Modelling and optimization of a distributed flow shop group scheduling problem with heterogeneous factories

In this paper, we solve a distributed flow shop group scheduling problem with heterogeneous factories, which we call the distributed heterogeneous flow shop group scheduling problem (DHFGSP). The objective is to minimize the energy consumption cost of the critical factory (the factory with the highest energy consumption cost among all factories). Although the DHFGSP is very meaningful for today's production situation, it has not captured attention so far. Firstly, in this paper, a mixed integer linear model is developed. Secondly, four heuristic methods are presented based on specific scheduling rules and energy consumption cost criteria features. Thirdly, an effective iterative greedy algorithm based on Q-learning (Q_PIG) is proposed. In the Q_PIG, a family ordering rule is proposed to exchange with families in other factories to explore better quality solutions during the local search. Moreover, a Q-learning algorithm is embedded to select operations (family operations or job operations) for the current solution. The embedding of Q-learning enables the current solution to execute high-quality operations. Comprehensive experiments show that the Q_PIG is very effective for the problem solved.