Design and control of a large call center: Asymptotic analysis of an LP-based method
Coauthor(s): Achal Bassamboo, J. Richard Harrison.
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This paper analyzes 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. The system manager?s objective is to minimize the sum of personnel costs and abandonment penalties. We
consider a limiting parameter regime that is natural for call centers and relatively easy to analyze, but apparently novel in
the literature of applied probability. For that parameter regime, we prove an asymptotic lower bound on expected total cost,
which uses a strikingly simple distillation of the original system data. We then propose a method for staffing and routing
based on linear programming (LP), and show that it achieves the asymptotic lower bound on expected total cost; in that
sense the proposed method is asymptotically optimal.
Source: Operations Research
Bassamboo, Achal, J. Michael Harrison, and Assaf Zeevi. "Design and control of a large call center: Asymptotic analysis of an LP-based method." Operations Research 54, no. 3 (2006): 419-435.