Determine the optimal demand allocation

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Reference no: EM13227408

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).

Reference no: EM13227408

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