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

*(English)*Zbl 1394.90089Summary: 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.

##### MSC:

90B06 | Transportation, logistics and supply chain management |

90B80 | Discrete location and assignment |

90C08 | Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) |

90B50 | Management decision making, including multiple objectives |

##### Keywords:

facility planning; order picking methods; route-selecting order batching model; lower bound algorithm; S-shape routing method
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\textit{S. Hong} and \textit{Y. Kim}, Eur. J. Oper. Res. 257, No. 1, 185--196 (2017; Zbl 1394.90089)

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