Chapter 6, Problem 3CQD

Summary Introduction

Interpretation:

Summary score of center of gravity, cost and qualitative criteria.

Concept Introduction:

Location is one of the most important aspect of business. Business must be located within close vicinity of market. It is advantageous if it s close to warehouse, market, suppliers of goods, customers etc, it leads to reduction in cost, thereby economies of scale.

Center of gravity is an approach to select a business facility with the minimum cost. It coordinates all the facilities like transportation, warehouse, market, suppliers of raw material, customer etc. and gives the best location for a business facility.

Explanation of Solution

Center of gravity is calculated as follows:

Center of gravity $=\frac{x_1{d}_1+x_2{d}_2+x_3{d}_3\mathrm{....}{x}_n{d}_n}{d_1+d_2+d_3\mathrm{....}{d}_n}$

Center of gravity $=\frac{1\times 290,000+11\times 95,000+4\times 145,000+2\times 80,000+10\times 120,000}{290,000+95,000+145,000+80,000+120,000}$

Center of gravity $=\frac{290,000+1,045,000+580,000+160,000+1,200,000}{730,000}$

Center of gravity $=\frac{3,275,000}{730,000}$

Center of gravity $=4.48$

  $\text{x}\text{coordinate}\text{=}\text{4}\text{.48}$ (population center)

Center of gravity $=\frac{y_1{d}_1+y_2{d}_2+y_3{d}_3\mathrm{....}{y}_n{d}_n}{d_1+d_2+d_3\mathrm{....}{d}_n}$

Center of gravity $=\frac{11\times 290,000+11\times 95,000+8\times 145,000+1\times 80,000+2\times 120,000}{290,000+95,000+145,000+80,000+120,000}$

Center of gravity $=\frac{3,190,000+1,045,000+160,000+80,000+240,000}{730,000}$

Center of gravity $=\frac{5,715,000}{730,000}$

Center of gravity $=7.82$

  $y\text{coordinate}\text{=}7.84$ (population center).

According to the center of gravity, the best location for stadium coordinates is (4.48, 7.84)

Stadium coordinate $\left(4.48,7.84\right)$

It is nearest to 3^rd population center

2^nd nearest to population center 1

Population center 1 is better as it has more population compared to other centers.

Transportation like airport and shopping center is also nearest to the location. So, stadium can be build at this location coordinate (4.48, 7.84).

Following is the score for each criterion that ranges from 1- 3

Criteria /Score	1	2	3
Gain environmental group(s) endorsement	No	Almost	Yes
Traffic access and congestion	Poor	Moderate	Good
Permit (road, utility, etc)	Ready	Mostly Ready	Not Ready
Long term economic growth and development	3	4	5
Chance to preserve a huge area of the country	High	Moderate	Low

Based on the above score, it is easy to give the score to the location site. Following is the score of the site for A, B, C and D along with weightage. The long term economic growth and development is given the higher weightage because it will give good growth opportunity to the site.

Location/Criteria	Weight	Site A	Site B	Site C	Site D
Gain environmental groups endorsement	0.15	2	1	1	3
Traffic access and congestion	0.10	3	1	1	2
Permit (road, utility, etc)	0.20	3	2	1	3
Long term economic growth and development	0.35	2	1	2	3
Chance to preserve a huge area of the country	0.20	2	1	3	1

Following is the calculation of the score for all the site using weightage

Location/Criteria	Weight	Site A	Site B	Site C	Site D
Gain environmental groups endorsement	0.15	0.30	0.15	0.15	0.45
Traffic access and congestion	0.10	0.30	0.10	0.10	0.20
Permit (road, utility, etc)	0.20	0.6	0.4	0.2	0.6
Long term economic growth and development	0.35	0.70	0.35	0.70	1.05
Chance to preserve a huge area of the country	0.20	0.40	0.20	0.60	0.20
Total	1.00	2.30	1.20	1.75	2.50

  $0.15\times Gainenvironmental+0.10\times Trafficaccess+0.20\times Permit+0.35\times Longtermeconomic$

  $+0.2\times Chancetopreserve$

  $SiteA=0.15\times 2+0.10\times 3+0.20\times 3+0.35\times .2+0.20\times 2$

  $SiteA=0.30+0.30+0.60+0.70+0.40$

  $SiteA=2.30$

The score of Site A is 2.30. Similarly, the score of Site B, C and D is 1.20, 1.75 and 2.50 respectively. Site D score is better than other sites; hence Site D is more preferable.

Following is the total cost for all the site A, B, C and D

	Site A	Site B	Site C	Site D
Stadium land cost (million)	18.0	22.0	0.0	22.0
Additional utility cost (million)	1.0	0.5	3.0	0.5
New round cost (million)	2.0	0.5	15.0	2.0
Total cost (million)	21.0	23.0	18.0	24.5
Acres	241	209	-	106
Total cost / acres (million)	0.0871	0.110048	18.0	0.231132

Site D consist of maximum cost, but the weightage score is higher compared to Site A. Site A has comparable score and consists of less cost compared to Site D. Shopping Mall 1 and Airport is near to Site A whereas Population center 2 and Airport is near to Site D. Hence, it is recommended that firm must choose Site D to build a stadium.