MILP Modeling and Optimization of Multi-Objective Three-Stage Flexible Job Shop Scheduling Problem With Assembly and AGV Transportation

In the real manufacturing environment, the machining stage of the jobs and the assembly stage of the products are often completed in different workshops. In addition, automatic guided vehicle (AGV) plays an indispensable role in the transportation of jobs from machining workshop to assembly workshop. This paper studies multi-objective three-stage flexible job shop scheduling problem (FJSP-T-A) with minimizing both the makespan and the total energy consumption. In FJSP-T-A, jobs are first machined in flexible job shop, then are transported to assembly workshop by AGVs, and finally are assembled in assembly workshop. To solve this problem, a mixed-integer linear programming model (MILP) is developed and the optimal Pareto front for small-scale instances are solved by using the$\varepsilon $-method. FJSP-T-A is NP-hard, and an efficient multi-population co-evolutionary algorithm (MPCEA) is proposed to efficiently solve large-scale instances. In the MPCEA, we design a strategy to select relatively high-quality individuals to enhance the algorithm’s convergence speed, and design a multi-objective variable-neighborhood search (MOVNS) method to improve the local search ability. Experiments are conducted to prove the effectiveness of the MILP model and the MPCEA.