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On Optimal Allocation of Indivisibles Under Uncertainty

Author

Listed:
  • Vladimir I. Norkin

    (International Institute for Applied Systems Analysis, Laxenburg, Austria)

  • Yuri M. Ermoliev

    (International Institute for Applied Systems Analysis, Laxenburg, Austria)

  • Andrzej Ruszczyński

    (International Institute for Applied Systems Analysis, Laxenburg, Austria)

Abstract

The optimal allocation of indivisible resources is formalized as a stochastic optimization problem involving discrete decision variables. A general stochastic search procedure is proposed, which develops the concept of the branch-and-bound method. The main idea is to process large collections of possible solutions and to devote more attention to the most promising groups. By gathering more information to reduce the uncertainty and by narrowing the search area, the optimal solution can be found with probability one. Special techniques for calculating stochastic lower and upper bounds are discussed. The results are illustrated by a computational experiment.

Suggested Citation

  • Vladimir I. Norkin & Yuri M. Ermoliev & Andrzej Ruszczyński, 1998. "On Optimal Allocation of Indivisibles Under Uncertainty," Operations Research, INFORMS, vol. 46(3), pages 381-395, June.
    • Handle: RePEc:inm:oropre:v:46:y:1998:i:3:p:381-395
    DOI: 10.1287/opre.46.3.381
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    References listed on IDEAS

    as
    1. T. W. Edward Lau & Y. C. Ho, 1997. "Universal Alignment Probabilities and Subset Selection for Ordinal Optimization," Journal of Optimization Theory and Applications, Springer, vol. 93(3), pages 455-489, June.
    2. Schultz, R. & Stougie, L. & Van Der Vlerk, M., 1993. "Two-Stage Stochastic Integer Programming. A Survey," Papers 520, Groningen State, Institute of Economic Research-.
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    Cited by:

    1. Eun, Joonyup & Kim, Sang-Phil & Yih, Yuehwern & Tiwari, Vikram, 2019. "Scheduling elective surgery patients considering time-dependent health urgency: Modeling and solution approaches," Omega, Elsevier, vol. 86(C), pages 137-153.
    2. V.I. Norkin & G.C. Pflug & A. Ruszczynski, 1996. "A Branch and Bound Method for Stochastic Global Optimization," Working Papers wp96065, International Institute for Applied Systems Analysis.
    3. Sushil R. Poudel & Md Abdul Quddus & Mohammad Marufuzzaman & Linkan Bian & Reuben F. Burch V, 2019. "Managing congestion in a multi-modal transportation network under biomass supply uncertainty," Annals of Operations Research, Springer, vol. 273(1), pages 739-781, February.
    4. Kabli, Mohannad & Quddus, Md Abdul & Nurre, Sarah G. & Marufuzzaman, Mohammad & Usher, John M., 2020. "A stochastic programming approach for electric vehicle charging station expansion plans," International Journal of Production Economics, Elsevier, vol. 220(C).
    5. Sigurdur Ólafsson, 2004. "Two-Stage Nested Partitions Method for Stochastic Optimization," Methodology and Computing in Applied Probability, Springer, vol. 6(1), pages 5-27, March.
    6. Walter Gutjahr & Alois Pichler, 2016. "Stochastic multi-objective optimization: a survey on non-scalarizing methods," Annals of Operations Research, Springer, vol. 236(2), pages 475-499, January.
    7. Gyana R. Parija & Shabbir Ahmed & Alan J. King, 2004. "On Bridging the Gap Between Stochastic Integer Programming and MIP Solver Technologies," INFORMS Journal on Computing, INFORMS, vol. 16(1), pages 73-83, February.
    8. Quddus, Md Abdul & Shahvari, Omid & Marufuzzaman, Mohammad & Usher, John M. & Jaradat, Raed, 2018. "A collaborative energy sharing optimization model among electric vehicle charging stations, commercial buildings, and power grid," Applied Energy, Elsevier, vol. 229(C), pages 841-857.
    9. Sigrún Andradóttir & Andrei A. Prudius, 2009. "Balanced Explorative and Exploitative Search with Estimation for Simulation Optimization," INFORMS Journal on Computing, INFORMS, vol. 21(2), pages 193-208, May.
    10. Gutjahr, W. J. & Hellmayr, A. & Pflug, G. Ch., 1999. "Optimal stochastic single-machine-tardiness scheduling by stochastic branch-and-bound," European Journal of Operational Research, Elsevier, vol. 117(2), pages 396-413, September.
    11. Walter J. Gutjahr & Alois Pichler, 2016. "Stochastic multi-objective optimization: a survey on non-scalarizing methods," Annals of Operations Research, Springer, vol. 236(2), pages 475-499, January.
    12. Alrefaei, Mahmoud H. & Alawneh, Ameen J., 2004. "Selecting the best stochastic system for large scale problems in DEDS," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(2), pages 237-245.
    13. K. Haeggloef, 1996. "The Implementation of the Stochastic Branch and Bound Method for Applications in River Basin Water Quality Management," Working Papers wp96089, International Institute for Applied Systems Analysis.
    14. Quddus, Md Abdul & Shahvari, Omid & Marufuzzaman, Mohammad & Ekşioğlu, Sandra D. & Castillo-Villar, Krystel K., 2021. "Designing a reliable electric vehicle charging station expansion under uncertainty," International Journal of Production Economics, Elsevier, vol. 236(C).
    15. W. J. Gutjahr & C. Strauss & E. Wagner, 2000. "A Stochastic Branch-and-Bound Approach to Activity Crashing in Project Management," INFORMS Journal on Computing, INFORMS, vol. 12(2), pages 125-135, May.
    16. B.J. Lence & A. Ruszczynski, 1996. "Managing Water Quality under Uncertainty: Application of a New Stochastic Branch and Bound Method," Working Papers wp96066, International Institute for Applied Systems Analysis.
    17. Mahmoud H. Alrefaei & Sigrún Andradóttir, 2005. "Discrete stochastic optimization using variants of the stochastic ruler method," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(4), pages 344-360, June.

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