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Computing compromise sets in polyhedral framework. (English) Zbl 0949.90096

From the introduction: In [J. Optim. Theory Appl. 102, 69-82 (1999; Zbl 0934.90066)], the authors stated that, under certain conditions, the compromise set in multicriteria problems enjoys monotonicity properties similar to those in the bicriteria case. The proofs in that paper were not constructive, that is, we established different properties without an explicit description of the compromise set. It seems to be a hard problem to get a suitable parameterization of that set in the general case.
The aim of this note is to give an explicit description of the compromise set provided the linearity of the production-transformation function. This particular case arises in some engineering and economics problems. Thus, the feasible set in consumer theory is bounded by a budgetary constraint defined by a hyperplane with coefficients equal to the prices of the different goods.

MSC:

90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
90C29 Multi-objective and goal programming
91B38 Production theory, theory of the firm

Citations:

Zbl 0934.90066
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References:

[1] Blasco, F.; Cuchillo-Ibáñez, E.; Morón, M. A.; Romero, C., On the monotonicity of the compromise set in multicriteria problems, J. Optim. Theory Appl., 102, 69-82 (1999) · Zbl 0934.90066
[2] Yu, P. L., Multiple-Criteria Decision Making: Concepts, Techniques and Extensions (1985), Plenum Press: Plenum Press New York
[3] Ballestero, E.; Romero, C., Multiple Criteria Decision Making and its Applications to Economic Problems (1998), Kluwer Academic: Kluwer Academic Boston, MA
[4] Freimer, M.; Yu, P. L., Some new results on compromise solutions for group decision problems, Management Science, 23, 688-693 (1976) · Zbl 0365.90012
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