Case Study: The American Steel Planning Problem

Submitted: 30 Apr 2008

Operations Research Topics: LinearProgramming, IntegerProgramming, NetworkOptimisation, TransshipmentProblem

Application Areas: Logistics


Problem Description

Note This case study is an extension of the American Steel Transshipment Problem.

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.

American Steel are planning their production levels, inventory levels and shipment plans for the next quarter (3 months). 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 than 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

One added consideration is union action in Kansas City during June that will increase the transportation costs out of Kansas City by 5%.

The monthly demand for the next quarter at American Steel's four field warehouses is shown in Table 2.

Table 2 Monthly Demands

Field Warehouses April May June
Albany, N.Y. 3000 2000 4000
Houston 7000 5000 6000
Tempe 4000 1000 3000
Gary 5000 6000 7000

The Youngstown and Pittsburgh mills can produce up to 10,000 tons and 15,000 tons of steel per month, respectively. However, the Youngstown mill is undergoing maintenance in May and can only produce 5000 ton of steel.

Finally, there is a holding cost of $25/1000 ton at the mills, $10/1000 ton at the regional warehouses and $25/1000 ton at the field warehouses.

The management want to know the best production levels, inventory levels and shipments to minimise their operating cost during the quarter.

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Student Tasks

  1. Solve the American Steel Planning Problem. Write a management summary of your solution.

    Hint You can use transshipment.mod but with 2-dimensional nodes incorporating location and time, e.g., (Youngstown, April).

    What to hand in Your model, data and script files. Your management summary.

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Topic revision: r8 - 2009-10-06 - MichaelOSullivan
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