Stateline Shipping and Transport

Stateline Shipping and Transport Co.

Tim Ilderton

Dr. Yaw Kyei

Quantitative Methods- MAT 540

March 20, 2013

1. The transportation model for this problem has 18 decision variables and they are the cost to move the waste from 1 of 6 plants to 1 of 3 disposal sites. The plants are represented numerically from 1-6 and the disposal sites are represented alphabetically as a, b, and c.

We are trying to minimize the costs so what we are doing is multiplying the cost to transport a barrel of waste from a plant to the disposal site by the number of barrels transported. The objective function is represented by the following formula.

Minimize Z = 12x1a+15x1b+17x1c+14x2a+9x2b+10x2c+13x3a+20x3b+11x3c+17x4a+16x4b+

19x4c+7x5a+14x5b+12x5c+22x6a+16x6b+18x6c

Next we have our constraints of which there are 9. They represent the barrels needing to be shipped from the plants and the barrels that each disposal site can receive. The first six are supply constraints which are the amount of waste that has to be shipped from each plant. They are:

x1A + x1B + x1C = 35

x2A + x2B + x2C = 26

x3A + x3B + x3C = 42

X4A+ x4B + x4C = 53

x5A + x5B + x5C = 29

x6A + x6B + x6C = 38

The first constraint represents the amount of waste that needs to be shipped from Kingsport to a disposal site. I used an equal’s sign because this is the amount that has to be shipped, no more and no less. Notice that the first constraint contains all 1’s since Kingsport is the only plant represented in that constraint. The letters vary, because which plant the waste is shipped to is a non-factor in this constraint and will be represented in the next 3 constraints.

The next 3 constraints are the demand constraints and are represented as follows:

x1a+x2a+x3a+x4a+x5a+x6a<=65...