Computational Evaluation of Hierarchical Production Control Policies for Stochastic Manufacturing Systems

Abstract

This paper is concerned with near-optimal control of manufacturing systems consisting of two unreliable machines in tandem and having the objective of minimizing the total discounted cost of inventories/shortages over an infinite horizon. Asymptotic optimal feedback controls are constructed with respect to the rate of machine breakdown/repair as compared to the given discount rate. Performance of these controls, known as hierarchical controls, is compared with the optimal cost (when possible) and the costs obtained with two well-known heuristics, known as Kanban controls and two boundary controls. It is shown that hierarchical controls perform better than Kanban controls in some cases and no worse in others. Costs of hierarchical and two boundary controls are not significantly different, although the former is a simpler policy than the latter. Also examined computationally is the asymptotic nature of hierarchical controls.

Keywords: Production Planning, Hierarchical Controls, Stochastic Manufacturing System, Dynamic Programming, Asymptotic Optimality, Open-Loop Controls, Feedback Controls, Error Bounds, Computational Evaluations, Just-in-time inventory management, two-boundary controls, Kanban controls, CONWIP

JEL Classification: M11, C61