Capacity Expansion/Contraction of a Facility with Demand Augmentation Dynamics

Abstract

We analyze the cost-effective addition or removal of capacity from a facility governed by demand augmentation dynamics. That is, if the demand for goods or services exceeds the planned capacity of the facility during any period of a multiperiod planning horizon, then additional capacity must be introduced within that period to meet the deficit. The paper obtains an optimal management strategy that minimizes the sum of capital, labor, maintenance, and underpro-vision costs for N consecutive periods in the face of uncertain demands. Dynamic programming is used to demonstrate that, under certain conditions on the cost functions, an inventory-like (S′, S″) policy is optimal, appropriately interpreted to define the removal as well as the augmentation of capacity. The threshold levels S′ and S″, can be evaluated for each period without a costly search procedure. In addition, we show how to calculate various quantities of interest associated with the optimal policy.