Stat week 8

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 transportationcompany 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.