ebook ebooks e-book e-books downloaden bei MyEbooks.ch downloaden

Inventory Rationing A New Modeling Approach Using Markov Chain Theory

:	Karin Möllering
:	Inventory Rationing A New Modeling Approach Using Markov Chain Theory
:	Springer Gabler
:	9783658242558
:	1
:	CHF 38.00
:

:	Allgemeines, Lexika
:	English

:	188
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

The last decades have seen an increasing diversity of customer expectations and growing competitive pressure for a wide variety of industries. Customer segmentation and subsequent inventory rationing provide a way to cope with those customer demands while maintaining a competitive offer. The general idea resembles the yield management practised in the airline or hotel industries: Demand fulfilment for low priority customers might be refused or delayed in order to reserve stock for more important clients.

div>This dissertation thesis from Karin Möllering provides a comprehensive introduction to inventory rationing. It gives an overview of the different approaches studied and identifies state-of-the-art rules. In a second step, the book particularly focuses on an easy-to-implement but highly efficient rationing strategy. For this strategy, a mathematical model is developed that allows for optimization under different objectives.

Potential readership includes scholars of inventory control and management science, students interested in these areas as well as practitioners involved in formulating and implementing rationing strategies.

Karin Möllering published her work with Kölner Wissenschaftsverlag until 2018.

	Contents	8
	List of Tables	14
	List of Figures	16
	List of Abbreviations	18
	List of Symbols	20
	1 Introduction	23
	1.1 Motivation	24
	1.2 Research Objectives	25
	1.3 Outline	26
	Part I Foundations of Stochastic Inventory Control	29
	2 Basic Concepts of Inventory Management	30
	2.1 Inventory Management and Control	31
	2.2 Motivations for Holding Inventory	32
	2.3 Classification of Inventories	34
	2.3.1 The Strategic Perspective	34
	2.3.2 The Operational Perspective	35
	2.4 Inventory-related Costs	37
	2.4.1 Order Cost	37
	2.4.2 Holding Cost	38
	2.4.3 Penalty Cost	39
	2.5 Service Level	40
	3 Stochastic Inventory Control	42
	3.1 Characteristics of Inventory Models	43
	3.1.1 Management Decisions	43
	3.1.2 System-Inherent Characteristics	44
	3.2 Types of Inventory Control Policies	46
	3.3 Periodic Inventory Control	48
	3.3.1 Single-Period Inventory Control	49
	3.3.2 Multi-Period Inventory Control	50
	3.3.3 Service-Constraint Multi-Period Inventory Control	53
	Part II Essential Stochastic Processes	54
	4 Markov Chains	55
	4.1 The Markov Property	56
	4.2 Homogeneous Markov Chains	57
	4.3 Limit Distribution and Invariant Distribution	58
	4.4 Communication Classes	60
	4.5 Class Properties	61
	4.5.1 Aperiodicity	61
	4.5.2 Recurrency and Transiency	61
	4.5.3 Class Criteria	63
	4.6 Uniqueness of Limit Distributions	64
	4.7 Multi-Dimensional Markov Chains	65
	4.8 Applications of Markov Chains	66
	5 Numerical Solution of Infinite Markov Chains	67
	5.1 System Reduction Approaches	68
	5.1.1 Reduced System Approaches	68
	5.1.2 Geometric Tail Distributions	69
	5.2 State Space Reduction Approaches	70
	5.2.1 Augmentations	70
	5.2.2 Pointwise Convergence	72
	5.3 Algorithms	74
	5.3.1 Sheskin’s Partitioning Algorithm	74
	5.3.2 Power Iteration	76
	5.4 Criteria for Choosing a Specific Algorithm	76
	6 Comparing Stochastic Processes	78
	6.1 Stochastic Ordering for Distribution Functions	78
	6.2 The Sample Path Method	80
	Part III Stochastic Inventory Control with Customer Segmentation	82
	7 Introduction to Inventory Rationing	83
	7.1 Examples for Different Customer Classes	84
	7.2 Related Areas	85
	7.3 Rationing Rules	87
	7.4 Backorders and Backorder Clearing Mechanisms	89
	7.5 Literature Review	91
	7.5.1 Characterizations of the Optimal Policy	91
	7.5.2 Evaluations and Optimizations of Critical Level Policies	94
	7.5.3 Other Studies Involving Critical Level Rationing	98
	7.6 Classification of Our Work	99
	8 A Markov-Chain Based Modeling Approach	101
	8.1 Modeling Framework	102
	8.2 Recursive Expressions for Backorders	102
	8.3 Markov Chain	104
	8.4 Structural Results	105
	8.5 Proofs	108
	9 Prioritization by Penalty Costs	115
	9.1 Optimization Approach	116
	9.1.1 Convexity of Objective Function	116
	9.1.2 Transition Matrix	118
	9.1.3 Cost Function	119
	9.1.4 Numerical Optimization Algorithm	120
	9.2 Numerical Results	120
	9.2.1 Critical Level Policy versus Benchmark Policies	121
	9.2.2 Combination Heuristic	124
	9.3 Conclusion	124
	9.4 Proofs	126
	10 Prioritization by Service Levels	129
	10.1 Analytical Insights	130
	10.1.1 Service Level Constraints	130
	10.1.2 Potentially Optimal Parameter Constellations	133
	10.1.3 Structural Results for the Optimal Solution	135
	10.1.4 Cost Function	137
	10.1.5 Model Alteration: ?-Service Levels	138
	10.2 Numerical Results	139
	10.2.1 Optimization Algorithm	140
	10.2.2 Critical Level Policy versus Benchmark Policies	141
	10.2.3 Heuristic Approach	144
	10.3 Conclusion	145
	10.4 Proofs	147
	11 Dynamic Rationing Policies	153
	11.1 The Next Period Optimization Policy	154
	11.1.1 The Policy	154
	11.1.2 Structural results	155
	11.2 The Linear Critical Level Policy	156
	11.2.1 The Policy	156
	11.2.2 Structural results	157
	11.3 Efficiency of the Dynamic Rationing Policies	160
	11.3.1 Next Period Optimization and Constant Rationing Policy	161
	11.3.2 Linear Critical Level Policy and Constant Rationing Policy	165
	11.3.3 Next Period Optimization and Linear Critical Level Policy	168
	11.4 Conclusion	170
	11.5 Proofs	171
	12 Conclusion and Critical Review	174
	12.1 Contributions	174
	12.2 Critical Review	176
	12.3 Future Research	177
	Bibliography	179