A route-selecting order batching model with the S-shape routes in a parallel-aisle order picking system

This paper introduces a route-selecting order batching model with the S-shape routing method in parallel-aisle order picking (SRSB). Order pickers in a wide-aisle system prefer the S-shape route taking a u-turn at the last aisle to shorten the travel distance. Although u-turns improve operations, they actually increase computational complexity in order batching. Our study defines a route-set for the S-shape routes and composites a best fit route for batches from the predefined S-shape routes while partitioning orders into batches. The large-scale extension of the SRSB obtains near-optimal solutions by the tight lower bound of the by identifying the route-selection based relaxed batching model. A comparison of the heuristics solution and its pairing lower bound shows 3.5-6.8 percent optimal gaps on average in a six-aisle parallel-aisle system over a 200-500 orders time-window, which outperforms an available best large-scale algorithm with a 9.9 percent shorter travel distance on average. Using the identified lower bound, we evaluate other large-scale batching algorithms in the published literature. We find that a popular savings algorithm shows 8.3-19.8 percent optimal gaps over a variety of large-scale simulation cases.