This paper considers a warehouse sizing problem whose objective is to minim
ize the total cost of ordering, holding, and warehousing of inventory. Unli
ke typical economic lot sizing models, the warehousing cost structure exami
ned here is not the simple unit rate type, but rather a more realistic step
function of the warehouse space to be acquired. In the cases when only one
type of stock-keeping unit (SKU) is warehoused, or when multiple SKUs are
warehoused, but, with separable inventory costs, closed form solutions are
obtained for the optimal warehouse size. For the case of multi-SKUs with jo
int inventory replenishment cost, a heuristic with a provable performance b
ound of 94% is provided. (C) 2001 John Wiley & Sons, Inc.