Solving Multi-Objective Linear Fractional Programming Problems via Zero-Sum Game

This study presents a hybrid algorithm consisting of game theory and the first order Taylor series approach to find compromise solutions to multi-objective linear fractional programming (MOLFP) problems. The proposed algorithm consists of three phases including different techniques: in the first phase, the optimal solution to each LFP problem is found using the simplex method; in the second phase, a zero-sum game is solved to determine the weights of the objective functions via the ratio matrix obtained from a payoff matrix; in the last phase, fractional objective functions of the MOLFP problem are linearized using the 1st order Taylor series. A compromise solution is found by solving the single-objective LP problem constructed in the third phase by using the weights. This algorithm can provide compromise solutions to the problem by constructing different ratio matrices in the second phase. The novelty of this study is that the decision-makers can choose the most suitable solution for their strategy among the compromise solutions. Numerical examples are provided to illustrate the efficiency of the algorithm.