Technical Note—Capacity Expansion in Convex Cost Networks with Uncertain Demand

The purpose of this investigation is to suggest a simple algorithm for solving capacity expansion problems in networks with uncertain demand. We assume that the cost of expanding the capacity of each arc is a convex function and that there is a concave salvage value each arc is a convex function and that there is a concave salvage value associated with excess capacity. We adopt the two-stage programming approach but with the essential difference that our independent variable is an assumed first-stage demand. We show that the objective function of the equivalent convex program is a convex function of the assumed first-stage demand and use this fact to propose an algorithm.