Hierarchical Production Planning in a Stochastic Manufacturing System with Long-Run Average Cost: Asymptotic Optimality and Error Bounds

Abstract

This paper deals with an asymptotic analysis of hierarchical production planning in stochastic manufacturing systems consisting of a single or parallel failure-prone machines producing a number of different products without attrition. The objective is to choose production rates over time in order to minimize the long-run average expected cost of production and surplus. As the rate of machine break-down and repair approaches infinity, the analysis results in a limiting problem in which the stochatic machine capacity is replaced by the equilibrium mean capacity. The optimal value for the original problem is proved to converge to the optimal value of the limiting problem. This suggests a heuristic to construct an open-loop control for the original stochastic problem from the open-loop control of the limiting deterministic problem. We as well as obtain error bound estimates for constructed open-loop controls.

Keywords: Stochastic manufacturing system, hierarchical control, dynamic programming, viscosity solution, convergence rate, error bound, ergodic problem, long-run average cost

JEL Classification: M11, C61