Minimizing Multi-zone Orders in the Correlated Storage Assignment Problem

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Garfinkel, Maurice
Sharp, Gunter P.
Sokol, Joel S.
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A fundamental issue in warehouse operations is the storage location of the products it contains. Placing products intelligently within the system can allow for great reductions in order pick costs. This is essential because order picking is a major cost of warehouse operations. For example, a study by Drury conducted in the UK found that 63% of warehouse operating costs are due to order picking. When orders contain a single item, the COI rule of Heskett is an optimal storage policy. This is not true when orders contain multiple line items because no information is used about what products are ordered together. In this situation, products that are frequently ordered together should be stored together. This is the basis of the correlated storage assignment problem. Several previous researchers have considered how to form such clusters of products with an ultimate objective of minimizing travel time. In this dissertation, we focus on the alternate objective of minimizing multi-zone orders. We present a mathematical model and discuss properties of the problem. A Lagrangian relaxation solution approach is discussed. In addition, we both develop and adapt several heuristics from the literature to give upper bounds for the model. A cyclic exchange improvement method is also developed. This exponential size neighborhood can be efficiently searched in polynomial time. Even for poor initial solutions, this method finds solutions which outperform the best approaches from the literature. Different product sizes, stock splitting, and rewarehousing are problem features that our model can handle. The cyclic exchange algorithm is also modified to allow these operating modes. In particular, stock splitting is a difficult issue which most previous research in correlated storage ignores. All of our algorithms are implemented and tested on data from a functioning warehouse. For all data sets, the cyclic exchange algorithm outperforms COI, the standard industry approach, by an average of 15%.
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