Modeling and optimization of a product-service system with additional service capacity and impatient customers

Product-service system is a business model, in which a company offers a mix of products and services to maintain competitive edge, satisfy customer needs, and produce lower environmental impact than that produced by a traditional business model. This paper studies the modeling and optimization problems for a basic product-service system from the view point of operation management. The proposed system, modeled as a block structure Markov chain, features additional service capacity and impatient customers. The Matrix geometric methodology is applied to obtain the stationary distribution of the system. The performance indices for the system are derived based on the distribution, and the sensitivity of the performance with respect to the parameters is considered by numerical experiments. Meanwhile, the decision process of obtaining the optimal sets of additional service capacity opening threshold and the base store level is discussed from the point of view of profit optimization We propose algorithms to solve the problem, which are shown to be effective and efficiency by numerical experiments. The studies of the sensitivity of the optimal decision to the parameters propose some insight on system demand management and system improvement.