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Multiple‐attribute decision making with partial information: The comparative hypervolume criterion

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  • Johnnie R. Charnetski
  • Richard M. Soland

Abstract

A new approach is presented for analyzing multiple‐attribute decision problems in which the set of actions is finite and the utility function is additive. The problem can be resolved if the decision makers (or group of decision makers) specifies a set of nonnegative weights for the various attributes or criteria, but we here assume that the decision maker(s) cannot provide a numerical value for each such weight. Ordinal information about these weights is therefore obtained from the decision maker(s), and this information is translated into a set of linear constraints which restrict the values of the weights. These constraints are then used to construct a polytope W of feasible weight vectors, and the subsets Hi (polytopes) of W over which each action ai has the greatest utility are determined. With the Comparative Hypervolume Criterion we calculate for each action the ratio of the hypervolume of Hi to the hypervolume of W and suggest the choice of an action with the largest such ratio. Justification of this choice criterion is given, and a computational method for accurately approximating the hypervolume ratios is described. A simple example is provided to evaluate the efficiency of a computer code developed to implement the method.

Suggested Citation

  • Johnnie R. Charnetski & Richard M. Soland, 1978. "Multiple‐attribute decision making with partial information: The comparative hypervolume criterion," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 25(2), pages 279-288, June.
    • Handle: RePEc:wly:navlog:v:25:y:1978:i:2:p:279-288
    DOI: 10.1002/nav.3800250208
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    Cited by:

    1. R. Pelissari & M. C. Oliveira & S. Ben Amor & A. Kandakoglu & A. L. Helleno, 2020. "SMAA methods and their applications: a literature review and future research directions," Annals of Operations Research, Springer, vol. 293(2), pages 433-493, October.
    2. García-Cáceres, Rafael Guillermo, 2020. "Stochastic Multicriteria Acceptability Analysis – Matching (SMAA-M)," Operations Research Perspectives, Elsevier, vol. 7(C).
    3. Podinovski, Vladislav V., 2020. "Maximum likelihood solutions for multicriterial choice problems," European Journal of Operational Research, Elsevier, vol. 286(1), pages 299-308.

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