Assignment of parcels to loading stations in robotic sorting systems

Autonomous robots are increasingly used in warehouses in the recent decade, due to their flexible throughput capacity and low operating cost. Sorting may be the newest warehouse scene where autonomous robots are adopted. We consider a robotic sorting system with a two-tier layout where robots drive on the top mezzanine and sort parcels from loading stations (inputs) to drop-off points (outputs) via spiral conveyors connected to roll containers at the lower tier. We investigate the assignment optimization of arrival parcels to loading stations, to minimize the system throughput time. We first build an open queueing network to estimate the system performance and validate its accuracy by simulation. Then, we formulate an integer-programming model that takes the minimization of throughput time as the objective. We prove the computational complexity of the model by transferring it into an order batching problem, and design a Tabu search algorithm for solution. We evaluate the efficiency of the algorithm by both numerical experiments that take the Gurobi solver, the random and closest assignment rules as the comparison target, and a real case study. The results show that our algorithm can reduce the system throughput time by 7.09% and 8.76% and lower the manual cost by 11.99% and 17.50% over the random and the closest assignment rule, respectively. Moreover, it outperforms the Gurobi solver in large instances in terms of throughput time. The real case study shows that the system throughput time and the manual cost can be reduced by about 25% and 16%, compared with the assignment rule used in practice.