Autonomous Mobile Robots (AMRs) play a critical role in flexible material handling within modern manufacturing systems, enabling increased productivity and reduced operational waste. However, inefficiencies in task scheduling, routing, and battery management remain a significant operational challenge, as existing approaches typically rely on fixed charging schedules and fragmented decision-making, often resulting in unplanned downtime and missed deadlines. This paper proposes a Mixed Integer Linear Programming (MILP) optimization model that integrates multiple decision layers including task sequencing, routing, and charging detour selection into a unified mathematical framework. The model operates under interdependent constraints incorporating battery State of Charge (SOC), task durations, charging station availability, route feasibility, and task precedence. SOC transitions are tracked by accounting for energy consumption during both travel and task execution, as well as energy recovery during charging in the Constant Current (CC) phase. Moreover, routing feasibility is ensured through flow conservation and subtour elimination constraints. A weighted multi-objective function is formulated to minimize total task tardiness and total charging time, enabling data-driven routing and charging decisions without relying on predefined schedules. The model is validated through implementing it in diverse manufacturing scenarios, including multi-AMR fleets. Results demonstrate measurable improvements in charging stops, task tardiness, and production efficiency compared to standard baseline cases, confirming the proposed framework as a scalable and adaptive solution for modern manufacturing environments.

Keywords

Autonomous Mobile Robots (AMRs), Mixed Integer Linear Programming (MILP), Task Scheduling and Routing, Tardiness, Battery Management.