Research Reports from the Department of Operations

Authors

Bruce A. Powell

Document Type

Dissertation

Publication Date

11-1-1967

Abstract

A priority problem exists whenever a system differentiates between distinct classes of customers. Some dynamic, stochastic, periodic review inventory models are developed and analyzed under the assumption that a single customer will accept delivery of an order only if the order can be filled from on-hand inventory. Optimal policies are studied, and conditions under which the form of the optimal dynamic policy is a nondecreasing sequence of single critical numbers are presented. An extensive set of numerical examples suggest that the major factor in determining the form of the optimal policy is the function ~~(~) where ~ is the demand variable and ~(~) is the probability that the demand in the period is equal to ~. Then, inventory models are considered in which demands consist of an ordinary class of customers and N > 1 all-or-none customers. Finally, a queuing-inventory model is developed which assumes that demands arrive according to a Poisson process with a state-dependent intensity. This model applies when a transaction reporting inventory system is desirable. The cutoff priority discipline is used to analyze the system with respect to the relevant decision variables.

Keywords

Operations research, Inventory control--Mathematical models, Queuing theory, Dynamic programming, Demand (Economic theory)--Mathematical models, Poisson processes, Decision making--Mathematical models

Publication Title

Dissertation, Department of Operations, School of Management, Case Western Reserve University

Issue

Technical memorandum no. 90 ; 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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