Exact Solution of the Single-Picker Routing Problem with Scattered Storage

Katrin Heßler () and Stefan Irnich ()
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Katrin Heßler: Global Data & AI, Schenker AG, D-45128 Essen, Germany
Stefan Irnich: Chair of Logistics Management, Gutenberg School of Management and Economics, Johannes Gutenberg University Mainz, D-55128 Mainz, Germany

INFORMS Journal on Computing, 2024, vol. 36, issue 6, 1417-1435

Abstract: We present a new modeling approach for the single-picker routing problem with scattered storage (SPRP-SS) for order picking in warehouses. The SPRP-SS assumes that an article is, in general, stored at more than one pick position. The task is then the simultaneous selection of pick positions for requested articles and the determination of a minimum-length picker tour collecting the articles. It is a classical result of Ratliff and Rosenthal that, for given pick positions, an optimal picker tour is a shortest path in the state space of a dynamic program with a linear number of states and transitions. We extend the state space of Ratliff and Rosenthal to include scattered storage so that every feasible picker tour is still a path. The additional requirement to make consistent decisions regarding articles to collect is not modeled in the state space so that dynamic programming can no longer be used for the solution. Instead, demand covering can be modeled as additional constraints in shortest-path problems. Therefore, we solve the resulting model with a mixed-integer (linear) programming (MIP) solver. The paper shows that this approach is not only convenient and elegant for single-block parallel-aisle warehouse SPRP-SSs but also generalizable: the solution principle can be applied to different warehouse layouts (we present additional results for a two-block parallel-aisle warehouse) and can incorporate further extensions. Computational experiments with other approaches for the SPRP-SS show that the new modeling approach outperforms the available exact algorithms regarding computational speed.

Keywords: warehousing; picker routing; scattered storage (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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