MAT 540 Stateline Shipping and Transport Company

MAT 540 Stateline Shipping and Transport Company


Asked by 3 years ago
398.3k points

Assignment #4: Case Problem "Stateline Shipping and Transport Company"

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

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

  • 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.

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

1. 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.

There are two deliverables for this Case Problem, the Excel spreadsheets and an accompanying written description/explanation.  Please submit both of them electronically via the dropbox.

MAT 540
maddy

1 Answer

Answered by 3 years ago
393k points

I treat this problem similar to a transportation problem for optimization. In this case we want to find routes which will minimize the cost of transportation of the 6 plants to the 3 waste disposal sites. The following table represents cost and capacity.

Whitewater Los Canos Duras Availability (bbl)
Kingsport 12 15 17 35
Danville 14 9 10 26
Macon 13 20 11 42
Selma 17 16 19 53
Columbus 7 14 12 29
Allentown 22 16 18 38
Capacity (barrels) 65 80 105  -

for the above table let,

$x_{ij} = \text{quantity of waste transported from the }i_{th} \text{ plant to the } k_{th}\text{ waste center}$

where,

$i=1,2,3,4,5,6$ and $j=1,2,3$

hence we want to minimize the objective function,

$$C=12x_{11}+15x_{12}+17x_{13}+14x_{21}+9x_{22}+10x_{23}+13x_{31}+20x_{32}+11x_{33}+17x_{41}+16x_{42}$$

$$+19x_{43}+7x_{51}+14x_{52}+12x_{53}+22x_{61}+16x_{62}+18x_{63}$$

which is subject the following contraints,

$$x_{11}+x_{12}+x_{13}=35$$

$$x_{21}+x_{22}+x_{23}=26$$

$\ldots$

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