An algorithm for solving multiobjective problem with multiple Decision Makers

This article aims to develop an algorithm for solving multiobjective linear programming problems with multiple Decision Makers (DMs) which combines the interactive fuzzy method and a heuristic based on iterative computation. DMs’ preference can be quantified with a membership function and a threshold which means the minimum level of acceptance of a solution. The proposed heuristic can automatically search for the best set of weights for the linear utility function. Since the global goal for the proposed heuristic is to minimise the average of all the membership value deviation from the threshold, over- as well as under-achievement in the objective function will be penalised. The algorithm is implemented with Matlab and GAMS and applied to a problem in warehouses with three different objective functions. The results illustrates that the developed algorithm is effective in providing efficient solutions with respect to different preference structures of DMs.