Stackelberg game for critical job scheduling in service-oriented manufacturing plants

For solving the critical job-scheduling problem in the service-oriented manufacturing plants, a two level-nested Stackelberg game model was put forward, which was made up of two sub-games, that is, dynamic Stackelberg sub-game and static non-cooperative sub-game. The dynamic Stackelberg sub-game was for the decision between the critical job and non-critical jobs while static non-cooperative sub-game was for the decision among non-critical jobs. In the Stackelberg game model, the leader corresponded to the critical job, and followers corresponded to the non-critical jobs; the strategies of each job corresponded to the alternative machines related to operations of this job; the payoff of each job was defined as its corresponding cost including processing cost, inventory cost, transportation cost, and tardiness cost, etc. Therefore, the optimal scheduling results were determined by the Stackelberg equilibrium point of this game. In order to find the equilibrium point efficiently and effectively, a hybrid adaptive genetic algorithm was designed based on hill-climbing method. A numerical case study demonstrates the validity of the presented game model and its related resolving algorithm.