Scheduling flexible job shop problem subject to machine breakdown with game theory

Flexible job shop scheduling problem subject to machine breakdown is one of the challenging problems in manufacturing field. In this problem, robustness and stability are the two important measures to evaluate the quality of rescheduling. Considering these two objectives cannot be optimised simultaneously and the equilibrium of two objectives has game procedure, non-cooperative game theory with complete information is applied to build new scheduling model. In this game model, the two objectives can be seen as the two sides which take part in the game. Firstly, pre-scheduling without considering machine failure is generated, and then the operations affected by machine failure are obtained according to time at which machine breakdown happens. The decision made by each side should obtain better robust and stable performance. To achieve the optimal objects, Nash Equilibrium (NE) solution for each side is achieved. Considering NE solution may not exist or there are more than one NE solutions, concepts of ideal NE solution and near NE solution are proposed. To avoid huge decision searching space when the number of operations is more than two, an NE searching algorithm under multi-stage game based on the two concepts is also proposed to find NE or near NE solutions. In order to prove the feasibility and effectiveness of the method, classical problems are employed with random breakdown. The computational results show the feasibility and effectiveness of the new model and the new approaches.