Approximate Optimal Order Batch Sizes in a Parallel aisle Warehouse

The past warehousing literature dealing with order picking and batching assumes batch sizes are given. However, selecting a suitable batch size can significantly enhance the system performance. This paper is one of the earliest to search optimal batch sizes in a general parallel-aisle warehouse with stochastic order arrivals.We employ a sample path optimization and perturbation analysis algorithm to search the optimal batch size for a warehousing service provider facing a stochastic demand, and a central finite difference algorithm to search the optimal batch sizes from the perspectives of customers and total systems.We show the existence of optimal batch sizes, and find past researches underestimate the optimal batch size.

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