Stochastic call center staffing with uncertain arrival, service and abandonment rates: A Bayesian perspective

Stochastic call center staffing with uncertain arrival, service and abandonment rates: A Bayesian perspective

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Article ID: iaor20164049
Volume: 63
Issue: 6
Start Page Number: 460
End Page Number: 478
Publication Date: Sep 2016
Journal: Naval Research Logistics (NRL)
Authors: ,
Keywords: combinatorial optimization, stochastic processes, allocation: resources, scheduling, personnel & manpower planning
Abstract:

In this article, we introduce staffing strategies for the Erlang‐A queuing system in call center operations with uncertain arrival, service, and abandonment rates. In doing so, we model the system rates using gamma distributions that create randomness in operating characteristics used in the optimization formulation. We divide the day into discrete time intervals where a simulation based stochastic programming method is used to determine staffing levels. More specifically, we develop a model to select the optimal number of agents required for a given time interval by minimizing an expected cost function, which consists of agent and abandonment (opportunity) costs, while considering the service quality requirements such as the delay probability. The objective function as well as the constraints in our formulation are random variables. The novelty of our approach is to introduce a solution method for the staffing of an operation where all three system rates (arrival, service, and abandonment) are random variables. We illustrate the use of the proposed model using both real and simulated call center data. In addition, we provide solution comparisons across different formulations, consider a dynamic extension, and discuss sensitivity implications of changing constraint upper bounds as well as prior hyper‐parameters.

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