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.
Note to Practitioners
—Automated guided vehicles (AGVs) have been extensive application in various industries, prompting practitioners to integrate the scheduling of machines and AGVs during production planning. To address this realistic production problem, this study develops a novel MILP model. Through comprehensive analyses, integrated scheduling is decomposed into four sub-problems and the correlations between the four sub-problems are accurately presented. For each sub-problem, we establish the corresponding mathematical formulations. Practitioners can use the work in this paper to clearly understand the integrated scheduling problem, and can easily use the optimization software to solve the model. As in our case study, practitioners collate the production information according to their workshop, and the model can give the optimal solution for integrated scheduling in an acceptable time. The optimal solution obtained from the proposed model can guide the practitioners to maximize the productivity of the workshop.