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Optimizing Bernoulli Routing Policies for Balancing Loads on Call Centers and Minimizing Transmission Costs

Author

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  • L. D. Servi

    (GTE Laboratories)

  • S. Humair

    (Massachusetts Institute of Technology)

Abstract

We address the problem of assigning probabilities at discrete time instants for routing toll-free calls to a given set of call centers to minimize a weighted sum of transmission costs and load variability at the call centers during the next time interval. We model the problem as a tripartite graph and decompose the finding of an optimal probability assignment in the graph into the following problems: (i) estimating the true arrival rates at the nodes for the last time period; (ii) computing routing probabilities assuming that the estimates are correct. We use a simple approach for arrival rate estimation and solve the routing probability assignment by formulating it as a convex quadratic program and using the affine scaling algorithm to obtain an optimal solution. We further address a practical variant of the problem that involves changing routing probabilities associated with k nodes in the graph, where k is a prespecified number, to minimize the objective function. This involves deciding which k nodes to select for changing probabilities and determining the optimal value of the probabilities. We solve this problem using a heuristic that ranks all subsets of k nodes using gradient information around a given probability assignment. The routing model and the heuristic are evaluated for speed of computation of optimal probabilities and load balancing performance using a Monte Carlo simulation. Empirical results for load balancing are presented for a tripartite graph with 99 nodes and 17 call center gates.

Suggested Citation

  • L. D. Servi & S. Humair, 1999. "Optimizing Bernoulli Routing Policies for Balancing Loads on Call Centers and Minimizing Transmission Costs," Journal of Optimization Theory and Applications, Springer, vol. 100(3), pages 623-659, March.
    • Handle: RePEc:spr:joptap:v:100:y:1999:i:3:d:10.1023_a:1022642624300
    DOI: 10.1023/A:1022642624300
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    References listed on IDEAS

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    1. Daley, D. J., 1987. "Certain optimality properties of the first-come first-served discipline for G/G/s queues," Stochastic Processes and their Applications, Elsevier, vol. 25, pages 301-308.
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    Cited by:

    1. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.

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