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On Optimal Allocation of Indivisibles Under Uncertainty

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  • V.I. Norkin
  • Y.M. Ermoliev
  • A. Ruszczynski

Abstract

The optimal use of indivisible resources is often the central issue in the economy and management. One of the main difficulties is the discontinuous nature of the resulting resource allocation problems which may lead to the failure of competitive market allocation mechanisms (unless we agree to "divide" the indivisibles in some indirect way). The problem becomes even more acute when uncertainty of the outcomes of decisions is present. In this paper we formalize the problem as a stochastic optimization problem involving discrete decision variables and uncertainties. By using some concrete examples, we illustrate how some problems of "dividing indivisibles" under uncertainty can be formalized in such terms. Next, we develop a general methodology to solve such problems based on the concept of the branch and bound method. The main idea of the approach 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 specializing the solution the optimal decision can be found.

Suggested Citation

  • V.I. Norkin & Y.M. Ermoliev & A. Ruszczynski, 1994. "On Optimal Allocation of Indivisibles Under Uncertainty," Working Papers wp94021, International Institute for Applied Systems Analysis.
    • Handle: RePEc:wop:iasawp:wp94021
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    1. Schultz, R. & Stougie, L. & Van Der Vlerk, M., 1993. "Two-Stage Stochastic Integer Programming. A Survey," Papers 520, Groningen State, Institute of Economic Research-.
    2. 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.
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    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. 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).
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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).
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.

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