Some Insights into Near-Optimal Plans for Stochastic Manufacturing Systems

Abstract

We present some insights obtained from the considerable research that has accumulated in proving that a hierarchical decomposition based on the frequencies of occurence of different types of events in the system results in near-optimal decisions as the rates of some events become large compared to those of others. In the simple context of dynamic two-machine flowshops, we observe a capacity loss phenomenon which must be accounted for in any construction of a near-optimal decision. We also show that a threshold-type control known as Kanban control is nearly optimal in some cases and not in others.

Keywords: Hierarchical manufacturing systems, hierarchical decomposition, singular perturbations, time-scale decomposition, flowshop, production planning, threshold-type control, Kanban control, near-optimal solutions, stochastic control, optimal control, capacity loss phenomenon

JEL Classification: C00, C61, M11