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Aspiration-Based Search Algorithm (ABSALG) for Multiple Objective Linear Programming Problems: Theory and Comparative Tests

Author

Listed:
  • Vahid Lotfi

    (School of Management, University of Michigan--Flint, Flint, Michigan 48502)

  • Yong. S. Yoon

    (Korea Telecom, 17, Woomyun-dong Suhcho-ku, Seoul, Korea)

  • Stanley Zionts

    (School of Management, State University of New York, Buffalo, New York 14260)

Abstract

We develop an interactive method for multiple objective linear programming based on aspiration levels of a decision maker. The method assumes an unknown pseudoconcave preference structure of a decision maker throughout the decision process, and the decision maker's ability to select a preferred solution from p + 1 alternatives, where p is the number of objectives. In addition to presenting the supporting theory and algorithm, we perform a comparative study using a fictitious decision maker, comparing our approach to those of Steuer and Choo (Steuer, R. E., E. Choo. 1983. An interactive weighted Tchebycheff procedure for multiple objective programming. Math. Prog. 26 326--344.) and Reeves and Franz (Reeves, G. R., L. Franz. 1985. A simplified interactive multiple objective linear programming procedure. Comp. & Oper. Res. 12 589--601.). All three methods are interactive. During an iteration, each method presents several solution alternatives to the decision maker simultaneously. Our approach utilizes a Tchebycheff function that facilitates attainment of an optimum at a nonextreme point solution. The statistics collected in the comparative study provide insights into the nature of the algorithms and the behavior of the solution techniques with different categories of problem structure and different underlying utility functions.

Suggested Citation

  • Vahid Lotfi & Yong. S. Yoon & Stanley Zionts, 1997. "Aspiration-Based Search Algorithm (ABSALG) for Multiple Objective Linear Programming Problems: Theory and Comparative Tests," Management Science, INFORMS, vol. 43(8), pages 1047-1059, August.
    • Handle: RePEc:inm:ormnsc:v:43:y:1997:i:8:p:1047-1059
    DOI: 10.1287/mnsc.43.8.1047
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    Cited by:

    1. Lotfi, Vahid, 1995. "Implementing flexible automation: A multiple criteria decision making approach," International Journal of Production Economics, Elsevier, vol. 38(2-3), pages 255-268, March.
    2. Sun, Minghe, 2005. "Some issues in measuring and reporting solution quality of interactive multiple objective programming procedures," European Journal of Operational Research, Elsevier, vol. 162(2), pages 468-483, April.
    3. Chang, Ching-Ter, 2011. "Multi-choice goal programming with utility functions," European Journal of Operational Research, Elsevier, vol. 215(2), pages 439-445, December.
    4. M Köksalan & E Karasakal, 2006. "An interactive approach for multiobjective decision making," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(5), pages 532-540, May.
    5. Angur, Madhukar G. & Lotfi, Vahid & Sarkis, Joseph, 1996. "A hybrid conjoint measurement and bi-criteria model for a two group negotiation problem," Socio-Economic Planning Sciences, Elsevier, vol. 30(3), pages 195-206, September.

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