Technische Universität Berlin H 95, Straße des 17. Juni 135 10623 Berlin

Sebastian Vogel

Demand Fulfillment in Multi-Stage Customer Hierarchies Foreword by Prof. Dr. Herbert Meyr

Sebastian Vogel Darmstadt, Germany

Dissertation Technische Universität Darmstadt, 2013 D 17

ISBN 978-3-658-02863-3 DOI 10.1007/978-3-658-02864-0

ISBN 978-3-658-02864-0 (eBook)

The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at http://dnb.d-nb.de. Library of Congress Control Number: 2013944979 Springer Gabler © Springer Fachmedien Wiesbaden 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer Gabler is a brand of Springer DE. Springer DE is part of Springer Science+Business Media. www.springer-gabler.de

Foreword Strategically, manufacturing companies intend to operate on the edge so that ca.pacity and inventories (the so-called 8'Upply) are constrained and optimally baJanced with demand. However, due to short-term demand fluctuations, this balance is difficult to a.rhieve, and manufacturers often face temporary periods of under- and over-supply. In case of oversupply, production resourees are badly utilized. In case of under-supply, some customers cannot be served on time cr not at all. Demand Fhlfillment (DF) takes care of such ahortterm situations when demand is higher than supply, when supply cannat be increased on time and when same customers have to be preferred over others. Then, the ahn is offering a. better service to the more important customers rather than to the less important customers.

The PhD thesis of Sebastian Vogel concentrates on the special case of DF when MalreTo-Stock (MTS) situations prevail and customer heterogeneity ia caused by 8. multi-sta.ge sales hieraxchy. In MTS situations, custom.ers expect very short delivery times far final items. They want an immediate, but also reliable answer whether their requested products axe already on stock in a neaxby warehouse and just need to be delivered. Multi-stage sales hieraxchies can often be found in big, internationally operating companies. To handle the huge and wide-spread customer base, the sales organization is structured hieraxchically, e.g., a sales manager of a warld region is responsible for several countries within her region, a country manager is responsible for several sales districts within his country, and a district manager is responsible for all customers within bis district. Since production is often centralized and concentrated to one or a few production sites only, delivery times and delivery costs may be high and may vary substantially between the different regions, countriea, and districts. The obvious conflict between customer expectations and supply cha.in reality necessitates a planning process where first scaxce supply quantities axe quoted iteratively, level by level, to regions, countries and districts on the basis of demand forecasts in a rather mid-term, capacitated. allocation planning step. Then, reliable order promises are made on the basis of the bottem-Ievel quotas in the short term when real customer orders materialize. The quotas axe usually the results of negotiations between an upper level's sales manager and her corresponding subordinates at the lower levels. The danger of this myopic, iterative process is that quotas axe allocated to upper-Ievel segments which aclually do not contain sufficiently profitable lower-Ievel customer orders. Sebastian Vogel is (to the best of my knowledge) the first one to complement this iterative, decentral allocation steps by profit-based considerations which allow exploiting customer heterogeneity in a way usually only an imaginative, fully informed., central planner could do. Tc achieve this, he brings together ideas from different scientific disciplines lik.e supply cha.in management, supply chain planning, economies, graph theory, game

vi

Foreword

theory and operations research, respectively. His contribution ia not only to propose a. clever allocation mechanism. It ia rather to open a-until now widely ignored-field of research, to structure and model it, and to discuss various aspects of potential applications. Reading tbis book ja a pleasure. I can only recommend enjoying thls pleasure.

Hohenheim, June 2013 Prof. Dr. Herbert Meyr

Acknowledgments Completing this dissertation would not have been possible without the steady support I have received frorn many people and I would like to express sincere gratitucle to them. Prof. Herbert Meyr, then at Dannstadt University cf Technology, now at the University cf Stuttgart-Hohenheim, was a superb supervisor and first reviewer cf my dissertation: I have perceived him 88 an invaluable BOUXce cf suggestions, questions, comments and motivation. Clearly, he ia among the most knowledgeable, committed, helpful and upright people I have ever worlced with. Furthermore, I had. the privilege that Prof. Malte Fliedner, then a.t Darmstadt University cf Technology, now a.t the University cf Hamburg, challenged my thinking process and provided the second opinion on this dissertation. My fellow doctorru ca.ndidates were a stea.dy source of inspiration, support and distraction. I have also greatly benefited frorn disCUBSions with researchers at the a.nnual QBWL conferences and at multiple regional demand fulfillment workshops with participants from research groups at the Universities of Mannheim, Stuttgart-Hohenheim and Wiirzburg. The generoUB lea.ve of absence progrsm of my employer Booz & Company provided sponsorship and the necessary time off to fully focus on this research project. Last but not least: My family was a k.een supporter and invaluable source of motivation throughout the entire dissertation. In particular, I sm endlessly grateful to my pa.rents and my beloved. wife.

Dannstadt, June 2013 Sebastian Vogel

Contents

List of Tables

xv

List of Abbreviations

xvii

List of Symbols

xix

1. Introduction 1.1. Motivating Case Study . . . . . . . . . . . . . . 1.2. The Demand Fulfilhnent Problem in Multi-Stage 1.2.1. Heterogeneous Customer Segments . . . 1.2.2. Multi-Stage Customer Hierarchies. . . .

1 5 8 8 10 11 13 17

2. Supply Chain Planning and Demand Fulfillment 2.1. Supply Chain Planning . . . . . . . 2.1.1. Supply Chain Management. . . . . . . 2.1.2. Hierarchical Planning. . . . . . . . . . 2.1.3. Interrelations between Planning Tasks

21 21 22 25 33

. . . . . . . . . . . . . Customer Hierarchies . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.3. Iterative Disaggregation and Alloca.tion in Customer Hierarchies 1.3. Problem FOCUB and Research Questions . 1.4. Overview of Approach . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2.

2.3. 2.4.

2.5.

2.1.4. The Position of the Customer Order Decoupling Point 2.1.5. Advanced Planning Systems . . Demand Planning . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1. Objectives and Planning Tasks . . . . . . . . . . . . . 2.2.2. Demand Planning Structures and Forecasting Hierarchies. 2.2.3. Demand Planning Processes and Forecasting Procedures . 2.2.4. Demand Planning Controlling and Forecast Error Measures . 2.2.5. Hierarchical Forecasting . . . . Master Planning . . . . . . . . . . . . 2.3.1. Objectives and Planning Tasks 2.3.2. Basic Master Planning Model . Demand Fulfillment . . . . . . . . . . . 2.4.1. Objectives and Planning Tasks 2.4.2. Types of Demand Fulfillment Systems 2.4.3. Basic Model, for Demand Fulfillment . 2.4.4. State of the Art: Demand Fulfillment in MTS Environments Conclusions: Allocation Problems in Supply Chain Planning . . . .

37 42 46 47 50 51 58 63 77 77 79 81 81 86 89 98 . 105

Contents

x

3. Multi-Stage Customer Hierarchies 3.1. Formal Hierarchies . . . . . . . · 3.1.1. Trees and Hierarchies .. · 3.1.2. Aggregation and Disaggregation . . 3.2. Decision-Making in Hierarchies . . . . . . 3.3. Customer Hierarchies and Hierarchical Sales Organizations . . 3.3.1. Customer Segmentation and Customer Profitability 3.3.2. A Formal Model of Customer Hierarchies. . . . . . . 3.3.3. Hierarchical Sales OrganizatiOIlS . . . . . . . . . . . . 3.3.4. Customer Hierarchies in the Context of the Schneeweiß Framework 3.4. Forecast Misrepresentation in Customer Hierarchies . . . . . . . . . .. . 3.4.1. Sales Forecasting and Agency Problems. . . . . . . . . . . . .. . 3.4.2. Compensation Schemas for Demand-Constrained Supply Chains . 3.4.3. Compensation Schemes for Supply-Constrained Supply Chains. . 3.4.4. Forecast Misrepresentations: Empirical and Experimental Evidence 3.4.5. Application to Customer Hierarchies . . . . . . 3.5. Measures of Heterogeneity in Customer Hierarchies . 3.5.1. Inequality and Heterogeneity Measurement . . 3.5.2. Standard Heterogeneity Measnres . . . . . . . 3.5.3. Generalized Entropy Inequality Measures and Theil's Index. 3.5.4. Comparison of Heterogeneity Measures . . . . . . . . . . . . 4. Allocation Planning and Disaggregation in Customer Hierarchies

4.1. Notation and Formal Model . . . . . . . . . . 4.2. Existing Quantity-Based Allocation Schemes . . . . . . . 4.2.1. Type 1: Based on Demand, Pro Ra.ta . . . . . . . 4.2.2. Type 2: Based on Another Key Figure, Pro Rata 4.2.3. Type 3: Based on Demand, Disproportionally . . 4.2.4. Type 4: Based on Another Key Figure, Disproportionally . 4.2.5. Stochastic or Unknown Supply Quantities 4.3. Baeic Profit-Baaed Allocation Schemes . . . 4.3.1. Optimal Central Allocation (OCA) . 4.3.2. Optimal Decentral Allocation (ODA) 4.3.3. Intuitive Decentral Allocation (!DA) 4.4. A Novel Allocation Scheme for Decentral Planners (ADA) 4.4.1. Basic Idea ofthe New Seheme . . . . . . . . . . . . 4.4.2. Approximation of Thtal Profit in a Subtree . . . . . 4.4.3. Parameterization of the Total Profit Approximation . 4.4.4. Basic Solution Approach . . . . 4.4.5. Alternative Solution Approach. 4.5. Numerical Experiments. . . . . 4.5.1. Simulation Environment . . 4.5.2. Base Case . . . . . . . . . . 4.5.3. Different Levels of Sca.rcity . 4.5.4. Different Hierarchy Sizes .. 4.5.5. Different Levels of Customer Heterogeneity .

109 109 110 112 117 125 125 128 132 134 136 137 141 149 158 162 171 171 176 181 190 195

. . . . . . . . . . . . . . . . . . . . · · ·

196 202 205 205 207 208 209 211 215 215 218 220 220 222 224 227 234 246 246 250 252 252 253

Contents 4.5.6. Different Allocation Schemes at Different Hierarchy Levels 4.5.7. Summary and DiBcuBBion. . . . . . . . . . . . . . . . . . .

xi

. 255 . 261

5. Model Extensions: Forecast Errors and Enhanced Consumption Planning 263 5.1. Forecast Errors . . . . . . . . . . 264 5.1.1. Forecast Error Model. . . . . . 265 5.1.2. Nwnerica.l Experiments. . . . . 268 5.2. Enhanced Quota COIlBumption Rules . 279 5.2.1. Enhanced Consumption Rules in Customer Hierarchies . 281 5.2.2. Nwnerical ExperimentB. . . . . . . . . . . . . . . . . . 288 5.3. Quota Retention aod Virtual Safety Stocks . . . . . . . . . . . . 299 5.3.1. Stock. Retention in Multi-Echelon Inventory Systems . . 300 5.3.2. Virtual Safety Stocks in Multi-Stage Customer Hierarchies . 303 5.3.3. Nwnerica.l Experiments. . . . . . . . . . . . . . . . . . . . . 305 6. Summary and Conclusions

6.1. Summary . . . . . . . . 6.2. Managerial ImplicatioIlB 6.3. Directions for Further Research

315 · 315 · 322 · 324

A. Appendix 329 A.1. The Theil Index at Aggregate Levels in Multi-Stage Customer Hierarchies 329 A.2. The RelationBhip Between Theil's Index and the Lorenz Curve . 331 A.3. Proof of Lemma 6 . . . . . . . . . . . . . 338 A.4. Proofs of Lemmas 9 and 10 . . . . . . . . . . . . . . . . 340 A.4.1. Existence of a Unique Solution . . . . . . . . . . 340 A.4.2. Closed-Form Solution Based on Cramer's Rule . . 343 A.5. Comparative Statics of the ADA-Based Allocation . . 352 Bibliography

355

List of Figures 1.1. 1.2. 1.3. 1.4.

Perspectives on customer heterogeneity in demand fulfillment . Hierarchica.l aggregation in the oll industry case study .. Hierarchica.l disaggregation in the oil industry case study Forecast aggregation and quota. disaggregation in APS

4

6 8 13

2.1. Interrelations between hierarchical planning levels 2.2. Supply chaln planning matrix . . . . . . . . . . . 2.3. Ma.ke-to-stock decoupling point . . . . . . . . . . 2.4. Decoupling points and associated production environments 2.5. Order-driven tasks in the supply chain planning matrix 2.6. Software modules in the 8upply chain planning matrix. . 2.7. Structure of the following sections . . . . . . . . . . . . . 2.8. Forecasting needs per functional area and hierarchy level 2.9. Phases of the dernand planning process 2.10. Ba.sic hierarchiealsales organization . . . . . . . 2.11. Basic hierarchical forecasting methods . . . . . 2.12. Ability to foreca.st at different aggregation levels 2.13. Paths in a demand planning hierarchy . . . . . 2.14. Phases, decision problems and results of the demand fulfillment task . 2.15. Generic demand fulfillment system types . . . . . . . 2.16. Time structure in the batch order promising model . 2.17. Grouping orders to customers to customer segments.

34 37 39 40 40 46 47 51 53 57 64 73 76 82 87 92 93

3.1. Different hierarchy types . . . . . . . . . . . . . . . . . 3.2. Prototypica.l hierarchies in the Schneeweii framework 3.3. Customer hierarchy variantB due to different aggregation structures . 3.4. N aming conventions for customer hierarchies . . . . . . . . . . . . . . 3.5. Ragged hierarchy example: Geography and management levels . . . . 3.6. Analogy between income inequa.lity and customer heterogeneity measures . . 3.7. Income and profitability distribution . . . . . . . . . . . . . . 3.8. Lorenz curve depicting the income inequality in a population . . 3.9. Decomposability of the Gini coefficient: Example hierarchies . . 3.10. Stobachoff curve. . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11. Ca.lculation of the Theil index at the level of aggregate customer segments 3.12. Example hierarchy for heterogeneity measures . . . . . . 4.1. Allocation planning problem in a customer hierarchy . 4.2. Sequence of events in the a.llocation planning problem . 4.3. Allocation in wholesaJ.er-retailer settings . . . . . . . .

112 118 130 131 132 172 174 178 180 182 186 191

· 197 · 198 · 204

xiv

List of Figures 4.4. Profit-based schemes: Example hieraxchy and total profit function 4.5. Number of forecaat reparts per inter-nodallink. . . . . . . . . . . 4.6. Total profit Bt the intermediate nodes of the exa.mple hierarchy. . 4.7. Basic idea of ADA: Approximation of true profit function 7r1e via 7r", 4.8. Example of hiera.rchy with heterogeneous intermediate Dade k 4.9. Example of hierarchy with homogenoous intermediate Dade k . 4.10. Multiplier seaxch algorithm: Example hieraxchy . . . . . . . 4.11. Multiplier seaxch: Same marginal profit at nodes 1 and 2 . . 4.12. Multiplier search: Same marginal profit at nodes 1, 2 and 3 . 4.13. Multiplier sea.rch: Same marginal profit at nodes 1, 2 and 4 . 4.14. Multiplier seaxch: Allocation to Dades 1, 2 and 4 in optimal solution. 4.15. Base case results . . . . . . . . . . 4.16. Different shortage rates - results . . . . . . . . . . 4.17. Different hierarchy sizes - results . . . . . . . . . . 4.18. Different levels of customer heterogeneity - results 4.19. Alternative profit intervals - results . . . . . . . .

. 214

. 216 . 217 . 221

. 234 . 235 . . . . . . . . . .

236 237 239 239 240 251 252 254 254 256

5.1. Example hierarchy: Allocation under ODA and ADA with forecast eITors . 5.2. Results per shortage rate and forecast error setting (3-level hierarchy). . 5.3. Results per shortage rate end Corecast error setting (5-level hier8