Modelling and analysis for capacity expansion planning in warehousing

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 optimal warehouse size over 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 expansion schedule corresponds to a shortest path in a network. Managerial insights are provided through experimentation with the model.