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Computational bounds for elevator control policies by large scale linear programming

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  • Stefan Heinz
  • Jörg Rambau
  • Andreas Tuchscherer

Abstract

We computationally assess policies for the elevator control problem by a new column-generation approach for the linear programming method for discounted infinite-horizon Markov decision problems. By analyzing the optimality of given actions in given states, we were able to provably improve the well-known nearest-neighbor policy. Moreover, with the method we could identify an optimal parking policy. This approach can be used to detect and resolve weaknesses in particular policies for Markov decision problems. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Stefan Heinz & Jörg Rambau & Andreas Tuchscherer, 2014. "Computational bounds for elevator control policies by large scale linear programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(1), pages 87-117, February.
    • Handle: RePEc:spr:mathme:v:79:y:2014:i:1:p:87-117
    DOI: 10.1007/s00186-013-0454-5
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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.
    2. Daniela Pucci de Farias & Benjamin Van Roy, 2004. "On Constraint Sampling in the Linear Programming Approach to Approximate Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 462-478, August.
    3. Daniel Adelman & Adam J. Mersereau, 2008. "Relaxations of Weakly Coupled Stochastic Dynamic Programs," Operations Research, INFORMS, vol. 56(3), pages 712-727, June.
    4. Daniela Pucci de Farias & Benjamin Van Roy, 2006. "A Cost-Shaping Linear Program for Average-Cost Approximate Dynamic Programming with Performance Guarantees," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 597-620, August.
    5. D. P. de Farias & B. Van Roy, 2003. "The Linear Programming Approach to Approximate Dynamic Programming," Operations Research, INFORMS, vol. 51(6), pages 850-865, December.
    6. Benjamin Hiller & Torsten Klug & Andreas Tuchscherer, 2011. "Improved Destination Call Elevator Control Algorithms for Up Peak Traffic," Operations Research Proceedings, in: Bo Hu & Karl Morasch & Stefan Pickl & Markus Siegle (ed.), Operations Research Proceedings 2010, pages 251-256, Springer.
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