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Probability and Math Finance Seminar

Michael Harrison, Stanford University

Staffing and Routing in Large Call Centers:
A Method Based on Stochastic Fluid Models

Abstract

We consider a call center model with m customer classes and r agent pools. The model is one with doubly stochastic arrivals, which means that the m-vector λ of instantaneous arrival rates is allowed to vary both temporally and stochastically. Two levels of call center management are considered: staffing the r pools of agents, and dynamically routing calls to agents. In our initial formulation, the system manager's objective is to minimize the sum of personnel costs and abandonment penalties.

We propose a method in which the routing problem is treated as a linear program, using as input a real-time estimate of the prevailing λ vector; the higher-level staffing problem is then reduced to a stochastic program that uses historical arrival data as input. This method is exactly optimal if one replaces the original system model, in which customers are discrete, by what we call a stochastic fluid model. In a limiting regime of practical interest, involving high call volumes and large server pools, the proposed method is asymptotically optimal for the original discrete model.

In our second formulation of the system manager's problem, the objective is to minimize personnel costs subject to service-level constraints. That problem is reduced to the one described above by dualizing the service-level constraints. That is, one can set the abandonment penalties in our initial formulation so that the resulting management policy is optimal for our second formulation. Finding the "right" penalty values is an iterative process, but even with this added computational burden, our proposed method is feasible for problems of realistic size.

Based on joint work with Achal Bassamboo and Assaf Zeevi.

TUESDAY, March 18, 2008
Time: 4:30 P.M.
Location: DH 1212