Cooperative game theory based coordinated scheduling of production and transportation of parallel machines with deterioration effects

Abstract

Cooperative game theory is used to study the production and transportation scheduling problem of parallel machines with deterioration effects. Jobs with an initial scheduling order are processed on parallel machines and then transported to customers. Penalties are incurred for early or late completion if the jobs are not completed on the due dates. Considering that jobs can rearrange the scheduling order in the coalition through cooperation to bring about cost savings, the cooperative game model is constructed by considering the jobs as players and taking the maximum cost savings of the coalition as the characteristic function. It is proven that when jobs have the same normal processing time and deterioration rate, the cooperative game has a non-empty core, and a core allocation can be obtained from the β-rule allocation method. A Dual Replay Buffer Double DQN (DRB-DDQN) algorithm is designed to get the optimal schedule of the coalition. Experiments demonstrate the effectiveness of the DRB-DDQN and β-rule allocation method in solving the game scheduling problem.