×

Equitable aggregations and multiple criteria analysis. (English) Zbl 1067.90079

Summary: In the past decade, increasing interest in equity issues resulted in new methodologies in the area of operations research. This paper deals with the concept of equitably efficient solutions to multiple criteria optimization problems. Multiple criteria optimization usually starts with an assumption that the criteria are incomparable. However, many applications arise from situations which present equitable criteria. Moreover, some aggregations of criteria are often applied to select efficient solutions in multiple criteria analysis. The latter enforces comparability of criteria (possibly rescaled). This paper presents aggregations which can be used to derive equitably efficient solutions to both linear and nonlinear multiple optimization problems. An example with equitable solutions to a capital budgeting problem is analyzed in detail. An equitable form of the reference point method is introduced and analyzed.

MSC:

90B50 Management decision making, including multiple objectives
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Behringer, F. A., Linear multiobjective maxmin optimization and some Pareto and lexmaxmin extensions, OR Spektrum, 8, 25-32 (1986) · Zbl 0598.90084
[2] Dubois, D.; Fortemps, Ph.; Pirlot, M.; Prade, H., Leximin optimality and fuzzy set-theoretic operations, European Journal of Operational Research, 130, 20-28 (2001) · Zbl 1068.90617
[3] Ehrgott, M., Discrete decision problems, multiple criteria optimization classes and lexicographic max-ordering, (Stewart, T. J.; van den Honert, R. C., Trends in Multicriteria Decision Making (1998), Springer: Springer Berlin), 31-44 · Zbl 0923.90126
[4] Fandel, G.; Gal, T., Redistribution of funds for teaching and research among universities: The case of North Rhine-Westphalia, European Journal of Operational Research, 130, 111-120 (2001) · Zbl 1012.91501
[5] Kalcsics, J.; Nickel, S.; Puerto, J.; Tamir, A., Algorithmic results for ordered median problems, Operations Research Letters, 30, 149-158 (2002) · Zbl 1010.90036
[6] Kostreva, M. M.; Ogryczak, W., Linear optimization with multiple equitable criteria, RAIRO Operations Research, 33, 275-297 (1999) · Zbl 0961.90059
[7] Kostreva, M. M.; Ogryczak, W., Equitable approaches to location problems, (Thill, J.-C., Spatial Multicriteria Decision Making and Analysis-A Geographic Information Sciences Approach (1999), Ashgate: Ashgate Brookfield), 103-126
[8] (Lewandowski, A.; Wierzbicki, A. P., Aspiration Based Decision Support Systems-Theory, Software and Applications (1989), Springer: Springer Berlin) · Zbl 0754.00006
[9] López-de-los-Mozos, M. C.; Mesa, J. A., The maximum absolute deviation measure in location problems on networks, European Journal of Operational Research, 135, 184-194 (2001) · Zbl 1077.90547
[10] Luss, H., On equitable resource allocation problems: A lexicographic minimax approach, Operations Research, 47, 361-378 (1999) · Zbl 1047.91043
[11] Marchi, E.; Oviedo, J. A., Lexicographic optimality in the multiple objective linear programming: The nucleolar solution, European Journal of Operational Research, 57, 355-359 (1992) · Zbl 0767.90077
[12] Marsh, M. T.; Schilling, D. A., Equity measurement in facility location analysis: A review and framework, European Journal of Operational Research, 74, 1-17 (1994) · Zbl 0800.90631
[13] Marshall, A. W.; Olkin, I., Inequalities: Theory of Majorization and Its Applications (1979), Academic Press: Academic Press New York · Zbl 0437.26007
[14] Miettinen, K.; Mäkelä, M. M., On scalarizing functions in multiobjective optimization, OR Spectrum, 24, 193-213 (2002) · Zbl 1040.90037
[15] Ogryczak, W., On the lexicographic minimax approach to location problems, European Journal of Operational Research, 100, 566-585 (1997) · Zbl 0921.90106
[16] Ogryczak, W., Inequality measures and equitable approaches to location problems, European Journal of Operational Research, 122, 374-391 (2000) · Zbl 0961.90053
[17] Ogryczak, W., Multiple criteria linear programming model for portfolio selection, Annals of Operations Research, 97, 143-162 (2000) · Zbl 0961.91021
[18] Ogryczak, W., On goal programming formulations of the reference point method, Journal of the Operational Research Society, 52, 691-698 (2001) · Zbl 1179.90301
[19] Ogryczak, W.; Studziński, K.; Zorychta, K., DINAS: A computer-assisted analysis system for multiobjective transshipment problems with facility location, Computers and Operations Research, 19, 637-647 (1992)
[20] Ogryczak, W.; Śliwiński, T., On solving linear programs with the ordered weighted averaging objective, European Journal of Operational Research, 148, 80-91 (2003) · Zbl 1037.90045
[21] Ogryczak, W.; Tamir, A., Minimizing the sum of the k largest functions in linear time, Information Processing Letters, 85, 117-122 (2003) · Zbl 1050.68155
[22] Rawls, J., The Theory of Justice (1971), Harvard University Press: Harvard University Press Cambridge
[23] Steuer, R. E., Multiple Criteria Optimization-Theory, Computation and Applications (1986), John Wiley and Sons: John Wiley and Sons New York · Zbl 0663.90085
[24] White, D. J., A bibliography on the applications of mathematical programming multiple-objective methods, Journal of the Operational Research Society, 41, 669-691 (1990) · Zbl 0707.90083
[25] Wierzbicki, A. P., A mathematical basis for satisficing decision making, Mathematical Modelling, 3, 391-405 (1982) · Zbl 0521.90097
[26] (Wierzbicki, A. P.; Makowski, M.; Wessels, J., Model Based Decision Support Methodology with Environmental Applications (2000), Kluwer: Kluwer Dordrecht) · Zbl 0992.91003
[27] Yager, R. R., On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Transactions on Systems, Man and Cybernetics, 18, 183-190 (1988) · Zbl 0637.90057
[28] Yager, R. R., On the analytic representation of the Leximin ordering and its application to flexible constraint propagation, European Journal of Operational Research, 102, 176-192 (1997) · Zbl 0948.90112
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.