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Staffing optimization with chance constraints for emergency call centers
Thuy Anh Ta,Pierre L'Ecuyer,Fabian Bastin +2 more
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TLDR
A sample average approximation (SAA) version of this staffing problem with probabilistic constraints in an emergency call center whose solution converges to that of the exact problem when the sample size increases.Abstract:
We consider a staffing problem with probabilistic constraints in an emergency call center. The aim is to minimize the total cost of agents while satisfying chance constraints defined over the service level and the average waiting time, in a given set of time periods. We provide a mathematical formulation of the problem in terms of probabilities and expectations. We define a sample average approximation (SAA) version of this problem whose solution converges to that of the exact problem when the sample size increases. We also propose a quick and simple simulation-based (heuristic) algorithm to compute a good (nearly optimal) staffing solution for the SAA problem. We illustrate and validate our algorithm with a simulation model based on real data from the 911 emergency call center of Montreal, Canada.read more
Citations
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Proceedings ArticleDOI
Modeling bursts in the arrival process to an emergency call center
TL;DR: This work shows how to estimate the model parameters for each burst by maximum likelihood, how to model the multivariate distribution of those parameters using copulas, and how to simulate the burst process from this model.
Journal ArticleDOI
On a multistage discrete stochastic optimization problem with stochastic constraints and nested sampling
TL;DR: In this article, the authors consider a multistage stochastic discrete program, where constraints on any stage might involve expectations that cannot be computed easily and are approximated by simulation.
Dissertation
Stochastic optimization of staffing for multiskill call centers
TL;DR: This thesis shows that under some assumptions that hold in call center examples, one can obtain the optimal solutions of the original problem by solving its SAA with large enough sample sizes, and indicates the viability of the SAA approach in this context, in both theoretical and practical aspects.
On a two-stage discrete stochastic optimization problem with stochastic constraints and nested sampling
TL;DR: A sample average approximation approach that uses nested sampling that is able to prove that the optimal values and solutions of the SAA converge to the true ones with probability one when the sample sizes at both stages increase to infinity, and proves exponential convergence of the probability of a large deviation for the optimal value of theSAA.
References
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Modeling Daily Arrivals to a Telephone Call Center
TL;DR: Stochastic models of time-dependent arrivals are developed, with focus on the application to call centers, including the essential features of the arrival process, the goodness of fit of the estimated models, and the sensitivity of various simulated performance measures of the call center to the choice of arrival process model.
Journal ArticleDOI
Staffing Multiskill Call Centers via Linear Programming and Simulation
TL;DR: An iterative cutting-plane algorithm on an integer program for minimizing the staffing costs of a multiskill call center subject to service-level requirements that are estimated by simulation is studied.