Julia's Food Booth

Week 7 Assignment 3, Case Julia's Food Booth

Will Tyler

Dr. Vargha Azad

MAT540 Quantitative Methods

Mar. 16th 2013

1. Develop a transportation model for shipping from the 6 plants directly to the 3 disposal sites. Describe and implement the model.

The transportation model is looking for the lowest cost to transfer barrels of waste from 6 plants that can go to 3 different disposal sites, resulting in 18 decision variables. X = the number of barrels, i = the plants and j = the disposal sites. For simplicity I have named the plants 1 - 6 and the sites A, B and C.

The objective function is to minimize the transportation costs of the following table:

| | Waste Disposal Sites | |

Plant | Whitewater | Los Canos | Duras |

Kingsport | 12 | 15 | 17 |

Danville | 14 | 9 | 10 |

Macon | 13 | 20 | 11 |

Selma | 17 | 16 | 19 |

Columbus | 7 | 14 | 12 |

Allentown | 22 | 16 | 18 |

The formula for the objective function is

Minimize Z = 12+ 15+ 17+ 14+ 9+ 10+ 13+ 20 +11

+17 +16 +19 +7 +14 +12 +22 +16 +18

Each plant produces a different amount of barrels each week and each disposal site is limited to the amount it can handle. The amounts produced and the capacity of each site is shown below.

Plant | Bbls Produced | | | Waste Disposal Sites | | |

Kingsport | 35 | | | Whitewater | Los Canos | Duras |

Danville | 26 |   | Capacity | 65 | 80 | 105 |

Macon | 42 | | | | | |

Selma | 53 | | | | | |

Columbus | 29 | | | | | |

Allentown | 38 | | | | | |

Since the total capacity of the 3 sites is more than the barrels produced they will be able to handle this unbalanced transportation model with no problems. Since all of the barrels can be disposed we come up with the following 6 constraints:

+ + = 35

+ + = 26

+ + = 42

+ + = 53

+ + = 29

+ + = 38

This reflects the number of barrels (X) at the plant (1-6) going to the site (A,B or C) ensuring that all the barrels are disposed.

Because the sites are...