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

Author

Listed:
  • 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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    as
    1. Guo, Chuanyin & Wei, Fajie & Chen, Yao, 2017. "A note on second order cone programming approach to two-stage network data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 263(2), pages 733-735.
    2. Holmberg, Kaj & Ronnqvist, Mikael & Yuan, Di, 1999. "An exact algorithm for the capacitated facility location problems with single sourcing," European Journal of Operational Research, Elsevier, vol. 113(3), pages 544-559, March.
    3. Ho-Yin Mak & Ying Rong & Zuo-Jun Max Shen, 2013. "Infrastructure Planning for Electric Vehicles with Battery Swapping," Management Science, INFORMS, vol. 59(7), pages 1557-1575, July.
    4. Pierre Bonami & Miguel A. Lejeune, 2009. "An Exact Solution Approach for Integer Constrained Portfolio Optimization Problems Under Stochastic Constraints," Post-Print hal-00421756, HAL.
    5. Xue Bai & Ram Gopal & Manuel Nunez & Dmitry Zhdanov, 2012. "On the Prevention of Fraud and Privacy Exposure in Process Information Flow," INFORMS Journal on Computing, INFORMS, vol. 24(3), pages 416-432, August.
    6. John F. Shortle & Martin J. Fischer & Percy H. Brill, 2007. "Waiting-Time Distribution of M/D N /1 Queues Through Numerical Laplace Inversion," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 112-120, February.
    7. Juan Pablo Vielma & Shabbir Ahmed & George L. Nemhauser, 2008. "A Lifted Linear Programming Branch-and-Bound Algorithm for Mixed-Integer Conic Quadratic Programs," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 438-450, August.
    8. Long He & Ho-Yin Mak & Ying Rong & Zuo-Jun Max Shen, 2017. "Service Region Design for Urban Electric Vehicle Sharing Systems," Manufacturing & Service Operations Management, INFORMS, vol. 19(2), pages 309-327, May.
    9. Karl Sigman, 2016. "Using the M/G/1 queue under processor sharing for exact simulation of queues," Annals of Operations Research, Springer, vol. 241(1), pages 23-34, June.
    10. René Brandenberg & Lucia Roth, 2009. "New algorithms for k-center and extensions," Journal of Combinatorial Optimization, Springer, vol. 18(4), pages 376-392, November.
    11. John F. Shortle & Percy H. Brill & Martin J. Fischer & Donald Gross & Denise M. B. Masi, 2004. "An Algorithm to Compute the Waiting Time Distribution for the M/G/1 Queue," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 152-161, May.
    12. Hassan Hijazi & Pierre Bonami & Adam Ouorou, 2013. "Robust delay-constrained routing in telecommunications," Annals of Operations Research, Springer, vol. 206(1), pages 163-181, July.
    13. Samir Elhedhli, 2006. "Service System Design with Immobile Servers, Stochastic Demand, and Congestion," Manufacturing & Service Operations Management, INFORMS, vol. 8(1), pages 92-97, December.
    14. F. Maggioni & F. A. Potra & M. I. Bertocchi & E. Allevi, 2009. "Stochastic Second-Order Cone Programming in Mobile Ad Hoc Networks," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 309-328, November.
    15. Chuen-Teck See & Melvyn Sim, 2010. "Robust Approximation to Multiperiod Inventory Management," Operations Research, INFORMS, vol. 58(3), pages 583-594, June.
    16. Miyashiro, Ryuhei & Takano, Yuichi, 2015. "Mixed integer second-order cone programming formulations for variable selection in linear regression," European Journal of Operational Research, Elsevier, vol. 247(3), pages 721-731.
    17. Bin Han & Ilya O. Ryzhov & Boris Defourny, 2016. "Optimal Learning in Linear Regression with Combinatorial Feature Selection," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 721-735, November.
    18. P. Bonami & M. A. Lejeune, 2009. "An Exact Solution Approach for Portfolio Optimization Problems Under Stochastic and Integer Constraints," Operations Research, INFORMS, vol. 57(3), pages 650-670, June.
    19. Burak Kocuk & Santanu S. Dey & X. Andy Sun, 2016. "Strong SOCP Relaxations for the Optimal Power Flow Problem," Operations Research, INFORMS, vol. 64(6), pages 1177-1196, December.
    20. Boffey, Brian & Galvao, Roberto & Espejo, Luis, 2007. "A review of congestion models in the location of facilities with immobile servers," European Journal of Operational Research, Elsevier, vol. 178(3), pages 643-662, May.
    21. Chen, Kun & Zhu, Joe, 2017. "Second order cone programming approach to two-stage network data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 262(1), pages 231-238.
    22. Jianjun Li & Liwei Liu & Tao Jiang, 2018. "Analysis of an M/G/1 queue with vacations and multiple phases of operation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 51-72, February.
    23. Alper Atamtürk & Gemma Berenguer & Zuo-Jun (Max) Shen, 2012. "A Conic Integer Programming Approach to Stochastic Joint Location-Inventory Problems," Operations Research, INFORMS, vol. 60(2), pages 366-381, April.
    24. Conrado Borraz-Sánchez & Russell Bent & Scott Backhaus & Hassan Hijazi & Pascal Van Hentenryck, 2016. "Convex Relaxations for Gas Expansion Planning," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 645-656, November.
    25. Navneet Vidyarthi & Samir Elhedhli & Elizabeth Jewkes, 2009. "Response time reduction in make-to-order and assemble-to-order supply chain design," IISE Transactions, Taylor & Francis Journals, vol. 41(5), pages 448-466.
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