PRIN.OF OPERATIONS MANAGEMENT-MYOMLAB
PRIN.OF OPERATIONS MANAGEMENT-MYOMLAB
11th Edition
ISBN: 9780135226742
Author: HEIZER
Publisher: PEARSON
Question
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Chapter 8, Problem 23P

a)

Summary Introduction

To determine: The center-of-gravity coordinates the new store to be located.

Introduction: Location is one of the important element for a business that controls the cost and expenses. Location strategies support in framing other strategies for a firm where optimal location point will provide competitive advantage to a firm.

a)

Expert Solution
Check Mark

Answer to Problem 23P

The coordinates of the center of gravity are (66.69, 30.22).

Explanation of Solution

Given information:

Census Tract Population in census tract X,Y
101 2,000 (25, 45)
102 5,000 (25, 25)
103 10,000 (55, 45)
104 7,000 (50, 20)
105 10,000 (80, 50)
106 20,000 (70, 20)
107 14,000 (90, 25)

Center-of-gravity coordinates of the new store:

Derive the coordinates of the Center of gravity by proceeding sequentially as per the following steps given the population data and the coordinates of various census tracts.

PRIN.OF OPERATIONS MANAGEMENT-MYOMLAB, Chapter 8, Problem 23P , additional homework tip  1

The various Census tracts under consideration are shown below in the graph.

PRIN.OF OPERATIONS MANAGEMENT-MYOMLAB, Chapter 8, Problem 23P , additional homework tip  2

The x coordinate of the centre of gravity Cx is given by the formula

Cx=idix×QiiQi (1)

where dix is the x coordinate of the location i and Qi is the shipping load to and from the location i

The y coordinate of the centre of gravity Cy is given by the formula

Cy=idiy×QiiQi (2)

where diy is the y coordinate of the location i and Qi is the shipping load to and from the location i

Use equation (1) and calculate Cx as follows,

Cx=25×2,000+25×5,000+55×10,000+50×7,000+80×10,000+70×20,000+90×14,0002,000+5,000+10,000+7,000+10,000+20,000+14,000=4,535,00068,000=66.69

Use equation (2) and calculate Cy,

Cy=45×2,000+25×5,000+45×10,000+20×7,000+50×10,000+20×20,000+25×14,0002,000+5,000+10,000+7,000+10,000+20,000+14,000=2,055,00068,000=30.22

The coordinates of the center of gravity are (66.69, 30.22), marked in red color in the graph below.

PRIN.OF OPERATIONS MANAGEMENT-MYOMLAB, Chapter 8, Problem 23P , additional homework tip  3

Hence, the coordinates of the center of gravity are (66.69, 30.22).

b)

Summary Introduction

To determine: The change in center-of-gravity coordinates of the new store when 103 and 105 census tracts grow by 20%.

b)

Expert Solution
Check Mark

Answer to Problem 23P

The new coordinates of the center of gravity marginally shifts to (66.74, 31.18).

Explanation of Solution

Given information:

Census tract 103 and 105 grow by 20%.

Census Tract Population in census tract X,Y
101 2,000 (25, 45)
102 5,000 (25, 25)
103 12,000 (55, 45)
104 7,000 (50, 20)
105 12,000 (80, 50)
106 20,000 (70, 20)
107 14,000 (90, 25)

Calculation of change in center-of-gravity coordinates:

Derive the center of gravity, given that the population growth in census tracts 103 and 105 has increased by 20% as shown in the table.

PRIN.OF OPERATIONS MANAGEMENT-MYOMLAB, Chapter 8, Problem 23P , additional homework tip  4

Use equation (1) and calculate Cx as follows

Cx=25×2,000+25×5,000+55×12,000+50×7,000+80×12,000+70×20,000+90×14,0002,000+5,000+12,000+7,000+12,000+20,000+14,000=4,805,00072,000=66.74

Use equation (2) and calculate Cy

Cy=45×2,000+25×5,000+45×12,000+20×7,000+50×12,000+20×20,000+25×14,0002,000+5,000+12,000+7,000+12,000+20,000+14,000=2,245,00072,000=31.18

The new coordinates of the center of gravity marginally shifts to (66.74, 31.18) as shown below.

PRIN.OF OPERATIONS MANAGEMENT-MYOMLAB, Chapter 8, Problem 23P , additional homework tip  5

Hence, the new coordinates of the center of gravity marginally shifts to (66.74, 31.18).

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