This dissertation is focused on two examples of service systems where a fixed capacity has to be allocated among competing demand classes in a stochastic environment. In both cases, we employ the dynamic programming techniques to study the optimal capacity management problem.
First, we analyze a problem of allocating the homogeneous capacity faced by a rental company with heterogeneous customer base. We assume that one of the customer classes uses the reservation system and thus provides an advanced demand information which the company may use to improve its capacity allocation policies. We formulate the problem with dynamic programming techniques and derive several properties of the optimal control policies. Due to the difficulty of computing and implementing the optimal tactical control policies, we propose a simple heuristic capacity allocation policy based on a fluid approximation to the original problem dynamics and investigate its effectiveness through a series of numerical studies.
In the second case, we consider a problem of managing a medical diagnostic facility accessed by several groups of patients. We look at the operations of a typical hospital diagnostic facility that, in addition to outpatients, serves the inpatients whose requests for service can be further classified as emergency or non-emergency ones. Our analysis focuses on two inter-related tasks: establishing an appointment schedule for outpatient clients and the system of dynamic priority rules for admitting patients into the service. We formulate the problem of managing patient demands for service through a diagnostic facility as a finite horizon dynamic program and identify the properties of the optimal capacity management policies. Using empirical data, we conduct a series of numerical studies to evaluate the performance of heuristic rules for appointment acceptance and patient scheduling often observed in practice.