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Computational experience concerning payoff tables and minimum criterion values over the efficient set. (English) Zbl 0632.90074

Minimum criterion values from payoff tables have often been used in multiple objective linear programming (MOLP). The assumption has often been that the minimum criterion values from payoff tables provide reasonably accurate estimates of the minimum criterion values over the efficient set. In this paper, however, we report computational exprience that demonstrates that the discrepancies between the payoff table minima and the minima over the efficient set can often be large. This tends to imply that the field of multiple objective programming needs a better method than payoff tables for estimating the minimum criterion values over the efficient set. The paper concludes with a discussion of a simplex-based procedure for deterministically computing the minimum criterion values over the efficient set that has potential in large MOLP applications.

MSC:

90C31 Sensitivity, stability, parametric optimization

Software:

ADBASE; EFFACET
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Full Text: DOI

References:

[1] Belenson, S. M.; Kapur, K. C., An algorithm for solving multicriterion linear programming problems with examples, Operational Research Quarterly, 24, 1, 65-77 (1973) · Zbl 0261.90035
[2] Benayoun, R.; de Montgolfier, J.; Tergny, J.; Larichev, O., Linear programming with multiple objective functions: The step method (Stem), Mathematical Programming, 1, 3, 336-375 (1971) · Zbl 0242.90026
[3] Charnes, A.; Cooper, W. W.; Evans, J. P., Connectedness of the efficient extreme points in linear multiple objective programs (1972), College of Business Administration, University of North Carolina: College of Business Administration, University of North Carolina Chapel Hill, NC
[4] Dessouky, M. I.; Ghiassi, M.; Davis, W. J., Estimates of the minimum nondominated criterion values in multiple-criteria decision-making, Engineering Costs and Production Economics, 10, 95-104 (1986)
[5] Ecker, J. G.; Hegner, N. S.; Kouada, I. A., Generating all maximal efficient faces for multiple objective linear programs, Journal of Optimization Theory and Applications, 30, 3, 353-381 (1980) · Zbl 0393.90087
[6] Fandel, G., Optimale Entscheidung bei Mehrfacher Zielsetzung, (Lecture Notes in Economics and Mathematical Systems (1972), Springer: Springer Berlin), No. 76 · Zbl 0247.90032
[7] Gal, T., A general method for determining the set of all efficient solutions to a linear vectormaximum problem, European Journal of Operational Research, 1, 5, 307-322 (1977) · Zbl 0374.90044
[8] Gal, T., A note on the size reduction of the objective functions matrix in vector maximum problems, (Lecture Notes in Economics and Mathematical Systems (1980), Springer: Springer Berlin), 74-84, No. 177
[9] Grauer, M.; Lewandowski, A.; Wierzbicki, A., Didass—theory, implementation and experiences, (Lecture Notes in Economics and mathematical Systems (1984), Springer: Springer Berlin), 22-30, No. 229 · Zbl 0547.90053
[10] Hafkamp, W.; Nijkamp, P., Towards an integrated national-regional environmental-economic model, (Rinaldi, S.; etal., Environmental Systems Analysis of Management (1982), North-Holland: North-Holland Amsterdam), 653-664
[11] Isermann, H., The enumeration of the set of all efficient solutions for a linear multiple objective program, Operational Research Quarterly, 28, 3, 711-725 (1977) · Zbl 0372.90086
[12] Isermann, H., Operating manual for the Effacet multiple objective linear programming package (1984), Fakultat fur Wirtschaftswissenschaften, Universitat Bielefeld: Fakultat fur Wirtschaftswissenschaften, Universitat Bielefeld FRG
[13] Kok, M.; Lootsma, F. A., Pairwise-comparison methods in multiple objective programming, with applications in a long-term energy-planning model, European Journal of Operational Research, 22, 1, 44-55 (1985) · Zbl 0578.90040
[14] Kornbluth, J. S.H., Duality, indifference, and sensitivity analysis in multiple objective linear programming, Operational Research Quarterly, 25, 4, 599-614 (1974) · Zbl 0298.90042
[15] Masud, A. S.; Hwang, C. L., Interactive sequential goal programming, Journal of the Operational Research Society, 32, 391-400 (1981) · Zbl 0452.90069
[16] Rietveld, P., Multiple Objective Decision Methods and Regional Planning (1980), North-Holland: North-Holland Amsterdam
[17] Silverman, J.; Steuer, R. E.; Whisman, A. W., Computer graphics at the multicriterion computer/user interface, (Lecture Notes in Economics and Mathematical Systems (1985), Springer: Springer Berlin), 201-213, No. 242
[18] Spronk, J.; Telgen, J., An ellipsoidal interactive multiple goal programming method, (Lecture Notes in Economics and Mathematical Systems (1981), Springer: Springer Berlin), 380-387, No. 190 · Zbl 0465.90082
[19] Steuer, R. E., Operating manual for the Adbase multiple objective linear programming package (1983), College of Business Administration, University of Georgia: College of Business Administration, University of Georgia Athens, GA
[20] Steuer, R. E., Multiple Criteria Optimization: Theory, Computation, and Application (1986), Wiley: Wiley New York · Zbl 0663.90085
[21] Weistroffer, H. R., Careful usage of pessimistic values is needed in multiple objectives optimization, Operations Research Letters, 4, 1, 23-26 (1985) · Zbl 0569.90087
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