Benjiang Ma
School of Business, Central South University, 410083, Changsha, China
Chunqiao Tan
School of Business, Central South University, 410083, Changsha, China
Beiling Ma
School of Accounting, Hunan University of Commerce, 410205, Changsha, China
ABSTRACT
Based on the solution relation between Linear Multi-Objective Programming (LMOP) and its corresponding weighted linear single objective programming, the dominant set of Pareto efficient solution of (LMOP) is defined. It is pointed out that is an efficient solution of (LMOP) if and only if its dominant set is nonempty. It is proved that the efficient solutions of non-vertexes are considered to be eliminated relative to its some non-inferior vertexes. Further, it is seen that the linear multi-objective programming decision making is equivalent to a simple linear multi-objective programming which is easily transformed into a linear programming to get its solutions. Importantly, for (LMOP), some properties of non-inferior vertexes dominant set are discussed. By the definition of Pareto efficiency of feasible solution of (LMOP), it is proved that if is not the efficient solution of (LMOP) or is the efficient solution of non-vertex of (LMOP), its Pareto efficiency η = 0; if is non-inferior vertex of (LMOP), its Pareto efficiency 0<η≤1. And the sum of the Pareto efficiency of all non-inferior vertexes is equal to one. It is important for us to order these non-inferior vertexes according to their Pareto efficiency.
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How to cite this article
Benjiang Ma, Chunqiao Tan and Beiling Ma, 2013. Problems to Reselect Optimization to Pareto efficient solution for Linear Multi-objective Decision-making. Information Technology Journal, 12: 8095-8101.
DOI: 10.3923/itj.2013.8095.8101
URL: https://scialert.net/abstract/?doi=itj.2013.8095.8101
DOI: 10.3923/itj.2013.8095.8101
URL: https://scialert.net/abstract/?doi=itj.2013.8095.8101
REFERENCES
- Benayoun, R., J. de Montgolfier, J. Tergny and O. Laritchev, 1971. Linear programming with multiple objective functions: Step method (STEM). Math. Program., 1: 366-375.
CrossRef - Lin, J.G., 1976. Maximal vectors and multi-objective optimization. J. Optim. Theory Appl., 18: 41-64.
CrossRef - Wendell, R.E., 1980. Multiple objective mathematical programming with respect to multiple decision-makers. Oper. Res., 28: 1100-1112.
CrossRefDirect Link - Yu, P.L. and M. Zeleny, 1975. The set of all nondominated solutions in linear cases and a multicriteria simplex method. J. Math. Anal. Appl., 49: 430-468.
CrossRef