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MAT 540 Quantitative Methods- Stateline Shipping and Transport Company

Question # 00000702
Subject: Mathematics
Due on: 09/06/2013
Posted On: 09/04/2013 07:01 PM

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Stateline Shipping and Transport Company

Rachel Sundusky is the manager of the South-Atlantic office of the Stateline Shipping and Transport Company. She is in the process of negotiating a new shipping contract with Polychem, a company that manufactures chemicals for industrial use. Polychem want Stateline to pick up and transport waste products from its six plants to three waste disposal sites. Rachel is very concerned about this proposed arrangement. The chemical wastes that will be hauled can be hazardous to humans and the environment if they leak. In addition, a number of towns and communities in the region where the plants are located prohibit hazardous materials from being shipped through their municipal limits. Thus, not only will the shipments have to be handled carefully and transported at reduced speeds, they will also have to traverse circuitous routes in many cases. 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, 80, 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

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

__

Rachel wants to determine the shipping routes that will minimize Stateline’s total cost in order to develop a contract proposal to submit to Polychem for waste disposal. She particularly wants to know if it would be cheaper to ship directly from the plants to the waste sites or if she should drop and pick up some loads at the various plants and waste sites. Develop a model to assist Rachel and solve the model to determine the optimal routes.

Read the 'Stateline Shipping and Transport Company" Case Problem on pages 273-274 of the text. Analyze this case, as follows:

1.

In Excel, or other suitable program, develop a model for shipping the waste directly from the 6 plants to the 3 waste disposal sites.

2.

Solve the model you developed in #1 (above) and clearly describe the results. In Excel, or other suitable program, Develop a transshipment model in which each of the plants and disposal sites can be used as intermediate points.

3.

Solve the model you developed in #3 (above) and clearly describe the results.

4.

Interpret the results and draw conclusions that address the question posed in the case problem. What are the limits of the study? Write at least one paragraph.

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Stateline Shipping and Transport Company

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Stateline_Shipping_and_Transport_Company.docx (406.17 KB)
Preview: from xxx six xxxxxx to the xxxx waste disposal xxxxx + xxxxxxx xx barrels xxxxxxx from other xxxxx disposal sites xx i-th xxxxx xxxxxxxx site) xxx (Number of xxxxxxx shipped to xxxxx waste xxxxxxxx xxxxx from xxxx waste disposal xxxxxxxxx the three xxxxxx constraints xxx xxxxxxxxx + xx +) + xxx – (+) x 65(+ x x + xx + (+) xxx (+) ? xxxx ++ x xx + xxx – (+) x 105Thus the xxxxxx programming xxxxx xxx the xxxxxxxxxxxxx problem is xxxxxxxxxx as follows:Minimize x = xxx xxx 17+ xxx 9+ 10+ xxx 20 +11 x 17 xxx xxx +7 xxx +12 +22 xxx +18+ 6+ xx 9+ xx xx 6+ xxx 10 +12+ x + 5+ xxx 3+ xx xxx 9+ xxx 3 + xx 16+ 7+ xxx 7+ xx xxx 8+ xx 15 + xxx 14+ 12+ xxx 12+ xxx xxx 15Subject xxxx + = xx + (+ x + xx xxx (+ x + + x + + x 26 x xx + x +) – xxx ++ )+ x = xx x (+ x + +) xxx (++++) + x = xx x (+ x + +) xxx (++ + xx + x x 29 x (+ + x +) – xxxxxx + x x 38 x (+ + x +) – xxx + xxxx x ++ xx + (+) xxx (+) ? xxxx + x x +) x (+) – xxx ? 80(+ xx + xx x (+) xxx (+) ? xxxxx Solve the xxxxx you xxxxxxxxx xx #3 xxxxxxx and clearly xxxxxxxx the results xxxxxxxxx Danville xxxxx xxxxx Columbus xxxxxxxxxxxxxxxxxxxxxx 000Danville000 000Macon000 xxxxxxxxxxxx 0360Columbus000 000Allentown000 xxx ------------------------------------------------------------------------------------------------------Total xxxx xxxxxxxxx Whitewater xxx Canos Duras xxxxxx Accum SupplyKingsport xxx 0 xx xxxxxxxxxx 026 x 26 26Macon xx 78 42 xxxxxxx 00 x xx 0Columbus xxx 0 29 xxxxxxxxxxx 038.....
mat_excel.xlsx (13.58 KB)
Preview: Shipping xxxx ($ xxx barrel)KingsportDanvilleMaconSelmaColumbusAllentownWhitewaterLos CanosDurasPLANTWASTE.....
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