In this paper, a dynamic programming model is developed for the purpose of
establishing a warehouse capacity expansion schedule and underlying multi-i
tem inventory policy that are jointly optimal. The optimal warehouse size o
ver any segment of the planning horizon is obtained by solving a nonlinear
optimisation problem, this being accomplished efficiently by exploiting the
Kuhn-Tucker conditions. Repeating this procedure between each pair of time
periods results in a discrete state space, so that the optimal capacity ex
pansion schedule corresponds to a shortest path in a network. Managerial in
sights are provided through experimentation with the model.