Decision making under uncertain and dependent system rates in service systems

Abstract

In this paper, we propose decision analysis methods for determining the optimal number of agents of a service system where the system rates (arrival, service, and abandonment) are modeled as dependent random variables. In doing so, we take the Bayesian point of view of inference and obtain joint posterior distributions of the system rates. We solve the proposed stochastic staffing decision problem with augmented probability simulation based optimization methods. The novelty of our approach stems from the use of dependent system rates to determine optimal staffing in a constrained optimization setting for stochastic service systems. We demonstrate the implications of ignoring dependence and uncertainty in system rates on simulated data for general service systems, and illustrate the application of the proposed methodology on call center operations.