Game theoretic modelling of the integrated production and preventive maintenance scheduling problem in permutation flowshops

In this paper, the main purpose and work is to propose scheduling algorithm based on the non-cooperative game theory for the integrated permutation flowshop problem with preventive maintenance. The goal is to optimize two criteria simultaneously: minimization of total completion time (makespan) for production part and minimization of total Earliness/Tardiness of PM activities for maintenance part. Moreover, to cope with the concept of game types we proposed two player behaviors: non-rational and rational behavior. In this research, the Nash equilibrium in game theory based approach is used to deal with the multiple objectives. Computational experiment on both standard PFSP problems and non- standard PM instances shows the effectiveness of the proposed solving algorithms.