Research Reports from the Department of Operations

Authors

Chin-chih Ho

Document Type

Dissertation

Publication Date

1-1-1985

Abstract

A periodic review, stochastic demand, dynamic, combined production inventory and equipment replacement problem is considered. The production system is subject to deterioration and random failure with probability dependent on initial state and quantity produced in a period. The problem is formulated as a discounted Markov decision process with two-dimensional state and action spaces. Assumptions are presented which are sufficient to prove that a simply structured production and replacement policy is optimal in any finite or infinite horizon case. The objective is to minimize the total expected discounted cost. In the finite horizon case, two different types of models, namely, the dynamic stationary model and the dynamic nonstationary model, are considered. A positive lead time with integral constant value is involved in the nonstationary model. The inductive approach is used in this case. In the infinite horizon case, the cost and probability functions are assumed to be stationary. Under the set of sufficient assumptions, the limit function exists and is equal to the infinite horizon optimal cost function so that the infinite horizon optimal policy is likely to have the same structure as the finite horizon optimal policy. The computational aspects of the problem are considered. The method of successive approximations is suggested to find the finite and infinite horizon optimal policy.

Keywords

Operations research, Production control--Mathematical models, Inventory control--Mathematical models, Markov processes, Decision making--Mathematical models, Dynamic programming, Stochastic processes, Finite differences

Publication Title

Dissertation/Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University

Issue

Technical memorandum no. 549 ; Submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy.

Rights

This work is in the public domain and may be freely downloaded for personal or academic use

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