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Generalized Dynamic Programming for Stochastic Combinatorial Optimization

Author

Listed:
  • Robert L. Carraway

    (University of Virginia, Charlottesville, Virginia)

  • Thomas L. Morin

    (Purdue University, West Lafayette, Indiana)

  • Herbert Moskowitz

    (Purdue University, West Lafayette, Indiana)

Abstract

In stochastic versions of combinatorial optimization problems, the objective is to maximize or minimize a function of random variables. For many problems of this type, conventionally applied dynamic programming (DP) may fail to generate an optimal solution due to the potential violation of the monotonicity assumption of DP. We develop a generalization of DP that guarantees optimality even in the absence of monotonicity. We illustrate the methodology on a version of the stochastic traveling salesman problem for which a previously proposed DP algorithm (E. Kao) is potentially suboptimal due to the violation of monotonicity (M. Sniedovich). Using Generalized DP, we are able to modify the algorithm to guarantee optimality.

Suggested Citation

  • Robert L. Carraway & Thomas L. Morin & Herbert Moskowitz, 1989. "Generalized Dynamic Programming for Stochastic Combinatorial Optimization," Operations Research, INFORMS, vol. 37(5), pages 819-829, October.
    • Handle: RePEc:inm:oropre:v:37:y:1989:i:5:p:819-829
    DOI: 10.1287/opre.37.5.819
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    Citations

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    Cited by:

    1. Gendreau, Michel & Laporte, Gilbert & Seguin, Rene, 1996. "Stochastic vehicle routing," European Journal of Operational Research, Elsevier, vol. 88(1), pages 3-12, January.
    2. Zhouchun Huang & Qipeng Phil Zheng & Eduardo Pasiliao & Vladimir Boginski & Tao Zhang, 2019. "A cutting plane method for risk-constrained traveling salesman problem with random arc costs," Journal of Global Optimization, Springer, vol. 74(4), pages 839-859, August.
    3. Hongtao Lei & Gilbert Laporte & Bo Guo, 2012. "A generalized variable neighborhood search heuristic for the capacitated vehicle routing problem with stochastic service times," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 99-118, April.
    4. Elgesem, Aurora Smith & Skogen, Eline Sophie & Wang, Xin & Fagerholt, Kjetil, 2018. "A traveling salesman problem with pickups and deliveries and stochastic travel times: An application from chemical shipping," European Journal of Operational Research, Elsevier, vol. 269(3), pages 844-859.
    5. Murthy, Ishwar & Sarkar, Sumit, 1997. "Exact algorithms for the stochastic shortest path problem with a decreasing deadline utility function," European Journal of Operational Research, Elsevier, vol. 103(1), pages 209-229, November.
    6. Astrid S. Kenyon & David P. Morton, 2003. "Stochastic Vehicle Routing with Random Travel Times," Transportation Science, INFORMS, vol. 37(1), pages 69-82, February.
    7. Kang, Seungmo & Ouyang, Yanfeng, 2011. "The traveling purchaser problem with stochastic prices: Exact and approximate algorithms," European Journal of Operational Research, Elsevier, vol. 209(3), pages 265-272, March.
    8. Robert L. Carraway & Robert L. Schmidt & Lawrence R. Weatherford, 1993. "An algorithm for maximizing target achievement in the stochastic knapsack problem with normal returns," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(2), pages 161-173, March.
    9. Hossein Hashemi Doulabi & Gilles Pesant & Louis-Martin Rousseau, 2020. "Vehicle Routing Problems with Synchronized Visits and Stochastic Travel and Service Times: Applications in Healthcare," Transportation Science, INFORMS, vol. 54(4), pages 1053-1072, July.

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