Minimum Average-Cost Froduction Plan in a Multi-Product Stochastic Manufacturing System
Proceedings of the 1996 IEEE Conference on Emerging Technologies and Factory Automation, Kauai,HI, November 18-21, 1996, 361-365
Posted: 6 May 2020
Date Written: 1996
Abstract
This paper is concerned with the problem of production planning in a flexible manufacturing system consisting of a single or parallel failure-prone machines producing a number of different products. The objective is to choose the rates of production of the various products over time in order to meet their demands at the minimum long-run average cost of production and surplus. It is shown using the vanishing discount approach for the average cost problem that the Hamilton-Jacobi-Bellmlan equation in terms of directional derivatives has a solution consisting of the minimal average cost and the so-called potential function. The result helps in establishing a verification theorem, and in specifying an optimal control policy in terms of the potential function. The results settle a hitherto open problem as well as generalize known results.
Keywords: Production planning, stochastic dynamic programming, vanishing discount approach, optimal control, long-run average cost
JEL Classification: C61, M11, M20
Suggested Citation: Suggested Citation
