Most of real-life problems, including design, optimization, scheduling and control, etc., are inherently
characterized by multiple conflicting objectives, and thus multi-objective linear programming
(MOLP) problems are frequently encountered in the literature. One of the biggest difficulties
in solving MOLP problems lies in the trade-off among objectives. Since the optimal solution of one
objective may lead other objective(s) to bad results, all objectives must be optimized simultaneously.
Additionally, the obtained solution will not satisfy all the objectives in the same satisfaction degree.
Thus, it will be useful to generate a set of compromise solutions in order to present it to the decision
maker (DM). With this motivation, after determining a modified payoff matrix for MOLP, all possible
ratios are formed between all rows. These ratio matrices are considered a two person zero-sum
game and solved by linear programming (LP) approach. Taking into consideration the results of the
related game, the original MOLP problem is converted to a single objective LP problem. Since there
exist numerous ratio matrices, a set of compromise solutions is obtained for MOLP problem. Numerical
examples are used to demonstrate this approach.
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