A hybrid collaborative framework for integrated production scheduling and vehicle routing problem with batch manufacturing and soft time windows

This paper studies a new integrated production scheduling and vehicle routing problem where the production of customer orders is performed under a batch manufacturing environment and order deliveries are made by multi-trip heterogeneous vehicles in soft time windows. A bi-objective mixed-integer programming model with maximizing total profits and minimizing total weighted earliness and tardiness has been established. We develop a hybrid collaborative framework to solve this problem, which nests the collaborative mechanism in an opti-mization mode based on the hybrid algorithm. In the collaborative mechanism, a property on the ideal optimal departure time of the tour is first proposed, based on which an exact strategy is developed to simultaneously coordinate batch manufacturing and tour departure schedules. High-quality integrated solutions are provided by simultaneously making both production scheduling and vehicle routing decisions. Then, in order to get the best integrated solution, we adopt a multi-objective evolutionary algorithm improved by an adaptive large neigh-borhood search strategy based on the specific problem and coding form to realize the optimization mode. Computational experiments are performed on a dataset containing 30 instances of various scales. The results show that the proposed hybrid collaborative framework performs well in cardinality, convergence, distribution and spread, which is a very competitive method to solve this problem.