Table Of ContentLecture Notes in Economics and Mathematical Systems
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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)
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Managing Editors
Prof. Or. M. Beckmann
Brown U nlverslty
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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
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ISBN 978-3-540-17795-1 ISBN 978-3-642-48902-0 (eBook)
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© 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
