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Full Description
Decision Criteria and Optimal Inventory Processes provides a theoretical and practical introduction to decision criteria and inventory processes. Inventory theory is presented by focusing on the analysis and processes underlying decision criteria. Included are many state-of-the-art criterion models as background material. These models are extended to the authors' newly developed fuzzy criterion models which constitute a general framework for the study of stochastic inventory models with special focus on the real world inventory theoretic reservoir operations problems. The applications of fuzzy criterion dynamic programming models are illustrated by reservoir operations including the integrated network of reservoir operation and the open inventory network problems.
An interesting feature of this book is the special attention it pays to the analysis of some theoretical and applied aspects of fuzzy criteria and dynamic fuzzy criterion models, thus opening up a new way of injecting the much-needed type of non-cost, intuitive, and easy-to-use methods into multi-stage inventory processes. This is accomplished by constructing and optimizing the fuzzy criterion models developed for inventory processes.
Practitioners in operations research, management science, and engineering will find numerous new ideas and strategies for modeling real world multi- stage inventory problems, and researchers and applied mathematicians will find this work a stimulating and useful reference.
Contents
1 Introduction.- 1.1 Inventory Examples.- 1.2 Characteristics of Inventory Problems.- 1.3 Classification of Inventory Problems.- 1.4 Inventory Systems.- 1.5 Determination of Inventory Cost Parameters.- 1.6 Types of Decision Problem Situations.- 1.7 Decision Oriented Processes.- 1.8 Discrete Dynamic Programming (DDP).- 1.9 Stochastic Multistage Decision Processes.- 1.10 Decision Criteria in Inventory Systems.- 1.11 Balance Between Information and Decision.- 1.12 Unimodality and Strong Unimodality.- 2 Economic Criterion Models.- 2.1 Deterministic Inventory Models.- 2.2 Deterministic Inventory Models With Back logging.- 2.3 Stochastic Inventory Models.- 2.4 Critical Number Policy.- 2.5 Convex Ordering Cost.- 2.6 K-convex Functions.- 2.7 (s, S) Inventory Policy.- 2.8 Quantity Discount.- 2.9 Time Lag in Supply.- 3 Multidimensional Economic Criterion Models.- 3.1 Multicommodity Inventory Systems.- 3.2 Multivariable K-convex Functions.- 3.3 (?, S) Inventory Policy.- 3.4 Multilocation Inventory Systems.- 3.5 Decomposition of Multidimensional Problem.- 4 Bayesian Solutions of Economic Criterion Models.- 4.1 Bayesian Updating Process.- 4.2 Inventory Models.- 4.3 Optimal Inventory Policy.- 4.4 Conditions of Dimensional Reduction.- 5 Minimax Solutions of Economic Criterion Models.- 5.1 Game Problem with Economic Criterion.- 5.2 Maximizing Distributions.- 5.3 Minimax Solutions.- 5.4 Discussion.- 6 Probability Criterion Models.- 6.1 Basic Model.- 6.2 Time Lag in Supply.- 6.3 Bounded Emergency Order.- 6.4 Nonstationary Inventory Model.- 6.5 Batch Ordering.- 7 Multistage Game with Probability Criterion.- 7.1 Game Model.- 7.2 Minimizing Distributions.- 7.3 Maximin Solutions.- 8 Fuzzy Criterion Decision Processes.- 8.1 Fuzzy Criterion Sets and Fuzzy Criterion Functions.- 8.2 FuzzyCriterion Models.- 8.3 Basic Theorem.- 8.4 Infinite Horizon Problem.- 8.5 Stability Theorem.- 8.6 Bounded Critical Number Policy.- 8.7 Time Lag in Control.- 8.8 Inventory Control.- 8.9 Reservoir Operations.- 9 Multidimensional Fuzzy Criterion Dynamic Programming.- 9.1 Open Inventory Networks.- 9.2 Multidimensional Fuzzy Criterion Models.- 9.3 Basic Theorem.- 9.4 Existence and Uniqueness Theorem.- 9.5 Stability Theorem.- 9.6 (?, S) Control Policy.- 9.7 Decomposition of the Multidimensional Problem.- 9.8 Multi-Reservoir Joint Operations.- 10 Further Research and Extensions.- 10.1 Constructing Fuzzy Criterion Functions.- 10.2 Adaptive Fuzzy Criterion Models.- 10.3 Fuzzy Criterion Game Models.- 10.4 Some Computational Issues.- 10.5 Additional Applications.- A.l Compact and Convex Sets.- A.2 Continuous and Convex Functions.- A.3 Convergence of Sequence.- A.4 Borel Functions and Optimization.
