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Multiple Objective Linear Programming with Interval Criterion Weights

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  • Ralph E. Steuer

    (University of Kentucky)

Abstract

The purpose of this research is to develop a computer applicable methodology for analyzing multiple objective linear programming problems when interval, rather than fixed, weights are assigned to each of the objectives. Rather than obtaining a single efficient extreme point as one would normally expect with fixed weights, a cluster of efficient extreme points is typically generated when interval weights are specified. Then, from the subset of solutions generated, it is contemplated, that the decision-maker will be able to qualitatively identify his efficient extreme point of greatest utility (which should either be the decision-maker's optimal point or be close enough to it to terminate the decision process). The procedure presented in this paper involves converting the multiple objective linear programming problem with interval criterion weights into an equivalent vector-maximum problem. Once in such form, an algorithm for the vector-maximum problem can then be used to determine the subset of "efficient extreme" points corresponding to the interval weights specified. General computational experience regarding the operation of the equivalent vector-maximum problem is reported. Also, a numerical example is provided to illustrate the total procedure described.

Suggested Citation

  • Ralph E. Steuer, 1976. "Multiple Objective Linear Programming with Interval Criterion Weights," Management Science, INFORMS, vol. 23(3), pages 305-316, November.
    • Handle: RePEc:inm:ormnsc:v:23:y:1976:i:3:p:305-316
    DOI: 10.1287/mnsc.23.3.305
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    1. Köksalan, Murat & Büyükbasaran, Tayyar & Özpeynirci, Özgür & Wallenius, Jyrki, 2010. "A flexible approach to ranking with an application to MBA Programs," European Journal of Operational Research, Elsevier, vol. 201(2), pages 470-476, March.
    2. de Almeida, Jonatas Araujo & Costa, Ana Paula Cabral Seixas & de Almeida-Filho, Adiel Teixeira, 2016. "A new method for elicitation of criteria weights in additive models: Flexible and interactive tradeoffAuthor-Name: de Almeida, Adiel Teixeira," European Journal of Operational Research, Elsevier, vol. 250(1), pages 179-191.
    3. D. V. Borrero & M. A. Hinojosa & A. M. Mármol, 2016. "Stable solutions for multiple scenario cost allocation games with partial information," Annals of Operations Research, Springer, vol. 245(1), pages 209-226, October.
    4. Mathieu Martin & Zéphirin Nganmeni & Craig A. Tovey, 2021. "Dominance in spatial voting with imprecise ideals," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 181-195, July.
    5. Rehman, Tahir & Romero, Carlos, 1987. "Multiobjective and Goal Programming Techniques for Solving Agricultural Planning Problems," 1987 Occasional Paper Series No. 4 197536, International Association of Agricultural Economists.
    6. F. R. Fernández & M. A. Hinojosa & J. Puerto, 2002. "Core Solutions in Vector-Valued Games," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 331-360, February.
    7. H. P. Benson, 1998. "Hybrid Approach for Solving Multiple-Objective Linear Programs in Outcome Space," Journal of Optimization Theory and Applications, Springer, vol. 98(1), pages 17-35, July.
    8. Harold P. Benson & Serpil Sayin, 1997. "Towards finding global representations of the efficient set in multiple objective mathematical programming," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(1), pages 47-67, February.
    9. R. Ramesh & Mark H. Karwan & Stanley Zionts, 1989. "Interactive multicriteria linear programming: An extension of the method of Zionts and Wallenius," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(3), pages 321-335, June.
    10. Serpil Sayin, 2003. "A Procedure to Find Discrete Representations of the Efficient Set with Specified Coverage Errors," Operations Research, INFORMS, vol. 51(3), pages 427-436, June.
    11. Adiel T. Almeida-Filho & Adiel T. Almeida & Ana Paula C. S. Costa, 2017. "A flexible elicitation procedure for additive model scale constants," Annals of Operations Research, Springer, vol. 259(1), pages 65-83, December.
    12. Marmol, Amparo M. & Puerto, Justo & Fernandez, Francisco R., 2002. "Sequential incorporation of imprecise information in multiple criteria decision processes," European Journal of Operational Research, Elsevier, vol. 137(1), pages 123-133, February.
    13. Skold, Melvin D., 1987. "Agricultural Price Policies, Policy Goals, and Methods of Estimating Costs of Production," 1987 Occasional Paper Series No. 4 197533, International Association of Agricultural Economists.

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