+1-415-670-9189

info@expertsmind.com

# Center of Gravity Method Assignment Help

###
Location Evaluation Methods - Center of Gravity Method
**Center of Gravity Method of Plant Location**

The center of gravity method is used to find the optimal location for a distribution center that minimizes total transportation costs. This method takes into account factors such as markets, cost of goods, and cost of transportation. The center of gravity method aims at minimizing the total shipping cost, i.e. cost incurred for shipping from the distribution center to the different shipping points.

If the shipping quantities for all destination points are equal, the location at which the transportation cost will be minimum can be identified by taking the arithmetic averages of the X and Y coordinates of the destination. But if the shipping quantities are unequal, the location can be found using a weighted average approach (the quantities to be shipped are taken as weights).

The center of gravity of a geographical location can be identified by calculating the X and Y coordinate values of the location that would minimize transportation costs.

The coordinates of the center of gravity can be identified by

Where,

X_{c} = X coordinate of the center of gravity

Y_{c }= Y coordinate of the center of gravity

V_{i }= Volume of items transported to and from location i

X_{i }= X coordinate of location i

Yi= Y coordinate of the location i

**Problem **

Figure shows the X and Y coordinates of seven retail locations of a retail chain. Information regarding the quantity to be shipped to each of the seven locations is given in Table 1. Using the center of gravity method, identify the coordinates of the optimal location for the warehouse.

### Table 1

**Retail Outlet **

**X **

**Y **

**VOLUME **

A

4

10

80

B

3.5

15

100

C

4

6

120

D

10

2

130

E

16

6

100

F

8

5

150

G

14

13

90

### Solution

### Table 2

**Retail Outlet **

**X**_{i}

**Y**_{i}

**Volume (V**_{i})

**V**_{i}X_{i}

**V**_{i}Y_{i}

A

4

10

80

320

800

B

3.5

15

100

350

1500

C

4

6

120

480

720

D

10

2

130

1300

260

E

16

6

100

1600

600

F

8

5

150

1200

750

G

14

13

90

1260

1170

From Table 2, we can get the value of

Substituting these values in the equation for

Volume-weighted X coordinate = X_{c=}_{ }

Volume-weighted Y coordinate = Y_{c }=

The X and Y coordinates of the point of center of gravity are 8.45 and 7.53.

Figure 6.3 shows that the location of the warehouse is closest to the location of retail outlet F.

#### Figure: Location of Center of Gravity

Email based Operations Management assignment help - homework help at Expertsmind

Are you searching Operations Management expert for help with Center of Gravity Method questions? Center of Gravity Method topic is not easier to learn without external help? We at www.expertsmind.com offer finest service of Operations Management assignment help and Operations Management homework help. Live tutors are available for 24x7 hours helping students in their Center of Gravity Method related problems. We provide step by step Center of Gravity Method question's answers with 100% plagiarism free content. We prepare quality content and notes for Center of Gravity Method topic under Operations Management theory and study material. These are avail for subscribed users and they can get advantages anytime.

**Why Expertsmind for assignment help**

- Higher degree holder and experienced experts network
- Punctuality and responsibility of work
- Quality solution with 100% plagiarism free answers
- Time on Delivery
- Privacy of information and details
- Excellence in solving Operations Management questions in excels and word format.
- Best tutoring assistance 24x7 hours

**Center of Gravity Method of Plant Location**

_{c}= X coordinate of the center of gravity

_{c }= Y coordinate of the center of gravity

_{i }= Volume of items transported to and from location i

_{i }= X coordinate of location i

**Problem**

### Table 1

**Retail Outlet **

**X **

**Y **

**VOLUME **

A

4

10

80

B

3.5

15

100

C

4

6

120

D

10

2

130

E

16

6

100

F

8

5

150

G

14

13

90

### Table 2

**Retail Outlet **

**X _{i} **

**Y _{i} **

**Volume (V _{i}) **

**V _{i}X_{i} **

**V _{i}Y_{i} **

A

4

10

80

320

800

B

3.5

15

100

350

1500

C

4

6

120

480

720

D

10

2

130

1300

260

E

16

6

100

1600

600

F

8

5

150

1200

750

G

14

13

90

1260

1170

_{c=}_{ }_{c }=**Why Expertsmind for assignment help**