Service System Design Problems Under Demand Uncertainty

Abstract

The service system design problem aims to select the location and capacity of service facilities and customers’ assignments to minimize the setup, access, and waiting time costs. This thesis addresses the case when there is uncertainty about the demand for service, considering two service systems that can be modelled as independent networks of M/M/1 and G/M/1 queues. Robust optimization is used when the demand rate is unknown. However, the arrival pattern can still be reasonably approximated as a Poisson process or follow a General distribution, respectively. We use distributionally-robust optimization to address the case when the demand distribution is estimated from a limited sample. For both models, we reformulate both problems as mixed-integer second-order conic programs. For the M/M/1 model, these problems can be solved directly on commercial solvers. On the other hand, for the G/M/1 model, we use a Lagrangian-Relaxation approach to solve the problems.