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

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.