USG is a leading building supplies manufacturer in North America. For the Durock\textsuperscript{\textregistered} product line on which this project focuses, several dozen items are produced in three locations in the United States, and may pass through any one of a network of warehouses before being delivered to customers throughout the United States and Canada.
Currently, the production and distribution decisions are made through the use of a large scale linear program (LP). The goal of the LP is to minimize the total delivered cost (production, freight, and handling) for all items in the planning network, while meeting the managerial constraints of capacity at each plant and demand at each customer location. The input parameters (production costs, freight costs, handling costs, and demand) are drawn from a single point in time. The problem is extremely large, with upwards of 1500 customer locations being used in the current model. In addition, the number of items fluctuates between thirty and forty, and combined with the large number of warehouse locations and the choice between rail and truck modes of freight, over 90,000 decision variables are used in the current state.
Because the cost and demand parameters can not be precisely predicted from month to month, the problem incldues approximately 800 uncertain parameters. We therefore seek a method for optimizing the distribution network that accounts for these uncertainties.