Variable neighborhood search-based methods for integrated hybrid flow shop scheduling with distribution

With the rapid development of make-to-order pattern including E-commerce and takeout and catering service in restaurants, the study of integrated scheduling and distribution receives more and more attentions. Based on a practical order picking and distribution system, a three-stage hybrid flow shop scheduling problem with distribution is studied. Each order is processed on the hybrid flow shop which consists of identical parallel machines with sequence-dependent setup times at stage 1, identical parallel machines at stage 2 and dedicated machines at stage 3, followed by a multi-trip traveling salesman problem with capacitated vehicles for customers of different destination areas. A mixed-integer linear programming model is formulated to minimize the maximum delivery completion time. A variable neighborhood search (VNS)-based method, a four-layered constructive heuristic method (denoted by \(CH_{VNS}\)) and a hybrid heuristic method (denoted by \(CONS_{VNS}\)) which combines the VNS method and the \(CH_{VNS}\) method are developed to solve the problems with practical size. Computational experiments show the effectiveness and efficiency of the proposed methods.