Exact Solution of Picker Routing Problems in Zoned Warehouses with Scattered Storage

We present two picker routing problems in a warehouse split into multiple disjoint zones with a picker assigned to each zone. Scattered storage is applied, meaning an article can be stored at several pick positions in one or more zones, and capacity restrictions limit the number of collected articles for each picker. Both problems seek picker tours that collect all requested articles, with each tour operating within one zone. While the multi-zone picker routing problem (MZPRP) minimizes the total length of all picker tours, the balanced multi-zone picker routing problem (BMZPRP) balances the tour lengths by minimizing the length of the longest picker tour. Both problems constitute a three-level optimization problem. While on the higher levels, zone assignment decisions and the selection of pick positions must be made, on the lower level, picker tours for each zone are determined. To solve both problems, we use a network-flow model with covering constraints and varying objectives. This type of model was recently presented for the single picker routing problem with scattered storage, building on an extended state space of the dynamic-programming approach by Ratliff and Rosenthal. Our model contains a network for each zone, and demand-covering constraints across all zones ensure that the requested articles are collected. Computational experiments, including large instances with up to 200 articles, show that our solution approach efficiently solves the two problems within (milli-)seconds. An analysis of the number of zones demonstrates that in larger warehouse layouts, zoning reduces costs compared to single-Zone picker routing.