A profit-maximization location-capacity model for designing a service system with risk of service interruptions

This paper considers the design of an immobile service system in which each facility's service process is subject to the risk of interruptions. The location-capacity decisions and allocations are simultaneously made to maximize the difference between the service provider's profit and the sum of customers' transportation and waiting costs. An efficient Lagrangian-based solution algorithm is developed, which solves large-sized instances with up to 50 service facilities and 500 customers in a few seconds. Several sensitivity analyses and managerial insights are presented. The model is also applied to a case study on a logistics network design problem in the zinc mining industry.