Stateline Shipping and Transport Company”

Assignment #4: Case Problem “Stateline Shipping and Transport Company”

Courtney Boone
June 10, 2012
MATH 540 Quantitative Methods
Professor Gelonia Dent

Rachel has estimated the cost of shipping a barrel of waste from each of the six plants to each of the three waste disposal sites as shown in the following table: Waste Disposal Site | | | | 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 plants generate the following amounts of waste products each week: Plant | Waste per Week (bbl) | Kingsport | 35 | Danville | 26 | Macon | 42 | Selma | 53 | Columbus | 29 | Allentown | 38 |
The three waste disposal sites at Whitewater, Los Canos and Duras can accommodate a maximum of 65. 68 and 105 barrels per week, respectively.
In addition to shipping directly from each of the six plants to one of the three waste disposal sites, Rachel is also considering using each of the plants and waste disposal sites as intermediate shipping points. Trucks would be able to drop a load at a plant or disposal site to be picked up and carried on to the final destination by another truck and vice versa. Stateline would not incur any handling costs because Polychem has agreed to take care of all local handling of the waste materials at the plants and the waste disposal sites. In other words, the only cost Stateline incurs is the actual transportation cost. So Rachel wants to be able to consider the possibility that it may be cheaper to drop and pick up loads at intermediate points rather than ship them directly.
Rachel estimates the shipping costs per barrel between each of the six plants to be as follows: Plant | Kingsport | Danville | Macon | Selma | Columbus | Allentown | Kingsport | $--- | $6 | $4 | $9 | $7 | $8 | Danville | 6 | -- | 11 | 10 | 12 | 7 | Macon | 5 | 11 | -- | 3 | 7 | 15 | Selma | 9 | 10 | 3 | -- | 3 | 16 | Columbus | 7 | 12 | 7 | 3 | -- | 14 | Allentown | 8 | 7 | 15 | 16 | 14 | -- | The estimated shipping cost per barrel between each of the three waste disposal sites is as follows.
Waste Disposal Site Waste Disposal Site | Whitewater | Los Canos | Duras | Whitewater | $-- | $12 | $10 | Los Canos | 12 | -- | 15 | Duras | 10 | 15 | -- | It is clear that the minimum cost is $2822. This is based on having no intermediaries. If intermediaries are allowed, the price drops to $2630. In order to achieve such a cost the compant must use the following routes for transportation: Kingsport takes 19 bbl to Duras goes to Danville first, and then from Danville to Duras. 36 bbl waste from Shelma to Whitewater goes to Columbia first and then to Whitewater. Finally, 17 bbl going from Shelma to Duras must be transported to Macon first and then to Duras.