Benchmark for multi-agent pickup and delivery problem in a robotic mobile fulfillment system

The Robotic Mobile Fulfillment System (RMFS) is a "goods-to-worker" system that utilizes pods to store goods and employs robots for pods movement. In the RMFS, the multi-agent pickup and delivery (MAPD) problem which robots complete pickup and delivery tasks and ensure that there are no conflicts has been extensively studied. Several studies have made varying assumptions and layouts to address the MAPD problem, making it challenging to compare their proposed algorithms. This study presents a benchmark for MAPD based on eight factors that influence robot conflicts such as layout scale, pillar, cross-aisle, direction, storage strategy, the number of robots, the number of tasks, and dynamic events. The 12800 instances with 256 different combinations are designed based on 8 parameters with 2 levels that affect the number of conflicts. Identical task-set was used for 8 combinations with different numbers of robots, directions, and with or without cross-aisle. The robot and layout configurations ensure scalability for subsequent research. The objective of MAPD is to minimize the total completion time to demonstrate the robotic efficiency. Three different rules and algorithms were used to determine the lower bound and upper bound. The selection method based on hardness is proposed to obtain a more discriminant benchmark. The 2560 instances are selected to constitute the benchmark considering hardness, exhaustiveness, scalability, and amenity of statistical analysis. This benchmark can be utilized by researchers and practitioners for comparing different methods, rules, and algorithms for the MAPD problem in RMFS, and can be extended according to research problems, objectives, and actual system requirements, such as increasing conflicts for more challenging instances or decreasing conflicts for enhanced safety in the actual system. In conclusion, this paper proposes a benchmark for MAPD in RMFS to be utilized by researchers and practitioners through the analysis of conflicts, robots, and layout.