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.
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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