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Managing Response Time in a Call-Routing Problem with Service Failure

Fuqua School of Business, Duke University, Durham, North Carolina 27708
University of Washington Business School, Seattle, Washington 98195
fdv1{at}duke.edu
yongpin{at}u.washington.edu

Traditional research on routing in queueing systems usually ignores service quality related factors. In this paper, we analyze the routing problem in a system where customers call back when their problems are not completely resolved by the customer service representatives (CSRs). We introduce the concept of call resolution probability, and we argue that it constitutes a good proxy for call quality. For each call, both the call resolution probability (p) and the average service time (1/µ) are CSR dependent. We use a Markov decision process formulation to obtain analytical results and insights about the optimal routing policy that minimizes the average total time of call resolution, including callbacks. In particular, we provide sufficient conditions under which it is optimal to route to the CSR with the highest call resolution rate (pµ) among those available. We also develop efficient heuristics that can be easily implemented in practice.

Subject classifications: dynamic programming/optimal control; Markov: infinite state; probability: stochastic model applications; queues: Markovian; multichannel.
History: Received April 2003; revision received March 2004; revision received October 2004; revision received November 2004; accepted December 2004.

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