<p>As the use of autonomous mobile robots (AMRs) has increased in material handling systems, it has become essential to incorporate their unique characteristics and constraints into the pickup and delivery problem. Additionally, request scheduling and charging arrangements should be considered simultaneously to maintain battery feasibility during transportation tasks. Realistic charging and discharging assumptions must also be integrated into the model. Minimizing request delays is crucial, as delays can negatively impact productivity. This study addresses the scheduling problem in material handling systems, aiming to minimize the total tardiness of transportation requests while considering the specific characteristics of AMRs. This study also considers the partial recharging policy, nonlinear charging, and load-dependent discharging. A mixed-integer linear programming model was developed and an adaptive large neighborhood search (ALNS) algorithm was constructed to minimize total tardiness, with travel time minimization also included. A full factorial design with seven factors was conducted, revealing that layout, transportation request size, the number of AMRs, and battery levels are significant factors influencing total tardiness, while all factors significantly affect travel time. The results underscore the importance of considering charging and discharging mechanisms in effectively solving this problem.</p>