Service System Design with Immobile Servers, Stochastic Demand and Economies of Scale
The service system design problem seeks to locate facilities, determine their capacity, and assign customers to them in order to improve the service quality and the customers' experience while minimizing the capacity acquisition cost, the customer access cost, and the average waiting cost. While the centralization of facilities will lead to economies of scale, decentralizing them will lead to faster response times. Traditionally, the capacity acquisition costs were assumed linear with a xed setup cost. In this work, we explicitly account for economies of scale by modeling the cost as a concave function of capacity. In this thesis, we model and provide solution methodologies for the service system design problem with immobile servers, stochastic demand and economies of scale. We start by reformulating the problem, and then provide solution approaches based on piece-wise linearization, Second Order Cone Programming (SOCP), and Lagrangian Relaxation.Extensive numerical testing on a standard data set is provided and the results analyzed.