A Mathematical Programming Formulation for the Single-Picker Routing Problem in a Multi-Block Layout

Abstract

The Single-Picker Routing Problem (SPRP) arises in warehouses when items have to be retrieved from their storage locations in order to satisfy a given demand. It deals with the determination of the sequence according to which the requested items have to be picked in the picking area of the warehouse and the identification of the corresponding paths to be travelled by human operators (order pickers). The picking area typically possesses a block layout, i.e. the items are located in parallel picking aisles, and the order pickers can only change over to another picking aisle at certain positions by means of so-called cross aisles. Using this special structure, Scholz et al. (2016) developed a model formulation whose size is independent of the number of locations to be visited. They presented the model for a single-block layout and briefly described how it can be extended to the case of multiple blocks. However, by extending this formulation, the number of variables and constraints is multiplied by the number of blocks and, therefore, the model is not suitable for solving the SPRP in warehouses composed of several blocks. In this paper, the extension to multiple blocks is considered and it is pointed out how to drastically reduce the size of the formulation. Depending on the storage locations of the requested items, the number of variables can be decreased by up to 96%.