Decision Criteria and Optimal Inventory Processes

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.