Abstract
This paper is concerned with the optimal production planning in a dynamic stochastic manufacturing system consisting of a single machine that is failure prone and facing a constant demand. The objective is to choose the rate of production over time in order to minimize the 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 that the Hamilton–Jacobi–Bellman equation for the average cost problem has a solution giving rise to the minimal average cost and the so-called potential function. The result helps in establishing a verification theorem. Finally, the optimal control policy is specified in terms of the potential function.
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Sethi, S.P., Suo, W., Taksar, M.I. et al. Optimal Production Planning in a Stochastic Manufacturing System with Long-Run Average Cost. Journal of Optimization Theory and Applications 92, 161–188 (1997). https://doi.org/10.1023/A:1022696215389
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DOI: https://doi.org/10.1023/A:1022696215389