We study the coordinated scheduling problem of production and pre-production transportation for a single batching machine.The objective is to minimize the total production cost related to the completion time.The scheduling problem is transformed into a cooperative game model with the jobs as the players and the maximal cost savings of the coalition as the characteristic function.For the case of the same transportation time and processing time,it is proved that the cooperative game has a non-empty core,and the β rule can get a core allocation.For general problems,the Q-learning algorithm is designed to solve the optimal scheduling of the coalition,and the β rule is used to allocate the cost savings.Numerical examples verify the feasibility of the cooperative game model and the effectiveness of the Q-learning algorithm and β rule for cost savings allocation.
维普
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