Abstract: Product and service mix was provied with customers by a service-oriented manufacturing firm. The modelling and optimization of a production service system with two types of items and customers was considered in this paper. Two types of items were produced by the manufacturing facility in the first stage, then two types of orders were fulfilled at the service centre by the dedicated items in the second stage, one unit of item was depleted by each order. The problem is formulated as a Markov chain, this formulation was used to characterize the structure of the optimal scheduling policies. They show that the optimal service policy is a generalization of the well-known optimal production scheduling policy in classical production inventory system and service scheduling policy in classical service system. The benefits of the optimal service policy were showed by numerical experiments against several other policies.

Key words: service-oriented manufacturing, production service system, inventory service system, Markov chain, impatience