Question 1. Frijo-Lane Food Products owns farms in the Southwest and Midwest, where it grows and harvests potatoes. It then ships these potatoes to three processing plants in Atlanta, Baton Rouge, and Chicago, where different varieties of potato products, including chips, are produced. Recently, the company has experienced a growth in its product demand, so it wants to buy one or more new farms to produce more potato products. The company is considering six new farms with the following annual fixed costs and projected harvest:
Fixed Annual Projected Annual Harvest
Farm Costs ($1,000s) (thousands of tons)
1 $405 11.2
2 390 10.5
3 450 12.8
4 368 9.3
5 520 10.8
6 465 9.6
The company currently has the following additional available production capacity (tons) at its three plants, which it wants to utilize:
Available Capacity
Plant (thousands of tons)
A 12
B 10
C 14
The shipping costs ($) per ton from the farms being considered for purchase to the plants are as follows:
Plant (shipping costs, $/ton)
Farm A B C
1 18 15 12
2 13 10 17
3 16 14 18
4 19 15 16
5 17 19 12
6 14 16 12
The company wants to know which of the six farms it should purchase to meet available production capacity at the minimum total cost, including annual fixed costs and shipping costs.
Develop an appropriate mixed integer optimization model to solve this problem and implement it on Solver. Discuss your solution in a one-page business memo to the COO.
2. American Parcel Service (APS) has determined that it needs to add several new package distribution hubs to service cities east of the Mississippi River. The company wants to construct the minimum set of new hubs in the following 12 cities so that there is a hub within 300 miles of each city (i.e., every city is covered by a hub):
City Cities Within 300 Miles
1. Atlanta Atlanta, Charlotte, Nashville
2. Boston Boston, New York
3. Charlotte Atlanta, Charlotte, Richmond
4. Cincinnati Cincinnati, Detroit, Indianapolis, Nashville, Pittsburgh
5. Detroit Cincinnati, Detroit, Indianapolis, Milwaukee, Pittsburgh
6. Indianapolis Cincinnati, Detroit, Indianapolis, Milwaukee, Nashville, St.Louis
7. Milwaukee Detroit, Indianapolis, Milwaukee
8. Nashville Atlanta, Cincinnati, Indianapolis, Nashville, St. Louis
9. New York Boston, New York, Richmond
10. Pittsburgh Cincinnati, Detroit, Pittsburgh, Richmond
11. Richmond Charlotte, New York, Pittsburgh, Richmond
12. St. Louis Indianapolis, Nashville, St. Louis
Develop an appropriate integer optimization model and solve it with Solver. Hint: your only decision variables are whether or not to select a city as a hub.