Feedback Production Planning in a Stochastic Two-Machine Flowshop: Asymptotic Analysis and Computational Results

Abstract

This paper presents an asymptotic analysis of hierarchical production planning in a manufacturing system with two tandem machines that are subject to breakdown and repair. Since the number of parts in the buffer between the two machines needs to be non-negative, the problem is inherently a state constrained problem. As the rate of machines breakdown and repair approaches infinity, the analysis results in a limiting problem in which the stochastic machine capacity is replaced by the equilibrium mean capacity. The value function for the original problem is proved to converge to the value function of the limiting problem. This suggests a heuristic to construct a feedback control for the original stochastic problem from the feedback control of the limiting deterministic problem. Computational results are presented to illustrate our heuristic.

Keywords: aymptotic analysis, stochastic machine, state constrained problem

JEL Classification: C61, M11, M20