CAREER: Resource Allocation Under Uncertainty

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Integer programming is a powerful technique for solving problems that are combinatorial in nature, such as staff scheduling problems. To ensure that the assumptions underlying integer programming models are satisfied, one must typically apply strong simplifying assumptions to the system under study. Discrete event simulation is a powerful technique for estimating the performance that can be expected from complex systems. One can model virtually arbitrary complexity in (discrete-event) simulation models. This CAREER award aims to link these two management science techniques in an attempt to provide a powerful optimization approach that allows great model complexity. The approach to linking these methods requires that the simulation satisfies various structural properties, and that this structural information can be communicated to the integer program. The focus of this research is in identifying general conditions under which the linkage will be successful, identifying methods to reduce the computational requirements of the approach, and exploring various application methods and areas.In addition to potential contributions to the theory of management science, potential applications of this research include call centre staffing and ambulance allocation. In the call centre staffing problem one wishes to assign staff to shifts in a way that minimizes staffing costs, while ensuring that customer service is satisfactory. Many call centres exhibit complex customer routing and other characteristics that mean that simulation is the preferred method for predicting customer service for a given staffing level. It may be possible to achieve satisfactory customer service at less cost than is currently the case. In the ambulance allocation problem, one is trying to determine when and where to place ambulances to ensure satisfactory response time performance to calls. Again, simulation may be needed to predict response time performance, and again, it may be possible to achieve satisfactory response time performance at less cost than is currently the case.