Assigning parcel destinations to drop-off points in a congested robotic sorting system

Autonomous mobile robots are increasingly used for order picking, order delivery,and parcel sorting. This article studies a robotic sorting system that uses robots totransport parcels from loading stations to drop-off points. While this system providesmore flexible throughput capacity than conventional sorting systems, its perfor-mance is significantly affected by the robot travel distance and robot congestion.We study the problem of assigning parcel destinations to drop-off points to mini-mize the throughput time, trading off travel distance and congestion. First, an openqueuing network (OQN) with finite capacity queues is constructed to estimate thecongested throughput time. A decomposition method based on the analysis of thetandem queuing network of each aisle is developed to solve the OQN. Second, usingthe obtained throughput time as an objective and the destination assignments as deci-sions, we formulate an optimization model and solve the problem using an adaptivelarge neighborhood search (ALNS) algorithm. We validate the accuracy of the OQNby simulation and verify the efficiency of the ALNS algorithm by comparing it withGurobi, a tabu search algorithm, several heuristic assignment rules, and the rule usedby our case company, that assigns high demands close to loading stations. The resultsshow that the ALNS solution provides a relatively low throughput time by dispers-ing destinations with high demands over drop-off points. In addition, we investigatethe effects of different system layouts and travel path topologies. We also show thatthe ALNS assignment rule produces substantially lower operational costs than theheuristic assignment rules for a given required throughput capacity.