Game theory-based integration of scheduling with flexible and periodic maintenance planning in the permutation flowshop sequencing problem

We introduce a novel game theory approach to the problem of integrating periodic and flexible preventive maintenance and production scheduling for permutation flowshops. Our main contribution is to propose game modeling that allows decision maker to have compromise solutions meeting at best production and maintenance criteria. To achieve this, two new games formulations for the problem are proposed, and a stable solution for the players is obtained through the concept of equilibrium. The first game follows a constructive approach while the second one follows an improvement one. Moreover, to cope with the concept of game types, we proposed two player’s behaviors: rational and non-rational. Extensive experiments are carried out to validate our proposed approaches and developed methods. Besides, the results of the proposed methods are compared against the state of the art, highlighting our contributions and showing improvements.