Case Study: The American Steel Planning Problem

Submitted: 30 Apr 2008

Operations Research Topics: LinearProgramming, IntegerProgramming, NetworkOptimisation, TransshipmentProblem

Application Areas: Logistics


Problem Description

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 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. For example, the shipment from Youngstown to Kansas City is contracted out to a railroad company with a minimal shipping clause of 1000 tons/month. However, the railroad cannot ship more then 5000 tons/month due the shortage of rail cars.

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.

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Problem Formulation

The formulation...

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Computational Model

The computational model...

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The results...

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In conclusion...

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Topic revision: r5 - 2008-04-29 - MichaelOSullivan
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