Capacity Expansion and Contraction Of A Facility With Economies Of Scale

We present a model of capacity expansion in which capacity can be either expanded or contracted over time. Our model allows for economies of scale often associated with capacity expansion. Furthermore, we incorporate lump-sum penalty costs incurred when capacity is added to accommodate excess demand on an emergency basis. We use dynamic programming and K-convexity methods to characterize the nature of the optimal policy. We show that an expansion and contraction policy of a "simple" form is optimal if the demand distribution function is concave. Furthermore, we provide an example to demonstrate that, if the distribution function for the demand is not concave, one can always choose a set of parameter values for which the problem does not possess a simple optimal policy.