Principles Of Operations Management
Principles Of Operations Management
11th Edition
ISBN: 9780135173930
Author: RENDER, Barry, HEIZER, Jay, Munson, Chuck
Publisher: Pearson,
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Chapter 3, Problem 17P

Ross Hopkins, president of Hopkins Hospitality, has developed the tasks, durations, and predecessor relationships in the following table for building new motels. Draw the AON network and answer the questions that follow.

Chapter 3, Problem 17P, Ross Hopkins, president of Hopkins Hospitality, has developed the tasks, durations, and predecessor

a) What is the expected (estimated) time for activity C?

b) What is the variance for activity C?

c) Based on the calculation of estimated times, what is the critical path?

d) What is the estimated time of the critical path?

e) What is the activity variance along the critical path?

f) What is the probability of completion of the project before week 36?

a)

Expert Solution
Check Mark
Summary Introduction

To determine: The expected time for activity C.

Introduction: In the activity on nodes (AON) project network diagram, the nodes denote activities and the arrows show only the precedence and succession sequence.

Answer to Problem 17P

The expected time for activity C is 12 weeks.

Explanation of Solution

Given information:

Activity Immediate predecessor Time estimates
Optimistic Most likely Pessimistic
A 4 8 10
B A 2 8 24
C A 8 12 16
D A 4 6 10
E B 1 2 3
F E,C 6 8 20
G E,C 2 3 4
H F 2 2 2
I F 6 6 6
J D,G,H 4 6 12
K I,J 2 2 3

Calculation of expected time for activity C:

AON project network diagram shown below, given the precedence relationships of various activities,

Principles Of Operations Management, Chapter 3, Problem 17P , additional homework tip  1

Figure 1

With the given predecessor AON diagram is constructed. To Calculate the expected time for activity C given the data that the optimistic time estimate “a” of activity C of 8 weeks, the most likely time estimate “m” of 12 weeks and the pessimistic time estimate “b” of 16 weeks using the formula.

Expectedtime=a+4m+b6 (1)

Where ‘a’ is the optimistic time estimate, ‘m’ is the most likely time estimate and ‘b’ is the pessimistic time estimate

Substitute into the equation (1), the values of a=8 weeks, m=12 weeks and b=16 weeks to obtain the expected time for activity C.

t=8+(4×12)+166=726=12weeks

Therefore the expected time for activity C is calcualted by adding 8, 48 and16 and dividing the sum with 6 which gives 12weeks

Hence, the expected time for activity C is 12 weeks.

b)

Expert Solution
Check Mark
Summary Introduction

To calculate: The variance for activity C.

Answer to Problem 17P

The variance for activity C is 1.78 weeks.

Explanation of Solution

Given information:

Activity Immediate predecessor Time estimates
Optimistic Most likely Pessimistic
A 4 8 10
B A 2 8 24
C A 8 12 16
D A 4 6 10
E B 1 2 3
F E,C 6 8 20
G E,C 2 3 4
H F 2 2 2
I F 6 6 6
J D,G,H 4 6 12
K I,J 2 2 3

Calculation of variance for activity C:

Calculate the variance for activity C using the formula

σ2=(b-a6)2 (2)

Substitute in equation (2) the values of b=16 weeks and a=8 weeks and obtain

σ2=(1686)2=169=1.78

The variance of activity C is calculated by squaring the value obtained by dividing the difference of 16 and 8 with 6 which gives the resultant as 1.28 weeks.

The variance in activity C is 1.78 weeks.

c)

Expert Solution
Check Mark
Summary Introduction

To determine: The critical path.

Answer to Problem 17P

The critical path AàCàFàHàJàK.

Explanation of Solution

Given information:

Activity Immediate predecessor Time estimates
Optimistic Most likely Pessimistic
A 4 8 10
B A 2 8 24
C A 8 12 16
D A 4 6 10
E B 1 2 3
F E,C 6 8 20
G E,C 2 3 4
H F 2 2 2
I F 6 6 6
J D,G,H 4 6 12
K I,J 2 2 3

Calculation of critical path:

Using equation (1) and (2)calculate the expected times and variances for all the activitiesand obtain the values shown in table.

Principles Of Operations Management, Chapter 3, Problem 17P , additional homework tip  2

Figure 1, shows the AON diagram which gives the critical path. The critical path is AàCàFàHàJàK.

Hence, the critical path AàCàFàHàJàK.

d)

Expert Solution
Check Mark
Summary Introduction

To Compute: The estimated time of the critical path.

Answer to Problem 17P

The critical path AàCàFàHàJàK which is 40.18 weeks.

Explanation of Solution

Given information:

Activity Immediate predecessor Time estimates
Optimistic Most likely Pessimistic
A 4 8 10
B A 2 8 24
C A 8 12 16
D A 4 6 10
E B 1 2 3
F E,C 6 8 20
G E,C 2 3 4
H F 2 2 2
I F 6 6 6
J D,G,H 4 6 12
K I,J 2 2 3

Calculation of estimated time of the critical path:

Figure 1, shows the AON diagram which gives the critical path. The critical path is AàCàFàHàJàK.

The various paths and the expected completion times are listed in the table

Various paths Completion times
AàBàEàFàIàK 37.18 weeks
AàBàEàGàJàK 31.18 weeks
AàCàFàHàJàK 40.18 weeks
AàCàGàJàK 31.51 weeks
AàDàJàK 22.84 weeks

Hence, the estimated time of the critical path AàCàFàHàJàK is 40.18 weeks.

e)

Expert Solution
Check Mark
Summary Introduction

To determine: The variance of the critical path.

Answer to Problem 17P

The variance of the critical path is 10.03 weeks.

Explanation of Solution

Given information:

Activity Immediate predecessor Time estimates
Optimistic Most likely Pessimistic
A 4 8 10
B A 2 8 24
C A 8 12 16
D A 4 6 10
E B 1 2 3
F E,C 6 8 20
G E,C 2 3 4
H F 2 2 2
I F 6 6 6
J D,G,H 4 6 12
K I,J 2 2 3

Calculation of variance of the critical path:

The activity variance σ2along the critical path AàCàFàHàJàK is the sum of the variances of individual activities A, C, F, H, J and K.

Therefore,

σ2=1+1.78+5.44+0+1.78+0.03=10.03

The activity variance along the critical path is the sum of 1, 1.78, 5.44, 0, 1.78, 0.03 is 10.03 weeks.

Hence, the variance of the critical path is 10.03 weeks

f)

Expert Solution
Check Mark
Summary Introduction

To compute: The probability of completion of the project before week 36 weeks.

Answer to Problem 17P

The probability of completion of the project before week 36 weeks is 9.34%.

Explanation of Solution

Given information:

Activity Immediate predecessor Time estimates
Optimistic Most likely Pessimistic
A 4 8 10
B A 2 8 24
C A 8 12 16
D A 4 6 10
E B 1 2 3
F E,C 6 8 20
G E,C 2 3 4
H F 2 2 2
I F 6 6 6
J D,G,H 4 6 12
K I,J 2 2 3

Calculation of probability of completion of the project before week 36 weeks:

Use the normal distribution tables given that the estimated mean time is 40.18 weeks and the standard deviation is square root of 10.03 weeks.

First compute the standard deviation σ by computing the square root of 10.03 weeks.

σ=10.03=3.17weeks

Calculate the z value as shown below

z=36-40.183.17=-1.32

For a z value of -1.32, the probability is 9.34%.

Therefore, there is a probability of 9.34% that the project may be completed on or before 36 weeks.

Hence, the probability of completion of the project before week 36 weeks is 9.34%.

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Students have asked these similar questions
Q1: Given the information below, draw the network (AOA) and find the probability of finishing the job in (40) weeks? Solve using PERT. Activity notation Weeks 1-2 2-3 2-4 2-5 3-6 4-7| 5-7 6-8 7-8 8-9 2,7,8 5,6,9 3,7,8 4,5,6 6,9,10 6,8,11 4,6,7 5,7,10 4,8,9 4,7,9 [50%]
b) – Draw the Activity-on-Node (AON) diagram using the following representation for every node: Activity Description Expected Time ES EF LS LF Slack C.) Complete the following table, determine the expected time of completion assuming that the project starts at week 0 (zero) and identify the critical path for this project. Demonstrate all your calculations. On Critical Path? Activity Activity Description ES EF LS LF Slack Yes or No Locate new facilities 2 Order furniture Interview prospective staff Hire and train staff 3 4. Remodel facilities Receive and set up furniture Move in and start up 6 7 a) Complete the following table, calculate the project variance and project standard deviation. Demonstrate all your calculations.
Please explain how to solve this chart  in terms of engineering project managment How can I draw the network diagrams?How can I list the network paths?How can I determine the critical paths? How can I determine the float for each activity?

Chapter 3 Solutions

Principles Of Operations Management

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