Robust Capacity Planning Under Uncertainty

Abstract

The existence of uncertainty influences the investment, production and pricing decision of firms. Therefore, capacity expansion models need to take into account uncertainty. This uncertainty, may arise because of errors in the specification, statistical estimation of relationships and in the assumptions of exogenous variables. One such example is demand uncertainty. In this paper, a cautious capacity planning approach is described for solving problems in which robustness to likely errors is needed. The aim is to cast the problem in a deterministic framework and thereby avoid the complexities inherent in nonlinear stochastic formulations. We adopt a robust approach and minimize an augmented objective function that penalises the sensitivity of the objective function to various types of uncertainty. The robust or sensitivity approach is compared with Friedenfelds' equivalent deterministic demand method. Using numerical results from a large nonlinear programming capacity planning model, it is shown that as caution against demand uncertainty increases, the variance of the total objective function (profit) decreases. The cost of such robustness is a deterioration in the deterministic risky performance. This method is also applied to an industry simulation model in order to assess the effect of uncertainty in market demand on optimal capacity expansion and capacity utilisation.