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This paper proposes a new methaheurstic to solve the flow shop scheduling problem which is considered as an N P − hard problem for relatively high dimensions. The flow shop scheduling problems are commonly encountered in many industrial applications and manufacturing systems. For the purpose, a mixed integer linear programming model is presented to articulate the relationship between the objective function and the constraints of the problem. A proposed hybrid greedy algorithm based on the Nash equilibrium concept and the genetic operators is an attempt to outperform the classical algorithms frequently employed to approach the optimal solution of scheduling problems. In order to minimize the makespan criterion, various computational experiments were conducted for different size of the problem. Furthermore, a comparative study is performed to assess the developed methaheuristic against other algorithms. Simulations have shown that the proposed procedure is the most effective and robust. [ABSTRACT FROM AUTHOR]