Singular Perturbations in Manufacturing

Abstract

An asymptotic analysis for a large class of stochastic optimization problems arising in manufacturing is presented. A typical example of the problems considered in this paper is a production planning problem with random capacity and demand. In this example, it is assumed that the capacity of the system fluctuates faster than the other quantities. The general model considered here also has a fast controlled Markov process in its state description. By using the difference in the time scales of different quantities, the problem is simplified by “averaging” out the fast process. Then asymptotically optimal strategies are constructed from the optimal solutions of the limiting problems. The proofs of these results use the theory of viscosity solutions to dynamic programming equations. However, the formal construction of the asymptotically optimal strategies does not require knowledge of this theory.