Doctoral Dissertations

John Roy Gray

Date of Award

5-1999

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Management Science

Major Professor

M. M. Srinivasan

Committee Members

M. R. Bowers, K. C. Gilbert, R. S. Sawhney

Abstract

Since the introduction of the classical economic manufacturing quantities (EMQ) concept early in the twentieth century, many variants of the single-product EMQ model have been solved. These single-product EMQ models usually suppose the product is produced cyclically every T time units. This dissertation examines the general cyclical model (GCM), a generalization of the single-product EMQ. In the GCM n≥2 products are produced on a single facility according to cyclical schedules. The GCM, unlike some variants of the multiproducts, single-facility problem, permits each product i to be produced every Ti time units where it is not necessary that Ti = Tj if i ≠ j. However, a schedule of n products must be feasible; that is, only one product may occupy the facility at a time. Thus, the objective of the GCM is to find cycle times {Ti} that minimize the inventory and production costs subject to the restriction that the schedule is feasible. To mathematically address this feasibility problem, delay times {di} are introduced where di is the time at which the first use period of product i begins. Then conditions are given that are both necessary and sufficient to assure that a specified schedule {Ti, di} of n products is feasible. These feasibility conditions remove a major handicap suffered by previous researcher. Then delay-independent necessary and sufficient feasibility conditions are derived for the two-products and the three-products case of the GCM. Also, delay-independent necessary feasibility conditions are derived for the four-products case. Finally, an efficient algorithm is developed that finds feasible optimal schedules for the n-products model.

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