Optimal Production Planning in a Stochastic Manufacturing System with Long-Run Average Cost
Journql of Optimization Theory and Applications, Vol. 92, No. 1, pp. 161-188, January 1997
28 Pages Posted: 21 Jun 2009 Last revised: 31 Jan 2019
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.
Keywords: Production planning, stochastic dynamic programming, vanishing discount approach, optimal control, long-run average cost
JEL Classification: M11, C61
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