Scheduling Games In Processing Jobs

As a new branch of modern scheduling, scheduling games is a sort of cross of the scheduling theory and the game theory, which study game theory in scheduling problem and research on the scheduling problem in game theory. The scheduling games has attract high attention in scholars recently. According to different game players,scheduling games is divided into the job scheduling games and the machine scheduling games. So far, many achievements have been created for job scheduling games. In this paper the machine scheduling games is discussed.In machine scheduling games, the job processing time is usually regarded as a constant or a linear or nonlinear function, which has relation to the beginning time, the minimum makespan or the minimum total completion time as the processing cost. However, there are uncertain factors in processing time, this research is focus on the processing time of job and selection of target function. The main work is summarized as follows.1.Study on scheduling games for job processing time. Assuming that the job real processing time is uncertain variable which has the same uncertainty distribution, Nash Bargaining model of two-person cooperative scheduling game problem is established based on the minimum makespan. We prove the optimal solution condition and analyze the solution number and verify the application of model.2.Research in scheduling games for total weighted completion time. For the job processing time is a linear worse function of beginning processing time, we establish the objective function by taking the total weighted completion time as the processing cost and discuss the existing condition of solutions. After comparisons between our model and other two methods with numerical examples, we found that our model has a wide application and the interest distribution strategy for two sides is more reasonable.