Capacity expansion under stochastic demand

Abstract

The primary purpose of this thesis is to investigate the optimum expansion problem of a single capacity under the stochastic demand by evaluating the expected cost rate and risks simultaneously. Probability density function of the reconstruction epoch was introduced to formulate the generalized cost problem which was used to evaluate the expected cost rate and the corresponding risks. To cope with the time horizon problem, the concept of equivalent cost rate (ECR) was introduced. Properties of ECR show that the optimal expansion consists in equal size policy under the assumption on demand with linearly increasing mean rate and variance in time. The ultimate objective function is to minimize the combinations of the expected ECR and the corresponding risk. This formulation shows that the capacity expansion as a physical investment problem can be analyzed by the financial investment theory. An evaluation space concept was designed for this purpose. Numerical results were given to show the changing optimum expansion capacity under various situations. Finally, an evaluation curve was derived which may help greatly the top management for the strategic decisions on capacity expansion.