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

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

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. |

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 then 5000 tons/month due the shortage of rail cars.

Table 1 Arc Costs and Limits

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

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. |

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.

• steel_network.jpg:
  

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

The current monthly demand at American Steel's four field warehouses is shown in Table 2.

Table 2 Monthly Demands

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.|

Computational Model

Results

Conclusions

• Problem Description
• Problem Formulation
• Computational Model
• Results
• Conclusions

<--

-->

<--

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.


-->

• Problem Description
• Problem Formulation
• Computational Model
• Results
• Conclusions

Problem Formulation

Computational Model

Results

Conclusions

In conclusion...

Return to top

<-- Under Construction -->

<--
This template controls both the look and functionality of case study topics.
You should not need to alter the layout, only edit the data using the form above.

Set the view and edit templates:
Comment out the next line to use the TWiki default view 

 Set VIEW_TEMPLATE = CaseStudyView
 
Comment out the next line to use the TWiki default edit 

 Set EDIT_TEMPLATE = CaseStudyEdit
 
-->

<--
This topic can only be changed by: 

 Set ALLOWTOPICCHANGE = TWikiAdminGroup, MaintenanceGroup, ContributorGroup
 
-->

Case Study: The American Steel Planning Problem

Submitted: 30 Apr 2008

Operations Research Topics: LinearProgramming, IntegerProgramming, NetworkOptimisation, TransshipmentProblem

Application Areas: Logistics

Contents

• Problem Description
• Problem Formulation
• Computational Model
• Results
• Conclusions
• StudentTasks

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

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

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.

Return to top

Problem Formulation

The formulation...

Return to top

Computational Model

The computational model...

Return to top

Results

The results...

Return to top

Conclusions

In conclusion...

Return to top

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.

Return to top