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Determining The Optimal Order Picking Batch Size In Single Aisle Warehouses

Author

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  • Le-Duc, T.
  • de Koster, M.B.M.

Abstract

This work aims at investigating the influence of picking batch size to average time in system of orders in a one-aisle warehouse under the assumption that order arrivals follow a Poisson process and items are uniformly distributed over the aisle's length. We model this problem as an M/G[k]/1 queue in which orders are served in batches of exactly orders. The average time in system of the M/G[k]/1 queue is difficult to obtain for general service times. To circumvent this obstacle, we perform an extensive numerical experiment on the average time in system of the model when the service time is deterministic (M/D[k]/1) or exponentially distributed (M/M[k]/1). These results are then compared with the corresponding times in system of the actual model taken from simulation runs. A variance analysis is carried out and its result elicits that the M/D/[k]/1 queue is a very good approximation for the average time in system of orders. Correspondingly, the optimal picking batch size of the real system can be approximated by the optimal batch size when service time is deterministic.

Suggested Citation

  • Le-Duc, T. & de Koster, M.B.M., 2002. "Determining The Optimal Order Picking Batch Size In Single Aisle Warehouses," ERIM Report Series Research in Management ERS-2002-64-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    • Handle: RePEc:ems:eureri:215
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    References listed on IDEAS

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    1. Warren B. Powell, 1985. "Analysis of Vehicle Holding and Cancellation Strategies in Bulk Arrival, Bulk Service Queues," Transportation Science, INFORMS, vol. 19(4), pages 352-377, November.
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    Cited by:

    1. Le-Duc, T. & de Koster, M.B.M., 2004. "Travel Time Estimation and Order Barching in a 2-Block Warehouse," ERIM Report Series Research in Management ERS-2004-098-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    2. Le-Duc, Tho & de Koster, Rene M.B.M., 2007. "Travel time estimation and order batching in a 2-block warehouse," European Journal of Operational Research, Elsevier, vol. 176(1), pages 374-388, January.

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    More about this item

    Keywords

    batch picking; batch service queue; batch size; order picking; warehousing;
    All these keywords.

    JEL classification:

    • C59 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Other
    • M - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics
    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management
    • R4 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics

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