Abstract
In this paper, a dynamic programming model is developed for the purpose of establishing a warehouse capacity expansion schedule and underlying multi-item inventory policy that are jointly optimal. The slate variable represents the warehouse size, while the stages are the time periods at which lot sizing and capacity expansion decisions are made. Through the use of an approximation inventory cost function and the Kuha-Tucker conditions, the state variable can be discretized, thus allowing the optimal capacity expansion schedule to be obtained by finding the shortest path in a network.