A new approach to the joint order batching and picker routing problem with alternative locations

The clustered and generalized vehicle routing problem (CGVRP) extends the well-known vehicle routing problem by grouping the demand points into multiple distinct zones, and within each zone, further separation is made by forming clusters. The objective of the CGVRP is to determine the optimal routes for a fleet of vehicles dispatched from a depot, visiting all zones within each cluster. This requires making two simultaneous optimization decisions. Firstly, each zone must be visited by exactly one node, and secondly, all zones within a cluster must be visited by the same vehicle. In this paper, we introduce two mixed-integer linear programming formulations for the CGVRP, aimed at solving a joint order batching and picker routing problem with alternative locations (JOBPR-AL) in a warehouse environment featuring mixed-shelves configuration. Both formulations are tested on three scenarios of randomly generated small- and medium-sized instances. Additionally, we propose a general rule approach for calculating a cost matrix in a rectangular environment. The results demonstrate the effectiveness of the proposed mathematical formulations in efficiently solving problems with up to 180 nodes.