The Research On Production Transportation Coordinated Game Scheduling Problem With Batching Machine

Manufacturing industry plays a leading role in the national economy.Production and transportation are two indispensable links in manufacturing enterprises.The coupling between production and transportation can reduce production costs,improve the production efficiency of manufacturing enterprises,and reduce energy consumption.In the production process,machines,orders,transportation,etc.interact with each other,and there are both cooperation and conflict.Game theory is widely used to solve decision-making problems with multiple agents,multiple objectives and conflicting objective functions of multiple agents.In order to obtain satisfactory scheduling schemes for various agents,it is of practical significance to study production and transportation coordination scheduling problems based on game theory.In this paper,the production and transportation coordinated and scheduling of single batching machine and multiple parallel batching machines are extracted from the soaking pit heating and ingot transportation links based on the production and casting process of iron and steel enterprises.Cooperative game theory and non-cooperative game theory are used to study respectively.（1）Aiming at the production and transportation coordinated scheduling problem of a single batching machine,a cooperative game model is established with the job as the game player and the saved cost as the characteristic function.The production and transportation coordinated scheduling problem is transformed into the cost saving problem of maximizing the cooperative game alliance.Aiming at the problem of the same transportation time and processing time,this paper analyzes the nature of the game and proves that the cooperative game is a ₀σ-group additive game,so it is a balanced game with a non-empty core.It is proved that theβrule based cost allocation method is a kind of core allocation,and the above conclusions are verified by numerical examples.For general problems,Q-learning algorithm is designed to solve the optimal scheduling order of each federation,and the characteristic value of each connected federation are obtained.Cost savings are allocated throughβrules.The feasibility of the cooperative game model and the effectiveness of the Q-learning algorithm in solving the optimal scheduling andβrule cost allocation of the alliance are verified by numerical examples.（2）In this part,a mixed integer programming model is established to minimize the total completion time of jobs,considering the constraints of the number of transport vehicles,transport capacity of transport vehicles,and batching machine capacity,etc.There is a competitive relationship between customer orders,and a non-cooperative game model is established with the jobs as the game player,the job can choose the transport vehicle and the batching machine as the strategy,and the completion time of the job as the payoff.Due to the complexity of the problem scale,the definition of approximate Nash equilibrium solution is given based on the concepts of Nash equilibrium solution and ideal Nash equilibrium solution.The mapping between the objective function,approximate Nash equilibrium solution and Q-learning algorithm reward is established,and the Q-learning algorithm is used to solve the approximate Nash equilibrium solution of the non-cooperative game model of the scheduling problem of multiple parallel batching machines.