An Interactive Programming Method for Solving the Multiple Criteria Problem

Abstract

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.

A Precise Guidance for Fair Local Communities' Development Investments Allocation, Case Study: Damietta Governorate, Egypt

“…Here is a listing of many decision techniques found in the literature; Multi criteria evaluation methods, the outranking approach (Software Electra) by Roy (B. Roy, 1981) and Roy and Vincke (B. Roy and P. Vincke, 1981), other methods developed by some French-Belgian school researchers are: Oreste by Roubens (M. Roubens, 1982) and Pastijn and Leysen (H. Pastijn and J. Leysen, 1989). Others by Newman J.W., 1971), Steuer R. and Choo E.U., 1983;Wierzbicki A., 1980;Zadeh L.A., 1965;Zimmermann H.J., 1991;Zionts S. and Wallenius J., 1976. …”

Designing a Generalized Multiple Criteria Decision Support System

“…(5) They may use a variety of multiple-criteria techniques to compute the efficient solution (e.g., ordinal comparisons [Geoffrion, 1970;Geoffrion et al, 1972;Dyer, 19731, preference modelling [ Vincke ,198 1 1, aspiration levels, pairwise alternative comparisons [ Zionts and Wallenius , 1983 I , aggregation (of the criteria) and/or disaggregation (of a wholistic preference) Jacquet-Lagrsze, 1979 1, consistency checks owma man, 19631, implicit utility functions [Fishburn, 1970;Keeney and Raiffa, 19761 constructed by automatic adaptation to the user's answers [ ~acquet-~agr$ze and Siskos , 1982 3, outranking relations [Roy, 1973;Roy, 1974;Roy, 19771, [ROY, 1978;Bernabeu, 1980 I, linear multicriteria systems [Zionts and Wallenius , 1976;Winkels , 198 1 …”

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