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.

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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