Lecture Notes in Economics and Mathematical Systems For Information abQut Vols. 1-128, please contact your bookseller or Spnnger-Verlag Vol 129 H·J Luthi, Komplementarltats-und F,xpunktalgorlthmen In Vol 157 Optlmlzalion and Operations Research Proceedings 1977 der mathematlschen Programmlerung Spleltheorle und Okonomle Edited by R Henn, B Korte, and W Oettli VI, 270 pages 1978 VII. 145 Selten 1976 Vol 158 L J Cherene, Set Valued Dynamical Systems and Economic Vol 130 Multiple Criteria DecIsion Making. Jouy·en-Josas. France Flow VIII, 83 pages 1978 Proceedings 1975 Edited by H Thlrlez and S Z,onts VI. 409 pages Vol 159 Some Aspects of the Foundations of General EqUilibrium 1976 Theory The Posthumous Papers of Peter J Kalman Edited by J Green Vol 131 Mathematical Systems Theory Proceedings 1975 Edited VI, 167 pages 1978 by G Marcheslnl and S K Mltter X, 408 pages 1976 Vol 160 Integer Programmmg and Related Areas. A ClaSSified Vol 132 U H Funke. Mathematical Models In Marketing A Collec Bibliography Edited by D Hausmann XIV, 314 pages 1978 tion of Abstracts Xx, 514 pages 1976 Vol 161 M J Beckmann, Rank m Organizations VIII, 164 pages 1978 Vol. 133 Warsaw Fall Seminars In Mathematical Economics 1975 Edited by M W Los, J Los. and A Wieczorek V 159 pages 1976 Vol 162 Recent Developments m Variable Structure Systems, Eco nomiCS and Biology Proceedmgs 1977 Edited by R R Mohler and Vol 134 Computing Methods In Applied SCiences and Engineering A Rubertl VI, 326 pages 1978 Proceedings 1975 VIII. 390 pages 1976 Vol 135 H Haga. A DiseqUilibrium - EqUilibrium Model with Money Vol 163 G Fandel, Optlmale Entscheldungen In Organlsatlonen and Bonds A KeyneSian - Walraslan SynthesIs VI, 119 pages 1976 VI, 143 SMen 1979 Vol 136 E Kofler und G Menges, Entscheldungen bel unvollstandlger Vol 164 C L Hwang and A S M Masud, Multiple Objective De Information XII, 357 Selten 1976 CISion Makmg - Methods and Applications A State-of-the-Art Survey Vol 137 R Wets, Grundlagen Konvexer Optlmlerung VI, 146 Selten XII, 351 pages 1979 1976 Vol 165 A Maravall, Identification m DynamiC Shock-Error Models Vol 138 K Okuguchl, Expectations and Stability In Oligopoly Models VIII, 158 pages 1979 VI, 103 pages 1976 Vol 166 R Cunmghame-Green, Mmlmax Algebra XI, 258 pages Vol 139 Production Theory and Its Applications Proceedings Edited 1979 by H Albach and G Bergendahl VIII. 193 pages 1977 Vol 167 M Faber, Introduction to Modern Austrian Capital Theory Vol 140 W Eichhorn and J Voeller. Theory of the Price Index X, 196 pages 1979 Flsher's Test Approach and Generalizations VII. 95 pages 1976 Vol 168 Convex AnalYSIS and Mathematical Economics Proceedings Vol 141 Mathematical Economics and Game Theory Essays In Honor 1978 Edited by J Krlens V, 136 pages 1979 of Oskar Morgenstern Edited by R Henn and 0 Moeschlin XIV. 703 pages 1977 Vol 169 A Rapoport et ai, Coalition Formation by Sophisticated Players VII, 170 pages 1979 Vol 142 J S. Lane, On Optimal Populalion Paths V, 123 pages 1977 Vol 143 B Naslund, An AnalYSIS of Economic Size Distributions Vol 170 A E Roth, Axiomatic Models of Bargalnmg V, 121 pages XV, 100 pages 1977 1979 Vol 144 Convex AnalySIS and Its Applications Proceedings 1976 Vol 171 G F Newell, ApprOXimate BehaVior of Tandem Queues XI, Edited by A Auslender VI, 219 pages 1977 410 pages 1979 Vol 145 J Rosenmuller, Extreme Games and Their Solulions IV, Vol 172 K Neumann and U Stemhardt, GERT Networks and the 126 pages 1977 Time-Oriented Evaluation of Projects 268 pages 1979 Vol 146 In Search of Economic Indicators Edited by W H Strlgel Vol 173 S Erlander, Optimal Spatial Interaction and the Gravity XVI, 198 pages 1977 Model VII, 107 pages 1980 Vol 147 Resource Allocation and D,v,s,on of Space Proceedings Vol 174 Extremal Methods and Systems AnalYSIS Edited by A V Edited by T FUJII and R Sato VIII, 184 pages 1977 Fiacco and K 0 Kortanek XI, 545 pages 1980 Vol 148 C E Mandl, S,mulatlonstechnlk und Simulatlonsmodelle Vol 175 S K Srinivasan and R Subramanian, Probabilistic AnalysIs ,n den Sozlal-und Wlrtschaftswlssenschaften IX, 173 Selten 1977 of Redundant Systems VII, 356 pages 1980 Vol 149 Statlonare und schrumpfende Bevolkerungen Demogra· Vol 176 R Fare, Laws of Diminishing Returns VIII, 97 pages 1980 phlsches Null-und NegatlVwachstum In Osterrelch Herausgegeben von G Felchtlnger VI, 262 Selten 1977 Vol 177 Multiple Criteria DeCISion Making-Theory and Application Proceedlngs,1979 Edited by G Fandel and T Gal XVI, 570 pages Vol 150 Bauer et ai, Supercrltlcal Wing Sections III VI, 179 pages 1980 1977 Vol 178 M N Bhattacharyya, Comparison of Box-JenkinS and Bonn Vol 151 C A SchneewelB, Inventory-Production Theory VI, 116 pages Monetary Model Prediction Performance VII, 146 pages 1980 1977 Vol 152 Kirsch et ai, Notwendlge Optlmalitatsbedmgungen und Vol 179 Recent Results In StochastiC Programming Proceedings, Ihre Anwendung VI. 157 Selten 1978 1979 Edited by P Kall and A Prekopa IX, 237 pages 1980 Vol 153 Kombmatorlsche Entscheldungsprobleme Methoden und Vol 180 J F Brotchle, J ltv Dickey and R Sharpe, TOPAZ - General Anwendungen Herausgegeben von T M Liebling und M Rossler Plannmg Technique and Its Applications at the Regional, Urban, VIII, 206 Selten 1978 and FaCility Plannmg Levels VII, 356 pages 1980 Vol 154 Problems and Instruments of BUSiness Cycle AnalYSIS Vol 181 H D Sherali and C M Shetty, Optimization With Dlslunctlve Proceedmgs 1977 Edited by W H Strlgel VI, 442 pages 1978 Constramts VIII, 156 pages 1980 Vol 155 Mulliple Criteria Problem SolVing Proceedmgs 1977 Edited Vol 182 J Wolters, StochastiC Dynamic Properties of Lmear Eco by S Zionts VIII, 567 pages 1978 nometric Models VIII, 154 pages 1980 Vol 156 B Naslund and B Sellstedt, Neo-Rlcardlan Theory With Vol 183 K SChlttkowskl, Nonlmear Programming Codes VIII, 242 Applications to Some Current Economic Problems VI, 165 pages pages 1980 1978 continuation on page 189 Lectu re Notes in Economics and Mathematical Systems Managing Editors: M. Beckmann and W. Krelle 289 Bert R. Meijboom Planning in Decentralized Firms A Contribution to the Theory on Multilevel Decisions Springer-Verlag Berlin Heidelberg GmbH Editorial Board H.Albach M. Beckmann (Managing Editor) P.Ohrymes G. Fandei J. Green W. Hildenbrand W. Krelle (Managing Editor) H.P.Künzi K.Ritter R.Sato U.Schittko P.Schönfeld R.Selten Managing Editors Prof. Or. M. Beckmann Brown U nlverslty Providence, RI 02912, USA Prof. Dr. W. Krelle Institut für Gesellschafts- und Wirtschaftswissenschaften der Universität Bonn Adenauerallee 24-42, 0-5300 Bonn, FRG Author Or. Bert R. Meijboom AKB, Consultants for Management Science and Software Oevelopment P.O.Box 20720, NL-3014 DA Rotterdam, The Netherlands ISBN 978-3-540-17795-1 ISBN 978-3-642-48902-0 (eBook) DOI 10.1007/978-3-642-48902-0 Thl8 work 18 8ubJect to cOPYright. All nghts are reserved, whether the whole or part of the matenal 18 concerned, 8peclflcally the rlghts of translation, repnntlng, re-use of Illustrations, recltatlon, broadcastlng, reproductlon on mlcrofllms or In other ways, and storage In data banks. Duphcatlon of th,s pubhcatlon or parts thereof IS only permitted under the provIsions of the German COPYright Law of September 9, 1965, In ItS version of June 24, 1985, and a copynght fee must always be pald. Vlolatlons fall under the prosecutlon act of the German COPYright Law © Spnnger-Verlag Berhn Heldelberg 1987 Ursprünglich erschienin bei Springer-Verlag Berhn Heidelberg 1987 2142/3140-543210 aan Pap, Mam en Hedy aan Jacqueline PrefaCe The completion of this thesis gives me feelings of satisfaction and thankfulness. Satisfaction because its results appear to be worthwile and relevant, and thankfulness towards so many persons who contributed to the progress of the work. The project "Analysis of multilevel decisions" was granted by the common research pool of Tilburg University and Eindhoven University of Techno logy (Samenwerkingsorgaan Brabantse Universiteiten). During the 4-year lead time, the Department of Econometrics of Tilburg University provided not only a single room but also a pleasant and inspiring environment, for which I am very grateful. The research itself, particularly the inevitable scientific struggles, was perfectly coached by my promotors, Prof. Dr. P.A. Verheyen and Prof. Dr. J.F. Benders. I cannot give even the slightest description of the unique way in which they managed to do this. In all criticism they succeeded to maintain a positive, and thus stimulating, working atmosphere. The work also benefited from the suggestions gi ven by Prof. Dr. Th.M.A. Bemelmans, Prof. Dr. J.P.C. Kleijnen, Prof. Dr. P.H.M. Ruys and Prof. Dr. A. Schrijver. Furthermore I am indebted to Dr. Adam Wofniak (Warsaw University of Technology), who made me participate in his multi level experience and critically commented on an earlier draft of the thesis. Through the years I enjoyed the support of several internal services of Tilburg University. Especially I wish to mention the typing staff of the Faculty of Economics. Mrs. Petra Ligtenberg typed the present text in a most efficient way keeping cool under the author's ever increasing ner vous behaviour. Mr. Jan Pijnenburg assisted in completing the tables and figures, and Mr. Frans Buskens made the design for the front cover. Mrs. Hildegard Penn substantially improved the English text. VI Finally I wish to thank all colleagues, friends and relatives for en couragement, enthusiasm and, last but not least, friendship. January 1987 Bert Meijboom -Contents Preface v CHAPTER ONE INTRODUCTION 1.1. Problem statement 1.2. Outline of the book 4 1.3. Relevant economic literature 6 1.4. The multilevel approach 7 CHAPTER TWO 9 THE MODEL OF THE FIRM: MULTIPLE TECHNIQUES AND MAKE-OR-BUY DECISIONS 2.1. Introduction 9 2.2. The firm in input-output terminology 9 2.3. Multiple techniques for market products 13 2.4. Make-or-buy decisions for technical services 18 2.5. Summary 22 CHAPTER THREE 23 THE MODEL OF THE FIRM: COST ALLOCATIONS AND ORGANIZATIONAL STRUCTURE 3.1. Introduction 23 3.2. Cost allocation problems 24 3.3. Three illustrative examples 25 3.3.1. The Louderback-Moriarity approach 25 3.3.2. The reCiprocal allocation method 27 3.3.3. Fixed cost allocation via mathematical programming 29 3.4. Cost allocation and multilevel decisions 30 3.4.1. Motives for the analysis of allocation problems 30 3.4.2. Cost allocation in a decentralized organizational structure 32 3.5. The overall model 33 3.6. Summary 38 VIII CHAPTER FOUR 39 DECOMPOSITION BASED PLANNING: PRICE AND RESOURCE DIRECTIVE COORDINATION 4.1. Introduction 39 4.2. The planning problem 40 4.3. Price-directive planning according to the Dantzig-Wolfe decomposition method 43 4.4. Resource-directive planning according to Benders' decompo sition method 46 4.5. Discussion 49 4.6. Summary 53 CHAPTER FIVE 55 DECOMPOSITION BASED PLANNING: MIXED PRICE-RESOURCE DIRECTIVE APPROACHES 5.1. Introduction 55 5.2. Division-oriented mixed decomposition 56 5.3. Resource-oriented mixed decomposition 60 5.3.1. Development of the algorithm 61 5.3.2. Generation of globally feasible solutions 67 5.3.3. Economic interpretation 68 5.4. Summary 72 CHAPTER SIX 75 OVERALL ANALYSIS OF THE MODEL OF THE FIRM 6.1. Introduction 75 6.2. Properties of overall solutions 77 6.2.1. The case with common resources in excess supply 77 6.2.2. The case with common resources in limited supply 79 6.3. Numerical example 81 6.4. Establishment of the overall production plan 85 6.5. Incorporation of cost allocation mechanisms 86 6.5.1. The allocation of internal-TS costs 87 IX 6.5.2. Common cost allocation 88 6.6. Summary 90 CHAPTER SEVEN 91 MULTILEVEL ANALYSIS OF THE MODEL OF THE FIRM 7.1. Introduction 91 7.2. The multilevel approach for decentralized firms 91 7.3. Proposal for a two-level planning procedure 95 7.3.1. Outline of the planning procedure 96 7.3.2. Intermediate divisional activity plans 97 7.3.3. The information contents of exchanged data 101 7.3.4. Numerical example 104 7.4. Cost allocations during the planning process 108 7.4.1. Allocation of internal-TS costs 109 7.4.2. Common cost allocation 111 7.5. Summary 114 CHAPTER EIGHT 115 REVIEW AND EVALUATION 8.1. Review of the text 115 8.2. Evaluation of the results 116 APPENDIX A: appendix to CHAPTER TWO. 121 APPENDIX B: appendix to CHAPTER THREE. 129 APPENDIX C: appendix to CHAPTER FOUR. 131 C.1. Derivation of the price-directive planning procedure according to Dantzig-Wolfe 131 C.2. Derivation of the resource-directive planning procedure according to Benders 134 x APPENDIX D: appendix to CHAPTER FIVE. 139 D.1. Proof of Theorem 5.1 139 D.2. Further relaxation of problem (5.20) 140 D.3. A convergence proof for the algorithm as presented in section 5.3.1 141 APPENDIX E: appendix to CHAPTER SIX. 143 APPENDIX F: appendix to CHAPTER SEVEN. 149 LIST OF SYMBOLS 153 REFERENCES 163