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Elevator dispatching problem: a mixed integer linear programming formulation and polyhedral results

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  • Mirko Ruokokoski

    (School of Science, Aalto University)

  • Harri Ehtamo

    (School of Science, Aalto University)

  • Panos M. Pardalos

    (University of Florida)

Abstract

In the static elevator dispatching problem the aim is to design a route for each capacitated elevator to satisfy a set of transportation requests such that a cost function is minimized while satisfying a number of constraints. This problem is a crucial part in the control of an elevator group. So far, the problem has been formulated in various algorithmic-dependent forms, where part of the constraints have been given only verbally. In this paper we present a mixed-integer linear programming formulation of the problem where all constraints are given in explicit mathematical form. This allows, e.g., polyhedral analysis of the problem. We also present some new valid inequalities to strengthen the formulation. Furthermore, we study the polyhedral structure of the problem in a generic case arising in the down-peak traffic pattern. In particular, we show which equalities define a minimal equality system for the polytope of the problem, which is defined as the convex hull of the feasible solutions. In addition, we provide the dimension of the polytope and analyze which valid inequalities derived are facet inducing.

Suggested Citation

  • Mirko Ruokokoski & Harri Ehtamo & Panos M. Pardalos, 2015. "Elevator dispatching problem: a mixed integer linear programming formulation and polyhedral results," Journal of Combinatorial Optimization, Springer, vol. 29(4), pages 750-780, May.
    • Handle: RePEc:spr:jcomop:v:29:y:2015:i:4:d:10.1007_s10878-013-9620-1
    DOI: 10.1007/s10878-013-9620-1
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    References listed on IDEAS

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    1. Benjamin Hiller & Andreas Tuchscherer, 2008. "Real-Time Destination-Call Elevator Group Control on Embedded Microcontrollers," Operations Research Proceedings, in: Jörg Kalcsics & Stefan Nickel (ed.), Operations Research Proceedings 2007, pages 357-362, Springer.
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    3. Archetti, Claudia & Savelsbergh, Martin W.P. & Grazia Speranza, M., 2008. "To split or not to split: That is the question," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 44(1), pages 114-123, January.
    4. Stefan Ropke & Jean-François Cordeau, 2009. "Branch and Cut and Price for the Pickup and Delivery Problem with Time Windows," Transportation Science, INFORMS, vol. 43(3), pages 267-286, August.
    5. G. Dantzig & R. Fulkerson & S. Johnson, 1954. "Solution of a Large-Scale Traveling-Salesman Problem," Operations Research, INFORMS, vol. 2(4), pages 393-410, November.
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    Cited by:

    1. Janne Sorsa, 2019. "Real-time algorithms for the bilevel double-deck elevator dispatching problem," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 7(1), pages 79-122, March.
    2. Ruokokoski, Mirko & Sorsa, Janne & Siikonen, Marja-Liisa & Ehtamo, Harri, 2016. "Assignment formulation for the Elevator Dispatching Problem with destination control and its performance analysis," European Journal of Operational Research, Elsevier, vol. 252(2), pages 397-406.

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