Capacity Allocation of an Integrated Production and Service System

Manufacturing servitization has become a major trend in industry that is implemented by so called integrated production and service systems (IPSSs) to offer not only products but also their associated services. In this study, we explore the capacity allocation policy for an IPSS that consists of a manufacturing facility and a service center. The IPSS serves two classes of customers, each demanding a specific product produced at the manufacturing facility and, subsequently, the associated service offered by the service center. We formulate this problem of resource allocation as a Markov decision process. Our analysis suggests that it is optimal to serve the customer with the larger cost saving rate and slower service rate, where the cost saving rate equals service rate times the sum of holding cost and waiting cost. Then we explore production control policies coupled with optimal service ones. We demonstrate that, with light service traffic, the system under the optimal production policy becomes similar to a make-to-stock system. Such a system can effectively hedge the system uncertainty. Therefore, the optimal production policy for the IPSS is also a hedging point policy. Under this policy, switching and idling curves split the state space into three regions: one without any production, the two others for production of two type products, respectively. We also discuss the optimal control policies of the two extensions of the IPSS (one with multiple types of product and customers, and the other with a single product and two classes of customers) and find that the characters of the optimal production and service policy still hold. Finally, we develop three heuristic integrated scheduling policies. Numerical experiments show that one is very effective.