Integrated distributed flexible job shop scheduling and vehicle routing problem via Q-learning-based evolutionary algorithms

In recent years, optimizing the processes in manufacturing supply chains has received much attention from both academia and industry. Production and distribution are two pivotal parts of manufacturing supply chains and therefore, integrated production and distribution planning is essential to optimize the overall performance of supply chains. To address this problem, this study proposes a mixed integer programming model to minimize the maximum completion time, where a set of jobs is processed in a distributed flexible job shop environment, and then they are delivered to their corresponding customers by using a group of vehicles as planned routes. To solve the model, a Q-learning-based evolutionary algorithm with hybrid search strategies is proposed. To enhance the search process of the algorithm- (1) three heuristics are combined to produce quality solutions in the initial population, (2) problem-specific crossover, mutation, and iterated local search methods are designed, and their combinations are formed as three search strategies, and (3) a Q-learning method is used to adaptively choose effective search strategies for updating population. The developed model and algorithm are compared against the CPLEX (exact solver) and three well-known meta -heuristics from the literature. The numerical experiments suggest that the proposed algorithm shows promising performances in dealing with the problem under study.