This paper deals with the design of a warehouse or distribution center (CD). The number of doubled-sided racks, the height and the width of bays and aisles are calculated by closed-form formulas so that the distance traveled by an automated guided vehicle (AGV) and/or a human operator driving a hand cart, is minimized. The formulas developed allow the construction of the CD in the three dimensions, so that the cost of displacement is minimized. The main contribution of this work is the delivery of three-dimensional formulas for warehouses using an ABC type of scheme of general layout with easy-to-apply formulas. Other works present some difficulties in obtaining direct formulas since they need to solve a nonlinear minimization problem with linear constraints, forcing the use of iterative methods. In this work, such difficulty is resolved by using a Lagrangian function transforming the problem into one of unconstrained minimization.
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