RFC Bearings has just entered the U.S .market. It has three major DCs in the Atlanta, Boston, and Chicago areas.
Annual demand served by each DC is estimated to be:
Atlanta 10,000 Boston 20,000 Chicago 15,000
Four plants (Memphis, Philadelphia, Toledo) supply the DCs. Per-unit transportation costs and plant capacities are given in the following table:
|
Plant Location
|
Distribution Center
|
Plant
Capacity
|
|
Atlanta
|
Boston
|
Chicago
|
|
Memphis
|
$3
|
9
|
7
|
30,000
|
|
Philadelphia
|
5
|
2
|
4
|
35,000
|
|
Toledo
|
6
|
6
|
2
|
35,000
|
Using the notation:
XMA = Qty shipped from Memphis to Atlanta
XMB = Qty shipped from Memphis to Boston, etc.,
write down a model that will determine the optimal demand allocation (i.e. minimize transportation costs.)
Suppose now that the three locations (Memphis, Philadelphia, Toledo) are potential locations, i.e., each plant would only be constructed if it improves overall cost (i.e., transportation plus plant fixed costs). The data is repeated here with the (annualized) plant fixed costs shown additionally.
|
Plant Location
|
Distribution Center
|
Plant
Capacity
|
Annualized
Fixed Costs
|
|
Atlanta
|
Boston
|
Chicago
|
|
Memphis
|
$3
|
9
|
7
|
30,000
|
$50,000
|
|
Philadelphia
|
5
|
2
|
4
|
35,000
|
45,000
|
|
Toledo
|
6
|
6
|
2
|
35,000
|
48,000
|
What changes would you make to the model in part (a) so that we can determine the optimal locations of the plants as well as the optimal demand allocation (i.e. minimize both transportation as well as fixed costs).