Optimal capacity expansion under uncertainty

TLDR

Capacity expansion involves adding new facilities over time to meet growing demand. The study introduces a general mathematical model of capacity expansion that incorporates uncertain future demand, lead times, and random cost overruns. The model lets the decision maker control the investment rate in the current expansion project, and the optimal policy is derived using stochastic control theory. Numerical algorithms are presented that compute the optimal policy in simple cases.

Abstract

Capacity expansion is the process of providing new facilities over time to meet rising demand. A general mathematical model of this process is presented, incorporating uncertain future demand (including the possibility of ‘surprises’), non-zero lead times and random cost overruns. In this model the decision maker controls the rate of investment in the current expansion project. Optimization is studied by methods of stochastic control theory. Numerical algorithms are presented which determine the optimal policy in some simple cases.