Question

Facility Location Problem Karen Fowler owns the Rockey Mountain Coolers, a semiprofessional basketball 1. team in Northern Colorado. She wishes to move the Coolers east to either Atlanta or Charlotte. The table below gives the factors that Karen thinks are important, their weights, and the scores for Atlanta and Charlotte. Which site should she select in this example? Weight Chatlotte Factor Incentive Atlanta 0.4 80 60 Player Satisfaction Sports Interest Size of city 0.3 0.2 20 40 50 90 0.1 70 30 The fixed and variable costs for two potential plant sites for a ski equipment 2. manufacturer are computed as follows: Cost Victoria S1,000,000 $73/unit Perth $800,000 $112/unit Fixed Variable Graph the total-cost lines for the two potential sites Over what range is each city preferable? If expected volume of the ski equipment is 5,000 units, which site would you recommened? 3. The following table gives the map coordinates and the shipping loads for a set of cities that we wish to connect through a central "hub". Near which map coordinates should the hub be located? Shipping Load Map Coordinates (x. y) (5, 10) (6, 8) City A 5 10 15 C (4, 9) (9, 5) (7, 9) (3, 2) (2, 6) 5 15 E 10 5

Answer 1

1. Let's compute the weighted final score for both the sites.

Final Score = Σw_i*S_i

Weight	Atlanta	Chatlotte
0.4	80	60
0.3	20	50
0.2	40	90
0.1	70	30
Final Score	53	60

Hence, Chatlotte site should be selected as it has a better score.

2. Say x be the number of units produced.

Equation of Victoria: y = 1000000 + 73x
Equation of Perth: y = 800000 + 112x

Graph 2500000 2000000 1500000 Victoria Perth 1000000 500000 0 2000 4000 6000 8000 10000 12000

Here, y is the cost in dollars

The two lines meet at x = 5128.205.
Victoria is preferable till the number of units produced are in the range (0, 5128)
Perth is preferable till the number of units are more than or equal to 5129.

If expected volume is 5000 units (5000 < 5129), Victoria site should be recommended

3. The calculations are shown below:

City	x	y	Load	x*Load	y*Load
A	5	10	5	25	50
B	6	8	10	60	80
C	4	9	15	60	135
D	9	5	5	45	25
E	7	9	15	105	135
F	3	2	10	30	20
G	2	6	5	10	30
			65	335	475
			Cx	5.15
			Cy	7.31

The hub location should be (5.15, 7.31)