Optimal Scheduling Policies for a Production Service System with Two Items

Abstract

In this paper, we address the capacity allocation rules for a flexible production service system consisting of one flexible manufacturing facility and one service centre. The manufacturing facility produces two items in the first stage and the service centre serves two customers in the second stage. Each order served by the service centre depletes one unit of dedicated item produced by the manufacturing facility. The manager must make production and service capacity allocation decisions. The objective is to find an effective production and service scheduling rule to minimize the expected total cost over an infinite horizon. The service capacity allocation problem is formulated as a Markov decision process and use this formulation to characterize the structure of the optimal service allocation policy. We show that the optimal service scheduling policy is an extension of the well-known optimal service scheduling policy for classical service system. Then the characteristics of the optimal production policy are studied numerically since the analytic characteristics are not available.