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ILP Transportation Problem

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The table below indicates required supplies delivered to four destinations.
Destinations
Port D1 D2 D3 D4
A 70 80 90 56
B 100 75 100 85
C 42 60 89 62
Demand 500 600 450 700

The ports are supplied by one of two stock suppliers. Supplier 1 carries 1200 tonnes of supplies while Supplier 2 carries 1120 tons of supplies. These suppliers can only offer a single port and each port can only accommodate one supplier. Assume the costs for a supplier to supply are not part of the objective function. Formulate the ILP for this problem capturing the supplier choice of port and the transportation from the port to the destinations.

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Solution Preview

Please view the attached files (one Word document and one Excel file) as these will help you answer your question. I have attached an Excel file which solves the problem using Excel Solver. Go to Data - > Solver to see the objective function, decision variables and constraints. Optimal solution is available in the file.

Port-Supplier Selection - ILP
Problem definition: A commodity needs to be supplied to four destinations. ...

Solution Summary

The solution assists with answering the ILP transportation problem.

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See Also This Related BrainMass Solution

Linear programming model

See also attachment for formatting.

1. Solve the following linear programming model by using the computer:

Maximize Z = 5x1 + 8x2
Subject to
3x1 + 5x2 ≤ 50
2x1 + 4x2 ≤ 40
x1 ≤ 8
x2 ≤ 10
x1, x2 ≥ 0

2. Solve the following linear programming model by using the computer:

Minimize Z = 8x1 + 6x2
Subject to
4x1 + 2x2 ≥ 20
-6x1 + 4x2 ≤ 12
x1 + x2 ≥ 6
x1, x2 ≥ 0

3. Betty Malloy, owner of the Eagle Tavern in Pittsburgh, is preparing for Super Bowl Sunday, and she must determine how much beer to stock. Betty stocks three brands of beer - Yodel, Shotz, and Rainwater. The cost per gallon (to the tavern owner) of each brand is as follows:

Brand Cost/gallon
Yodel $1.50
Shotz 0.90
Rainwater 0.50

The tavern has a budget of $2,000 for beer for Super Bowl Sunday. Betty sells Yodel at a rate of $3.00 per gallon, Shotz at $2.50 per gallon, and Rainwater at $1.75 per gallon. Based on past football games, Betty has determined the maximum customer demand to be 400 gallons of Yodel, 500 gallons of Shotz, and 300 gallons of Rainwater. The tavern has a capacity to stock 1,000 gallons of beer; Betty wants to stock up completely. Betty wants to determine the number of gallons of each brand of beer to order so as to maximize profit.

a. Formulate a linear programming model for this problem (written in a format similar to the way Problems 1 and 2 were presented).
b. Solve this problem by using the computer.

4. A jeweler and her apprentice make silver pins and necklaces by hand. Each week they have 80 hours of labor and 36 ounces of silver available. It requires 8 hours of labor and 2 ounces of silver to make a pin, and 10 hours of labor and 6 ounces of silver to make a necklace. Each pin also contains a small gem of some kind. The demand for pins is no more than six per week. A pin earns the jeweler $400 in profit, and a necklace earns $100. The jeweler wants to know how many of each item to make each week to maximize profit.

a. Formulate an integer programming model for this problem (written in a format similar to the way Problems 1 and 2 were presented).
b. Solve this problem by using the computer (note: if using QM for Windows, be sure to use the Integer and Mixed Integer Programming Module).

5. A transportation problem involves the following costs, supply and demand.

To
From 1 2 3 4 Supply
1 $500 $750 $300 $450 12
2 650 800 400 600 17
3 400 700 500 550 11
Demand 10 10 10 10

a. Formulate a linear programming model for this problem (written in a format similar to the way Problems 1 and 2 were presented).
b. Solve this transportation problem by using the computer (note: if using QM for Windows, be sure to select the transportation module).

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