Plant Location

Cyber Industries currently has a warehouse in each of the following cities: A, B, C, D, and E. These warehouses supply customer regions throughout the U.S., It is convenient to aggregate customer areas and consider the customers to be located in cities 1 - 6. There is some feeling in Cyber that it is ``overwarehoused;" that is, it may be able to save substantial fixed costs by closing some warehouses without unduly increasing transportation and service costs. The table below summarizes relevant monthly data for this situation.

where is the monthly supply capacity at warehouse i, in tons, is the monthly fixed cost of using warehouse i, and is the monthly demand, in tons, in city j. Demand must be met exactly, and the monthly supply at each warehouse cannot be exceeded.

Formulate and solve the following versions of this problem:

1. Assume that each city must be supplied from a single warehouse.
2. Assume that multiple sourcing is possible, wherein a city's demand can be satisfied by deliveries from multiple warehouses.