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, the entry point of the uniformly distributed dock is modeled with a random variable, with a continuous uniform distribution, and the average travel path of the operator is consequently assessed as a function of the latter. Successively, the average roundtrip length of the operator is evaluated and minimized, leading to the optimal aspect ratio of the storage area.Findings: It is found that the optimal aspect ratio between the warehouse width (U) and length (V) equals 1.5. The obtained result - which is novel for the warehouse design research since no other contribution discussed it - shows that the operators' travel times are minimized with a storage area where 1 = 1.5V.Research limitations/implications: Warehouses with a dock on one side now represent the standard configuration of modern distribution centers'. 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 by providing indications on how to design this class of warehouses.Practical implications: Distribution managers find here guidance for defining a proper design of logistics centers and evaluating the operators' 'travel times to perform a roundtrip within the storage area. Indeed, the found aspect ratio indicates the optimal design for a storage area with the abovementioned assumptions.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. Hence, the added value and novelty of this contribution are given by the possibility to adopt the optimal aspect ratio to perform an adequate design of distribution centers and warehouses.