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An Interactive Programming Method for Solving the Multiple Criteria Problem

  • Stanley Zionts

    (European Institute for Advanced Studies in Management and School of Management, State University of New York at Buffalo)

  • Jyrki Wallenius

    (European Institute for Advanced Studies in Management and the Helsinki School of Economics and Business Administration)

In this paper a man-machine interactive mathematical programming method is presented for solving the multiple criteria problem involving a single decision maker. It is assumed that all decision-relevant criteria or objective functions are concave functions to be maximized, and that the constraint set is convex. The overall utility function is assumed to be unknown explicitly to the decision maker, but is assumed to be implicitly a linear function, and more generally a concave function of the objective functions. To solve a problem involving multiple objectives the decision maker is requested to provide answers to yes and no questions regarding certain trade offs that he likes or dislikes. Convergence of the method is proved; a numerical example is presented. Tests of the method as well as an extension of the method for solving integer linear programming problems are also described.

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File URL: http://dx.doi.org/10.1287/mnsc.22.6.652
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Article provided by INFORMS in its journal Management Science.

Volume (Year): 22 (1976)
Issue (Month): 6 (February)
Pages: 652-663

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Handle: RePEc:inm:ormnsc:v:22:y:1976:i:6:p:652-663
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