Problem
BACF is a manufacturer of chemical products with worldwide sales. The annual demand in each of the five regions (N. America, S. America, Europe, Asia and Africa) is shown in Table 1. All demand data is in millions of units. The vice president of supply chain is considering to reconfigure the company's global supply chain. He wants to consolidate plants in just a few countries. This improves economies of scale but increases transportation cost. The potential countries where the plants are located include Mexico, Brazil, Germany, India and South Africa. The variable transportation costs of shipping one million units from one country to each demand region are shown in Table 1. All cost data is in '000s of dollars.
BACF is considering two plant sizes in each location and plan to open at most one plant in each location. Low-capacity plants can produce 10 million units a year, whereas high-capacity plants can produce 20 million units a year. Running a plant incurs fixed costs. High-capacity plants exhibit some economies of scale and have fixed costs that are less than twice the fixed costs of a low-capacity plant, as shown in Table 2. All fixed costs are annualized. The variable costs of producing one million units in each country are also shown in Table 2. The vice president wants to know what the lowest cost supply chain configuration should look like.
Table 1: Demands (in millions of units) and variable transportation costs (in '000s of dollars)
Table 2: Variable production costs and fixed costs (in '000s of dollars)
Task
Formulate an Integer Linear Programming model for this problem and solve it via SOLVER or ASPE. Please do not abbreviate your formulation.