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Abstract This paper presents exact derivations of the first two moments of the total order picking time in a warehouse for three routing heuristics, under the assumption of random storage. The analysis is done for general order size distributions and provides exact closed expressions in terms of the probability generating function of the order size distribution. We also indicate how the methods and insights in this paper extend to different storage policies and multi-block warehouses. The exact results derived in this paper are used to investigate effects of routing heuristics, order size distributions and layouts on warehouse efficiency. As illustration, we model the warehouse as a queueing system. By using approximations of the average order-lead time in terms of the first two moments of the order picking time, we are able to find optimal warehouse layouts and batch pick sizes.
Engels et al. (2024) studied this question.