Optimal plant size with variable cost and revenue streams

This paper considers a capacity decision problem where the construction cost and revenue rates are functions of time. It is shown that the objective function, i.e., the net present value of the total revenues and salvage value minus the construction cost is a concave function for a wide range of problem parameters. The case of random length of product life cycle is also considered where the expected net present value of profit is maximized. Several numerical examples for both cases (i.e., known and random life cycle) are discussed with detailed sensitivity analyses for nonmonetary and monetary parameters in the problem.