Steiner TSP based on aisle as a unit for order picking

The picker routing problem (PRP) is one of the most crucial problems in warehouse management. It is also defined as the Steiner Traveling Salesman Problem (Steiner TSP). We deal with the Steiner TSP for a low-level picker-to-parts order picking system within a multi-block warehouse, which is much more complicated to be solved compared with those in a single block layout. After a series of preprocessing, such as reducing the vertices, transforming picking aisles and limiting the connections between vertices, we construct a Steiner graph with flexible nodes based on aisle as a unit. Different picking access modes as well as restrictions on connections for picking aisles are introduced. Then, a mixed integer linear programming model for Steiner TSP based on aisle as a unit is presented. We compare the numerical computation on the benchmarks in exiting literatures. Our Steiner graph can greatly reduce the scale of vertices and arcs without losing characteristics of the original problem. And the model has good overall performance, especially in large scale cases.