Optimal Production Planning in a Multi-Product StochasticManufacturing System with Long-Run Average Cost

Authors:
S. P. Sethi;W. Suo;M. I. Taksar;H. Yan
Affiliations:
School of Managment, The University of Texas at Dallas, Richardson, Texas;Faculty of Management, University of Toronto, Toronto, Ontario;Department of Applied Mathematics, SUNY at Stony Brook, Stony Brook, New York;Department of System Engineering and Engineering Managment, The Chinese University of Hong Kong, Shatin, Hong Kong
Venue:
Discrete Event Dynamic Systems
Year:
1998

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Abstract

This paper is concerned with the problem of productionplanning in a flexible manufacturing system consisting of a singleor parallel failure-prone machines producing a number of differentproducts. The objective is to choose the rates of productionof the various products over time in order to meet their demandsat the minimum long-run average cost of production and surplus.The analysis proceeds with a study of the corresponding problemwith a discounted cost. It is shown using the vanishing discountapproach for the average cost problem that the Hamilton-Jacobi-Bellmanequation in terms of directional derivatives has a solution consistingof the minimal average cost and the so-called potential function.The result helps in establishing a verification theorem, andin specifying an optimal control policy in terms of the potentialfunction. The results settle a hitherto open problem as wellas generalize known results.