A stochastic optimization model for planning capacity expansion in a service industry under uncertain demand

A stochastic optimization model for capacity expansion for a service industry that incorporates uncertainty in future demand is developed. Based on a weighted set of possible demand scenarios, the model generates a recommended schedule of capacity expressions, and calculates the resulting sales under each scenario. The capacity schedule specifies the size, location, and timing of these expansions that will maximize the company’s expected profit. The model includes a budget constraint on available resources. By using Lagrangean relaxation and exploiting the special nested knapsack structure in the subproblems, an algorithm was developed for its solution. Based on the initial computational results, this algorithm appears to be more efficient than linear programming for this special problem.