A Novel Mathematical Model for the Flexible Job-Shop Scheduling Problem With Limited Automated Guided Vehicles

Automated Guided Vehicles (AGVs) have found widespread application in discrete manufacturing systems. In flexible job-shop environments, the integrated scheduling of machines and AGVs is a significant research direction to improve the productivity. However, the existing mathematical model assigns non-existent transport tasks to the corresponding AGVs, resulting in poor performance. To tackle this weakness, this paper proposes a novel mixed integer linear programming (MILP) model. Firstly, the flexible job-shop scheduling problem with limited AGVs (FJSPLA) is decomposed into four sub-problems, and the interactions and dependencies between the sub-problems are elaborated. Secondly, the existence of transport tasks is explained in detail based on the disjunctive graph model. Subsequently, a more efficient MILP model is proposed, leveraging insights from the four sub-problems and the disjunctive graph model. Finally, comparison experiments are conducted, encompassing two benchmarks (FJSPT and EX), along with a real-world case. The proposed model exhibits a more streamlined formulation with fewer decision variables and constraints in comparison to existing models. It successfully proves optimality for the most challenging instance FJSPT7 as well as 15 instances in EX benchmark. Compared with the existing model, the experimental results not only demonstrate the effectiveness and superior performance of the proposed model but also show the practicality in addressing real workshop problems.