Data-driven assignment of delivery patterns with handling effort considerations in retail

We consider a supply chain with one warehouse and multiple stores. At the warehouse, the orders for the stores are picked and in the store, shelves are stacked from the backroom. We include handling costs at the warehouse and stores as these are main drivers for logistics costs. We find delivery patterns and order-up-to levels, both of which shall remain fixed for a certain time. As especially in retail stochastic non-stationary demand structures are prevalent, we extend the classic joint replenishment problem under dynamic demand by a stochastic yet distribution-free optimization approach based on historical data samples. We formulate a mixed integer linear program using the plant-location formulation and develop several hierarchical decomposition approaches and a genetic algorithm. We consider a cyclic approach for orders, which allows an order at the end of the time horizon to fulfill the demand at the beginning of the time horizon. Using this approach, there is no need for initial inventories to be set as an input; they are are optimized within the model. Furthermore, a metacalibration approach is introduced, which allows an automated setting of input parameters for the genetic algorithm. To derive insights into the performance of the models, random instances are solved and then the most promising models are used for a case study with a European retailer. The results for the controlled test instances are analyzed by a meta-modeling approach that provides insights into performance drivers for the investigated model variants. The average logistics cost savings of our model over a deterministic approach with safety stocks amount to 3.02 % for the controlled test instances. In a similar comparison for the case study, average results over different parameter combinations show a 20.60 % logistics costs saving potential.