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Convexification of Queueing Formulas by Mixed-Integer Second-Order Cone Programming: An Application to a Discrete Location Problem with Congestion

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  • Amir Ahmadi-Javid

    (Department of Industrial Engineering & Management Systems, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran)

  • Pooya Hoseinpour

    (Department of Industrial Engineering & Management Systems, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran)

Abstract

Mixed-integer second-order cone programs (MISOCPs) form a novel class of mixed-integer convex programs, which can be solved very efficiently as a result of the recent advances in optimization solvers. This paper shows how various performance metrics of M/G/1 queues can be modeled by different MISOCPs. To motivate the reformulation method, it is first applied to a challenging stochastic location problem with congestion, which is broadly used to design socially optimal service systems. Three different MISOCPs are developed and compared on different sets of benchmark test problems. The new formulations efficiently solve very large-size test problems that cannot be solved by the two existing methods developed based on linear programming within reasonable time. The superiority of the conic reformulation method is next shown over a state-space decomposition method recently used to solve an assignment problem in queueing systems. Finally, the general applicability of the method is shown for similar optimization problems that use queue-theoretic performance measures to address customer satisfaction and service quality.

Suggested Citation

  • Amir Ahmadi-Javid & Pooya Hoseinpour, 2022. "Convexification of Queueing Formulas by Mixed-Integer Second-Order Cone Programming: An Application to a Discrete Location Problem with Congestion," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2621-2633, September.
    • Handle: RePEc:inm:orijoc:v:34:y:2022:i:5:p:2621-2633
    DOI: 10.1287/ijoc.2021.1125
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