A model for storage facility design with energy costs

The design of a warehouse or distribution center (DC) has become an essential tool for the optimization of the supply chain in most industries. Energy consumption in this type of facilities is an important issue which has not received much attention in the scientific community which has focused instead in two-dimensional routing optimization. In this paper the problem of designing a rectangular warehouse in a fully or partially automated factory or distribution center is addressed. In these facilities the movement is performed either by an AGV (Automated Guided Vehicle) or by automated robotics equipment of Cartesian movement attached to the storage racks. In the literature there exist works with formulas to design shelves in two and three dimensions buy they do not adequately consider the problem of movement in the Z-axis, thereby giving inefficient results with very high shelves and ignoring energy consumption and costs. This occurs because the known approaches consider the movement only on the X-Y plane as expensive as in height movement, which in general does not hold in actual facilities. The problem is exacerbated for heavy materials due to greater energy waste. In this paper the above problem is solved by a model with an extra component for the cost of movement in height. With the model and derived formulas, lower shelves with less energy consumption are generated. The formulas developed are optimal with respect to travel distances and they are obtained from solving a nonlinear optimization problem with linear constraints through a Lagrange transformation. The paper contribution is to optimize warehouse design for reduced energy consumption and pollution both relevant aspects in sustainable engineering systems. A practical application in a distributor of MRO items is presented along with measured energy cost impacts.