The Simultaneous Determination of Plant and Leased Warehouse Capacities for a Firm Facing Uncertain Demand in Several Regions

For each of several regions a firm has forecasted a probability distribution of future annual demand, and the plan is to build a single production facility to serve this demand. Each region is served by a simple leased warehouse with a lease cost which is a linear function of capacity. Any regional demand exceeding warehouse capacity is lost. The cost of building the plant is a nonlinear function of its capacity, and the unit cost of producing the product and supplying it to a region is constant. We develop an efficient algorithm based on the Kuhn-Tucker conditions for simultaneously determining the plant and warehouse capacities which will maximize the firm's expected profit. The paper includes a numerical example demonstrating the use of this algorithm.