Linear programming with multiple objective functions: Step method (stem)
Tóm tắt
This paper describes a solution technique for Linear Programming problems with multiple objective functions. In this type of problem it is often necessary to replace the concept of “optimum” with that of “best compromise”. In contrast with methods dealing with a priori weighted sums of the objective functions, the method described here involves a sequential exploration of solutions. This exploration is guided to some extent by the decision maker who intervenes by means of defined responses to precise questions posed by the algorithm. Thus, in this man-model symbiosis, phases of computation alternate with phases of decision. The process allows the decision-maker to “learn” to recognize good solutions and the relative importance of the objectives. The final decision (best compromise) furnished by the man-model system is obtained after a small number of successive phases.
Tài liệu tham khảo
R. Benayoun and J. Tergny, “Mathematical Programming with multi-objective functions: a solution by P.O.P. (Progressive Orientation Procedure),”Revue METRA, Vol. 9, no. 2 (1970) 279–299.
R. Benayoun, J.C. Holl and P. Leyrat, “Gestion prévisionnelle des cadres d'entreprises,” Communication au Symposium on Mathematical Models and Manpower Systems, Porto — (Sept. 1969).
P. Bod, “Programmation linéaire dans le cas de plusieurs fonctions objectif données simultanément,”Publ. Math. Inst. Hungar. Acad. Sc. (séries B) no. 8 (1963) 541–554.
G. Boldur and I.M. Stancu-Minasian, “La résolution de certains problèmes de programmation linéaire multidimensionnelle,” Session Scientifique du Centre de Calcul Economique et Cybernétique Economique Bucarest (1969).
S.K. Gupta, C. Maier-Rothe and M.F. Stankard, “Choosing between multiple objective alternatives: a linear programming approach,” Management Science Center, University of Pennsylvanie (Dec. 1968).
J. Saska, “Linear Multi-Programming, Economicko-Mathematicky,” Obzor 3 Geskolovenska Academie (Ved. 1968).
I.M. Stancu-Minasian, “The solution of transportation network in the case of multiple criteria,” The Center of Economic Computation and Economic Cybernetics, Bucarest (in preparation).