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A new mathematical model for selecting the most preferable alternative in a group decision making problem

This paper discusses the way of selecting the best alternative in a group decision making environment. For this purpose, each decision maker defines the weights vector of the ranks using pairwise comparisons and a mathematical model similar to the one in Data Envelopment Analysis (DEA) is developed. At first, a CCR type model is developed in which decision making units have one input (equal to one) and some outputs [16, 17, 18]. Then, some constraints will be added to the model in order to meet the requirements in such a way that it can be applied in a preferential voting system. Finally, some new objective functions will be added to the model in order to apply the majority decision rule. The resulted multi-objective function is converted in to a multi-objective linear programming model from which the optimal solution is obtained. It worth noting that some useful information can be obtained from the above mentioned model.