American Steel, an Ohio-based steel manufacturing company, produces steel at its two steel mills located at Youngstown
Question:
American Steel, an Ohio-based steel manufacturing company, produces steel at its two steel mills located at Youngstown and Pittsburgh. The company distributes finished steel to its retail customers through the distribution network of regional and field warehouses shown below:
The network represents the shipment of finished steel from American Steel's two steel mills located at Youngstown (node 1) and Pittsburgh (node 2) to their field warehouses at Albany, Houston, Tempe, and Gary (nodes 6, 7, 8, and 9) through three regional warehouses located at Cincinnati, Kansas City, and Chicago (nodes 3, 4 and 5). Also, some field warehouses can be directly supplied from the steel mills.
Table 1, presents the minimum and maximum flow amounts of steel that may be shipped between different cities along with the cost per 1000 ton/month of shipping the steel.
Table 1 Arc Costs and Limits
From node | To node | Cost | Minimum | Maximum |
Youngstown | Albany | 500 | - | 1000 |
Youngstown | Cincinnati | 350 | - | 3000 |
Youngstown | Kansas City | 450 | 1000 | 5000 |
Youngstown | Chicago | 375 | - | 5000 |
Pittsburgh | Cincinnati | 350 | - | 2000 |
Pittsburgh | Kansas City | 450 | 2000 | 3000 |
Pittsburgh | Chicago | 400 | - | 4000 |
Pittsburgh | Gary | 450 | - | 2000 |
Cincinnati | Albany | 350 | 1000 | 5000 |
Cincinnati | Houston | 550 | - | 6000 |
Kansas City | Houston | 375 | - | 4000 |
Kansas City | Tempe | 650 | - | 4000 |
Chicago | Tempe | 600 | - | 2000 |
Chicago | Gary | 120 | - | 4000 |
The current monthly demand at American Steel's four field warehouses is shown in Table 2.
Table 2 Monthly Demands
Field Warehouses | Monthly Demand |
Albany, N.Y. | 3000 |
Houston | 7000 |
Tempe | 4000 |
Gary | 6000 |
The Youngstown and Pittsburgh mills can produce up to 10,000 tons and 15,000 tons of steel per month, respectively. The management wants to know the least cost monthly shipment plan.
Show the related LP to your transportation model.
Global Business Today
ISBN: 978-1259686696
10th edition
Authors: Charles W. L. Hill Dr, G. Tomas M. Hult