Dynamic capacity expansion

Abstract

The purpose of this thesis is to investigate the problems of dynamic capacity expansion and production decision by using the optimal control theory. Two models are considered with two essential assumptions; perfect knowledge of future and decreasing marginal return on capacity in an economy. The first model considers the known demand function, inventory and backlogging policy, and investment policy. Because of the complexity in deriving the explicit optimal path under the demand fluctuations, only the optimality criteria are derived and economic interpretations are given. The comparison of shadow demand price with market supply price is applied to obtain the optimality criteria. The second model considers the revenue function that is a function of capacity, utilization and labor. Using the revenue function and excess capacity cost, the optimal capacity expansion paths are analytically derived. Some numerical examples are given to illustrate the derivation of the optimal paths.