Optimal shape for a rectangular warehouse with a lateral receive/ship dock

Purpose: This technical note provides the mathematical demonstration for obtaining the optimal aspect ratio for a rectangular storage area with a lateral receive/ship dock, representing the standard configuration of modern distribution centers and logistic warehouses. The proposed aspect ratio is the one that minimizes the travel times of operators, keeping the common assumption of a storage area having a uniform access probability.Design/methodology/approach: To obtain the optimal aspect ratio of the storage area we model the entry point of the uniformly distributed dock with a random variable with a continuous uniform distribution, and we consequently evaluate the average travel path of the operator as a function of the latter. Successively, we estimate and minimize the average roundtrip length of the operator, leading to the optimal aspect ratio of the storage area.Findings: We find that the optimal aspect ratio between the warehouse width (U) and length (V) equals 1.5. The obtained result shows that the operators' travel times are minimized with a storage area where .Research limitations/implications: Warehouses with a dock on one side now represent modern distribution centers' standard configuration. However, no optimal aspect ratio for the storage area has been discussed. For this reason, the paper fills this lack of scientific literature in the warehouse optimization research field by providing indications on how to design this class of warehouses.Practical implications: Distribution managers may find here guidance for defining a proper design of logistics centers and evaluating the operators' actual travel times to perform a roundtrip within the storage area.Originality/value: Traditional warehouse shape optimization models assume a single input/output point to the storage area. To our knowledge, no formal demonstration has been proposed for a warehouse with a dock on one entire side.