Integrated capacity allocation policies for a production service system with two-class customers and items

In this paper, we address the capacity allocation rules for a production service system consisting of one flexible manufacturing facility and a service centre. The manufacturing facility produces two-type items in the first stage and a service centre serves two-class customers in the second stage. Each customer 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 at any time. We first formulate the optimal service capacity allocation problem as a Markov decision process and show the optimal service policy is an extension of the well-known optimal service scheduling policy for classical service system. We then develop several heuristic production scheduling policies when the service centre is regulated by the optimal scheduling policy. Numerical examples verify the effectiveness and efficiencies of the proposed heuristics.