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. The analysis proceeds with a study of the corresponding problem with a discounted cost. It is shown using the vanishing discount approach for the average cost problem that the Hamilton-Jacobi-Bellman 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.
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Sethi, S., Suo, W., Taksar, M. et al. Optimal Production Planning in a Multi-Product Stochastic Manufacturing System with Long-Run Average Cost. Discrete Event Dynamic Systems 8, 37–54 (1998). https://doi.org/10.1023/A:1008256409920
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DOI: https://doi.org/10.1023/A:1008256409920