Capacity Expansion with Two Producing Regions and Concave Costs

A deterministic capacity expansion and shipment planning problem is considered for a single commodity that can be produced in two regions. Demand in each region is nondecreasing over a finite time horizon. Demand in a region in a time period must be satisfied, either by the current production capacity there or by a shipment from the other region. Capacity expansion and shipment costs are assumed to be concave and no inventory of stock is allowed. The problem is to find a schedule of capacity expansion in each region and a schedule of shipment between the two regions, such that the total cost over the time horizon is minimized. To solve this problem a dynamic programming algorithm is devised that is more efficient than known conventional procedures.