Question

In: Operations Management

3. The Covington Paper Inc. would like to determine the location of its new DC which...

3. The Covington Paper Inc. would like to determine the location of its new DC which will serve their six manufacturing facilities in Midwest. Information is provided below.

Find the optimal location with median method. show your work
Find the optimal location with gravity method. show your work

Plants	x- coordinate	y coordinates	Production in terms of # of TLs /period
A	6	20	220
B	48	12	330
C	25	36	560
D	12	5	330
E	30	50	225
F	18	20	115

Expert Solution

i. Finding the optimal location using the median method

Step 1:

The x-coordinates are rearranged in ascending order in a table corresponding to the production of the location.

And the cumulative production is calculated.

Plants	x coordinates in ascending order	Production of the plant	Cumulative production
A	6	220	220
D	12	330	550
F	18	115	665
C	25	560	1125
E	30	225	1450
B	48	330	1780 = N

The median of the cumulative production can be found by N/2, (N/2)+1

N/2 = 890, (N/2)+1 = 891 these median values fall under the cumulative production range of 1125, therefore, the x-coordinate is 25.

Step 2:

The y-coordinates are rearranged in ascending order in a table corresponding to the production of the location.

And the cumulative production is calculated.

Plants	y coordinates in ascending order	Production of the plant	Cumulative production
D	5	220	220
B	12	330	550
A	20	115	665
F	20	560	1125
C	36	225	1450
E	50	330	1780 = N

The median of the cumulative production can be found by N/2, (N/2)+1

N/2 = 890, (N/2)+1 = 891 these median values fall under the cumulative production range of 1125, therefore, the y-coordinate is 20.

The optimal location by the median method is (25,20)

b. )

Solution:

the optimal location formula is

Xp = xPr / Pr

Yp = yPr / Pr

x is the x coordinate of the plant location

y is the y coordinate of the plant location

And Pr is the production of each plant

Plants	x	y	Pr	xPr	yPr
A	6	20	220	1320	4400
B	48	12	330	15840	3960
C	25	36	560	14000	20160
D	12	5	330	3960	1650
E	30	50	225	6750	11250
F	18	20	115	2070	2300

			Pr = 1780	xPr = 43940	yPr = 43720

Xp = xPr / Pr

Xp = 43940 / 1780

Xp = 24.685

Yp = yPr / Pr

Yp = 43720 / 1780

Yp = 24.561

Therefore, the optimal location using center of gravity method is (24.685, 24.561)

keosha answered 3 months ago

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