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A Queuing-Linear Programming Approach to Scheduling Police Patrol Cars

Author

Listed:
  • Peter J. Kolesar

    (The New York City-Rand Institute, New York, New York)

  • Kenneth L. Rider

    (The New York City-Rand Institute, New York, New York)

  • Thomas B. Crabill

    (The New York City-Rand Institute, New York, New York)

  • Warren E. Walker

    (The New York City-Rand Institute, New York, New York)

Abstract

In any city the arrival rate of calls for police patrol-car service varies considerably through the day. Using queuing theory and integer linear programming, we present a method for scheduling patrol cars so that specified service standards are met at each hour of the day. Two models are used. The first is an M / M / n queuing model with time-dependent parameters that is solved numerically. The second is an integer linear program in which the decision variables are the number of patrol cars working each tour and the times at which they go out of service for meals. The program's constraints are determined by the output of the queuing model. Use of the method with data from the New York City Police Department indicates that it can lead to substantial improvements in police service.

Suggested Citation

  • Peter J. Kolesar & Kenneth L. Rider & Thomas B. Crabill & Warren E. Walker, 1975. "A Queuing-Linear Programming Approach to Scheduling Police Patrol Cars," Operations Research, INFORMS, vol. 23(6), pages 1045-1062, December.
    • Handle: RePEc:inm:oropre:v:23:y:1975:i:6:p:1045-1062
    DOI: 10.1287/opre.23.6.1045
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    Cited by:

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    2. Schlicher, Loe & Lurkin, Virginie, 2024. "Fighting pickpocketing using a choice-based resource allocation model," European Journal of Operational Research, Elsevier, vol. 315(2), pages 580-595.
    3. Defraeye, Mieke & Van Nieuwenhuyse, Inneke, 2016. "Staffing and scheduling under nonstationary demand for service: A literature review," Omega, Elsevier, vol. 58(C), pages 4-25.
    4. Thompson, Gary M. & Pullman, Madeleine E., 2007. "Scheduling workforce relief breaks in advance versus in real-time," European Journal of Operational Research, Elsevier, vol. 181(1), pages 139-155, August.
    5. Sukanya Samanta & Goutam Sen & Soumya Kanti Ghosh, 2022. "A literature review on police patrolling problems," Annals of Operations Research, Springer, vol. 316(2), pages 1063-1106, September.
    6. Linda V. Green & Peter J. Kolesar & João Soares, 2001. "Improving the Sipp Approach for Staffing Service Systems That Have Cyclic Demands," Operations Research, INFORMS, vol. 49(4), pages 549-564, August.
    7. Armann Ingolfsson & Susan Budge & Erhan Erkut, 2008. "Optimal ambulance location with random delays and travel times," Health Care Management Science, Springer, vol. 11(3), pages 262-274, September.
    8. Schwarz, Justus Arne & Selinka, Gregor & Stolletz, Raik, 2016. "Performance analysis of time-dependent queueing systems: Survey and classification," Omega, Elsevier, vol. 63(C), pages 170-189.
    9. Alexander Zeifman & Yacov Satin & Ivan Kovalev & Rostislav Razumchik & Victor Korolev, 2020. "Facilitating Numerical Solutions of Inhomogeneous Continuous Time Markov Chains Using Ergodicity Bounds Obtained with Logarithmic Norm Method," Mathematics, MDPI, vol. 9(1), pages 1-20, December.
    10. Thompson, Gary M. & Goodale, John C., 2006. "Variable employee productivity in workforce scheduling," European Journal of Operational Research, Elsevier, vol. 170(2), pages 376-390, April.
    11. Stolletz, Raik, 2008. "Approximation of the non-stationary M(t)/M(t)/c(t)-queue using stationary queueing models: The stationary backlog-carryover approach," European Journal of Operational Research, Elsevier, vol. 190(2), pages 478-493, October.
    12. Amir Rastpour & Armann Ingolfsson & Bora Kolfal, 2020. "Modeling Yellow and Red Alert Durations for Ambulance Systems," Production and Operations Management, Production and Operations Management Society, vol. 29(8), pages 1972-1991, August.
    13. Linda V. Green & Peter J. Kolesar, 1998. "A Note on Approximating Peak Congestion in Mt/G/\infty Queues with Sinusoidal Arrivals," Management Science, INFORMS, vol. 44(11-Part-2), pages 137-144, November.
    14. Ingolfsson, Armann & Campello, Fernanda & Wu, Xudong & Cabral, Edgar, 2010. "Combining integer programming and the randomization method to schedule employees," European Journal of Operational Research, Elsevier, vol. 202(1), pages 153-163, April.
    15. P. Daniel Wright & Matthew J. Liberatore & Robert L. Nydick, 2006. "A Survey of Operations Research Models and Applications in Homeland Security," Interfaces, INFORMS, vol. 36(6), pages 514-529, December.
    16. Hall, Randolph W., 2002. "Incident dispatching, clearance and delay," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(1), pages 1-16, January.
    17. Ward Whitt & Wei You, 2019. "Time-Varying Robust Queueing," Operations Research, INFORMS, vol. 67(6), pages 1766-1782, November.
    18. Brusco, Michael J. & Jacobs, Larry W., 2001. "Starting-time decisions in labor tour scheduling: An experimental analysis and case study," European Journal of Operational Research, Elsevier, vol. 131(3), pages 459-475, June.
    19. Ingolfsson, Armann & Amanul Haque, Md. & Umnikov, Alex, 2002. "Accounting for time-varying queueing effects in workforce scheduling," European Journal of Operational Research, Elsevier, vol. 139(3), pages 585-597, June.

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