A Bi-Level Programming Approach for Coordinated Task Sequencing and Collision-Free Path Planning in Robotic Mobile Fulfillment Systems

In Robotic Mobile Fulfillment Systems (RMFS), the tight coupling between Task Allocation and Sequencing (TAS) and Conflict-free Path Planning (CPP) poses substantial complexities for operational-level coordination. This paper presents a Bi-Level Programming (BLP) model that jointly captures the interdependent decisions of TAS and CPP. The upper level allocates tasks to Automated Guided Vehicles (AGV) to improve the efficiency and balance local workload, while the lower level generates dynamically collision-free routes that respect real-world movement constraints. To efficiently solve this complicated BLP model, we develop a hybrid metaheuristic algorithm (GA-A*-CP) that integrates a Genetic Algorithm (GA), an improved A* algorithm and a collision-avoidance prediction (CP) mechanism into a unified framework. A key feature of the proposed approach is its iterative closed-loop optimization structure, where TAS decisions guide the generation of CPP results, while the resulting execution feedback capturing spatial constraints and agent interactions is recursively used to refine TAS decisions. This bidirectional coupling enables the RMFS to adapt dynamically congestion and coordination complexity for enhancing operational interaction and coordination. Extensive computational experiments under varying task intensities and AGV configurations show that the proposed BLP approach consistently achieves lower execution costs and better responsiveness in comparison to conventional decoupled approaches. These results show that integrating data-driven feedback across decision layers enables the system to dynamically adapt its planning and allocation strategies in response to execution results. The proposed BLP approach advances the design of a more responsive and structurally coherent architecture for multi-agent logistics systems.