Simple models and insights for warehouse sizing

This study is concerned with minimizing the total discounted cost of operating an inventory system and providing the warehouse space necessary to accommodate the replenishment lots, under the assumption of constant product demand. The use of an approximation objective function for the single-item case allows the optimal warehouse size as well as the ratio of relevant investment costs to relevant inventory costs to be written in closed-form. Based upon the value of this ratio, circumstances are identified under which an integrated approach is justified, and others under which the inventory policy and storage capacity can be determined sequentially. The multi-item version of the problem under study is solved by the Lagrangian multiplier method, given that no coordination takes place between the items. Finding the optimal Lagrange multiplier can be accomplished efficiently by the Newton-Raphson method.