Markovian demand inventory models:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2010
|
| Schriftenreihe: | International series in operations research & management science
108 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XX, 253 S. graph. Darst. |
| ISBN: | 0387716033 9780387716039 |
Internformat
MARC
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| 650 | 4 | |a Inventories | |
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Datensatz im Suchindex
| _version_ | 1804140780648923136 |
|---|---|
| adam_text | Titel: Markovian demand inventory models
Autor: Beyer, Dirk
Jahr: 2010
Table of Contents
List of Figures ix
List of Tables xi
Preface xiii
Notation xvii
Part I INTRODUCTION
1. INTRODUCTION 3
1.1 Characteristics of Inventory Systems 3
1.2 Brief Historical Overview of Inventory Theory 5
1.3 Examples of Markovian Demand Models 12
1.4 Contributions 15
1.5 Plan of the Book 16
Part II DISCOUNTED COST MODELS
2. DISCOUNTED COST MODELS WITH BACKORDERS 21
2.1 Introduction 21
2.2 Review of the Related Literature 22
2.3 Formulation of the Model 23
2.4 Dynamic Programming and Optimal Feedback Policy 26
2.5 Optimality of (s, 5)-type Ordering Policies 31
2.G Nonstationary Infinite Horizon Problem 33
2.7 Cyclic Demand Model 37
2.8 Constrained Models 37
2.9 Concluding Remarks and Notes 39
vi Table of Contents
3. DISCOUNT COST MODELS WITH POLYNOMIALLY
GROWING SURPLUS COST 41
3.1 Introduction 41
3.2 Formulation of the Model 42
3.3 Dynamic Programming and Optimal Feedback Policy 44
3.4 Nonstationary Discounted Infinite Horizon Problem 49
3.5 Optimality of (s, 5)-type Ordering Policies 55
3.6 Stationary Infinite Horizon Problem 57
3.7 Concluding Remarks and Notes 57
4. DISCOUNTED COST MODELS WITH LOST SALES 59
4.1 Introduction 59
4.2 Formulation of the Model 60
4.3 Optimality of (s, S)-type Ordering Policies 63
4.4 Extensions 66
4.5 Numerical Results 69
4.6 Concluding Remarks and Notes 72
Part III AVERAGE COST MODELS
5. AVERAGE COST MODELS WITH BACKORDERS 83
5.1 Introduction 83
5.2 Formulation of the Model 86
5.3 Discounted Cost Model Results from Chapter 2 89
5.4 Limiting Behavior as the Discount Factor Approaches 1 90
5.5 Vanishing Discount Approach 98
5.6 Verification Theorem 102
5.7 Concluding Remarks and Notes 106
6. AVERAGE COST MODELS WITH POLYNOMIALLY
GROWING SURPLUS COST 107
6.1 Formulation of the Problem 107
6.2 Behavior of the Discounted Cost Model with Respect
to the Discount Factor 109
6.3 Vanishing Discount Approach 116
6.4 Verification Theorem 125
6.5 Concluding Remarks and Notes 130
MARKOVIAN DEMAND INVENTORY MODELS
vn
7. AVERAGE COST MODELS WITH LOST SALES 133
7.1 Introduction 133
7.2 Formulation of the Model 133
7.3 Discounted Cost Model Results from Chapter 4 137
7.4 Limiting Behavior as the Discount Factor Approaches 1 138
7.5 Vanishing Discount Approach 142
7.6 Verification Theorem 145
7.7 Concluding Remarks and Notes 150
Part IV MISCELLANEOUS
8. MODELS WITH DEMAND INFLUENCED
BY PROMOTION 153
8.1 Introduction 153
8.2 Formulation of the Model 155
8.3 Assumptions and Preliminaries 162
8.4 Structural Results 164
8.5 Extensions 170
8.6 Numerical Results 173
8.7 Concluding Remarks and Notes 174
9. VANISHING DISCOUNT APPROACH VS. STATIONARY
DISTRIBUTION APPROACH 179
9.1 Introduction 179
9.2 Statement of the Problem 182
9.3 Review of Iglehart (1963b) 184
9.4 An Example 187
9.5 Asymptotic Bounds on the Optimal Cost Function 192
9.6 Review of the Veinott and Wagner Paper 195
9.7 Existence of Minimizing Values of s and S 197
9.8 Stationary Distribution Approach versus Dynamic
Programming and Vanishing Discount Approach 203
9.9 Concluding Remarks and Notes 206
viii Table of Contents
Part V CONCLUSIONS AND OPEN RESEARCH
PROBLEMS
10. CONCLUSIONS AND OPEN RESEARCH PROBLEMS 211
Part VI APPENDICES
A. ANALYSIS 217
A.I Continuous Functions on Metric Spaces 217
A.2 Convergence of a Sequence of Functions 219
A.3 The Arzela-Ascoli Theorems 220
A.4 Linear Operators 222
A.5 Miscellany 223
B. PROBABILITY 225
B.I Integrability 225
B.2 Conditional Expectation 226
B.3 Renewal Theorem 227
B.4 Renewal Reward Processes 227
B.5 Stochastic Dominance 228
B.6 Markov Chains 229
C. CONVEX, QUASI-CONVEX AND X-CONVEX
FUNCTIONS 233
C.I PF2 Density and Quasi-convex Functions 233
C.2 Convex and K-convex Functions 234
References 241
Copyright Permissions 247
Author Index 249
Subject Index 251
List of Figures
1.1 Relationships between different chapters. 18
2.1 Temporal conventions used for the discrete-time
inventory problem. 25
4.1 Results for Case 1.1. 73
4.2 Results for Case 1.2. 74
4.3 Results for Case 1.3. 75
4.4 Results for Case 1.4. 76
4.5 Results for Case 2.1. 77
4.6 Results for Case 2.2. 78
4.7 Results for Case 2.3. 79
4.8 Results for Case 2.4. 80
8.1 Numerical results for Case 3.1. 175
8.2 Numerical results for Case 3.2. 176
8.3 Numerical results for Case 3.3. 177
8.4 Numerical results for Case 3.4. 178
9.1 Definitions of Sl and 5 . 197
List of Tables
4.1 Numerical results for the lost sales model with uni-
form demand distribution. 71
4.2 Numerical results for the lost sales model with trun-
cated normal demand distribution. 71
8.1 Numerical results for the MDP model with uniform
demand distribution. 172
8.2 Numerical results for the MDP model with trun-
cated normal demand distribution. 173
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| id | DE-604.BV035822870 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:05:25Z |
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| isbn | 0387716033 9780387716039 |
| language | English |
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| series | International series in operations research & management science |
| series2 | International series in operations research & management science |
| spelling | Markovian demand inventory models Dirk Beyer ... New York, NY Springer 2010 XX, 253 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series in operations research & management science 108 Mathematisches Modell Inventories Inventory control Mathematical models Markov processes Beyer, Dirk 1972- Sonstige (DE-588)124429041 oth Erscheint auch als Online-Ausgabe 978-0-387-71604-6 International series in operations research & management science 108 (DE-604)BV011630976 108 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018681588&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Markovian demand inventory models International series in operations research & management science Mathematisches Modell Inventories Inventory control Mathematical models Markov processes |
| title | Markovian demand inventory models |
| title_auth | Markovian demand inventory models |
| title_exact_search | Markovian demand inventory models |
| title_full | Markovian demand inventory models Dirk Beyer ... |
| title_fullStr | Markovian demand inventory models Dirk Beyer ... |
| title_full_unstemmed | Markovian demand inventory models Dirk Beyer ... |
| title_short | Markovian demand inventory models |
| title_sort | markovian demand inventory models |
| topic | Mathematisches Modell Inventories Inventory control Mathematical models Markov processes |
| topic_facet | Mathematisches Modell Inventories Inventory control Mathematical models Markov processes |
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