(r5) The American Steel Planning Problem < OpsRes

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CaseStudyForm
Title	The American Steel Planning Problem
DateSubmitted	30 Apr 2008
CaseStudyType	TeachingCaseStudy
OperationsResearchTopics	LinearProgramming, IntegerProgramming, NetworkOptimisation, TransshipmentProblem
ApplicationAreas	Logistics
ProblemDescription	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.
ProblemFormulation	The formulation...
ComputationalModel	The computational model...
Results	The results...
Conclusions	In conclusion...
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Topic revision: r5 - 2008-04-29 - MichaelOSullivan

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