Transportation System
A company which manufactures product in five plants ships locally using its own transportation system, but has orders which must be sent to locations too far to be serviced by the local fleet. It therefore contracts with a middle distance carrier to complete its shipping. The locations of the manufacturing plants and the amount of product available to be shipped per week are show in the chart below.
|
Manufacturing Locations
|
Units Available per Week
|
|
Columbia
|
450
|
|
Macon
|
370
|
|
Huntsville
|
550
|
|
Greensboro
|
290
|
|
Knoxville
|
360
|
|
Total Available
|
2020
|
The seven locations and their weekly demand are shown in the chart below.
|
Destination Cities
|
Weekly Demand
|
|
Norfolk
|
305
|
|
Charleston
|
253
|
|
Gainesville
|
328
|
|
Mobile
|
225
|
|
Memphis
|
420
|
|
Louisville
|
158
|
|
Roanoke
|
210
|
|
Total Available
|
1899
|
Shipping costs per unit (in dollars) between plants and the destination cities are as follows:
|
Shipping Costs
|
Norfolk
|
Charleston
|
Gainesville
|
Mobile
|
Memphis
|
Louisville
|
Roanoke
|
|
Columbia
|
27
|
13
|
31
|
42
|
48
|
51
|
44
|
|
Macon
|
42
|
27
|
19
|
23
|
18
|
36
|
43
|
|
Huntsville
|
42
|
31
|
23
|
16
|
20
|
39
|
36
|
|
Greensboro
|
28
|
25
|
36
|
48
|
37
|
32
|
17
|
|
Knoxville
|
47
|
31
|
43
|
39
|
16
|
14
|
34
|
The transportation company wants to identify its optimal shipping plan that will satisfy demand at the lowest aggregate shipping cost.
Questions:
- What is the transportation company trying to optimize? Are they trying to maximize or minimize?
- Write the objective function to support this analysis.
- What inputs do you need to support your analysis?
- Is there any extraneous data you have been given that you will not need?
- What criteria has the transportation company given you to support the analysis?
- Create a spreadsheet model that supports your analysis.
- How would you change your model if one of the locations was temporarily unavailable due to severe weather conditions? On a separate sheet in your Excel file, show how you might do this.