A Finite Horizon Dynamic Programming Model for Production and Repair Decisions

Abstract

In this research, a novel optimal single machine replacement policy in finite stages based on the rate of producing defective items is proposed. The primary objective of this paper is to determine the optimal decision using a Markov decision process to maximize the total profit associated with a machine maintenance policy. It is assumed that a customer order is due at the end of a finite horizon and the machine deteriorates over time when operating. Repair takes time but brings the machine to a better state. Production and repair costs are considered in the model and revenue is earned for each good item produced by the end of the horizon, there is also a cost for the machine condition at the end of the horizon. In each period, we must decide whether to produce, repair, or do nothing, with the objective of maximizing expected profit during the horizon.

Keywords:

• Machine maintenance
• Defective items
• Stochastic Dynamic Programming

Mathematics Subject Classification:

• Primary 90B25
• Secondary 62F15