Download or read book Optimal Production Planning in a Stochastic Manufacturing System with Long-Run Average Cost written by Suresh Sethi and published by . This book was released on 2019 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.