Loose-leaf for Operations Management (The Mcgraw-hill Series in Operations and Decision Sciences)
Loose-leaf for Operations Management (The Mcgraw-hill Series in Operations and Decision Sciences)
12th Edition
ISBN: 9781259580093
Author: William J Stevenson
Publisher: McGraw-Hill Education
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 17, Problem 11P

The following precedence diagram reflects three time estimates in weeks for each activity. Determine:

a. The expected completion time for each path and its variance.

b. The probability that the project will require more than 49 weeks.

c. The probability that the project can be completed in 46 weeks or less.

Chapter 17, Problem 11P, The following precedence diagram reflects three time estimates in weeks for each activity.

a)

Expert Solution
Check Mark
Summary Introduction

To determine: The expected completion time for each path and its variance.

Explanation of Solution

Given information:

Loose-leaf for Operations Management (The Mcgraw-hill Series in Operations and Decision Sciences), Chapter 17, Problem 11P

Activity Optimistic time Most likely time Pessimistic time
1 to 2 8 8 8
2 to 3 11 12 13
2 to 4 5 6 7
2 to 5 10 12 14
3 to 8 9 10 12
4 to 6 14 18 26
4 to 7 13 13 13
5 to 9 7 10 12
6 to 11 8 10 14
7 to 11 10.5 13 15.5
8 to 11 5 7 10
9 to 10 10 11 12
10 to 11 6 6 6

Formula to calculate expected time and variance:

Expected time=Optimistic time+(4×Most likely time)+Pessimistic time6

Standard deviation=Pessimistic time-Optimistic time6

Variance=(Pessimistic time-Optimistic time)262

Calculation of mean and variance:

Activity Optimistic time Most likely time Pessimistic time Expected time Standard deviation Variance
A B C (A+(4*B)+C)/6 (C-A)/6 (C-A)^2/6^2
1 to 2 8 8 8 8 0.000 0.000
2 to 3 11 12 13 12 0.333 0.111
2 to 4 5 6 7 6 0.333 0.111
2 to 5 10 12 14 12 0.667 0.444
3 to 8 9 10 12 10.17 0.500 0.250
4 to 6 14 18 26 18.67 2.000 4.000
4 to 7 13 13 13 13 0.000 0.000
5 to 9 7 10 12 9.83 0.833 0.694
6 to 11 8 10 14 10.33 1.000 1.000
7 to 11 10.5 13 15.5 13 0.833 0.694
8 to 11 5 7 10 7.17 0.833 0.694
9 to 10 10 11 12 11 0.333 0.111
10 to 11 6 6 6 6 0.000 0.000

Calculation of expected duration, variance and standard deviation for each path:

Path 1-2-3-8-11:

Expected duration=8+12+10.17+7.17=37.34

Variance=0+0.111+0.250+0.694=1.055

Standard deviation=Variance=1.055=1.027

Path 1-2-4-6-11:

Expected duration=8+6+18.67+10.33=43

Variance=0+0.111+4+1=5.111

Standard deviation=Variance=5.111=2.2607=2.261

Path 1-2-4-7-11:

Expected duration=8+6+13+13=40

Variance=0+0.111+0+0.694=0.805

Standard deviation=Variance=0.805=0.898

Path 1-2-5-9-11:

Expected duration=8+12+9.83+11+6=46.83

Variance=0+0.444+0.694+0.111=1.249

Standard deviation=Variance=1.249=1.1175=1.118

b)

Expert Solution
Check Mark
Summary Introduction

To determine: The probability that the project will require more than 49 weeks.

Answer to Problem 11P

The probability that the project will require more than 49 weeks is 0.0301.

Explanation of Solution

Calculation of probability of completion in more than 49 weeks:

Calculation of z value for all paths:

Formula:

Z=Specified time-Path meanPath standard deviation

Greater than 49 weeks:

Path 1-2-3-8-11:

Z=49-37.341.027=11.35

Since z value is greater than +3.00, probability of completion is 1.00.

Path 1-2-4-6-11:

Z=49-432.261=2.65

From the standard normal distribution table,

The probability value for (z = 2.261) is 0.9960.

Path 1-2-4-7-11:

Z=49-400.898=10.02

Since z value is greater than +3.00, probability of completion is 1.00.

Path 1-2-5-9-10-11:

Z=49-46.831.118=1.94

From the standard normal distribution table,

The probability value for (z = 1.94) is 0.9738.

Probability of completion in less than or equal to 49 weeks:

Probability=1.0000×0.9960×1.00×0.9738=0.9699

Calculation of probability of completion in greater than 49 weeks:

Probability=1.0000-0.9699=0.0301

The probability that the project will require more than 49 weeks is 0.0301.

c)

Expert Solution
Check Mark
Summary Introduction

To determine: The probability that the project will be completed in 46 weeks or less.

Answer to Problem 11P

The probability that the project will be completed in 46 weeks or less is 0.2085.

Explanation of Solution

Calculation of probability of completion in 46 weeks or less:

Calculation of z value for all paths:

Formula:

Z=Specified time-Path meanPath standard deviation

Path 1-2-3-8-11:

Z=46-37.341.027=8.43

Since z value is greater than +3.00, probability of completion is 1.00.

Path 1-2-4-6-11:

Z=46-432.261=1.33

From the standard normal distribution table,

The probability value for (z = 1.33) is 0.9082.

Path 1-2-4-7-11:

Z=46-400.898=6.68

Since z value is greater than +3.00, probability of completion is 1.00.

Path 1-2-5-9-10-11:

Z=46-46.831.118=0.74

From the standard normal distribution table,

The probability value for (z = -0.74) is 0.2296.

Probability of completion in less than or equal to 46 weeks:

Probability=1.0000×0.9082×1.0000×0.2296=0.2085

The probability that the project will be completed in 46 weeks or less is 0.2085.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
The following precedence diagram reflects three time estimates in weeks for each activity.Determine:a. The expected completion time for each path and its variance.b. The probability that the project will require more than 49 weeks.c. The probability that the project can be completed in 46 weeks or less.
A solved PERT problem is detailed in the table below. The expected time and variance values and the critical activities are given in the table below. Answer the following questions by filling the blanks (WRITE YOUR ANSWERS TO 2 DECIMAL PLACES. DO NOT ROUND UP OR DOWN): a. The expected project completion time for this problem is  and the standard deviation is . b. There is a 0.95 probability that the project will be completed by  weeks. Activity Expected time Variance Critical? A 10 0.36 Yes B 7 0.11 No C 7 0.25 No D 3 0.48 Yes E 5 1.60 Yes F 7 0.69 No G 2 3.69 Yes
The following estimates of activity times (in days) are available for a small project: Activity     Optimistic         Most Probable                       Pessimistic A                          4                           5.0                                      6 B                          8                           9.0                                      10 C                          7                           7.5                                      11 D                          7                           9.0                                      10 E                           6                           7.0                                      9 F                           5                           6.0                                      7 An analyst determined that the critical path consists of activities B-D-F. Compute the expected project completion time and the variance of this path. What is the probability the project will be completed in 25 days?

Chapter 17 Solutions

Loose-leaf for Operations Management (The Mcgraw-hill Series in Operations and Decision Sciences)

Ch. 17 - Why might a person wish to be involved with a...Ch. 17 - Prob. 12DRQCh. 17 - What are some aspects of the project managers job...Ch. 17 - What is the main benefit of a project organization...Ch. 17 - What trade-offs are associated with time and cost...Ch. 17 - Who needs to be involved in assessing the cost of...Ch. 17 - Prob. 3TSCh. 17 - Project management techniques have been used...Ch. 17 - Give three examples of unethical conduct involving...Ch. 17 - For each of the following network diagrams,...Ch. 17 - Chris received new word processing software for...Ch. 17 - Prepare a Gantt chart for each of the following in...Ch. 17 - a. Develop a list of activities and their...Ch. 17 - For each of the problems listed, determine the...Ch. 17 - PRINTED BY: 92248ddb24ccbc6@placeholder.10274.edu....Ch. 17 - Three recent college graduates have formed a...Ch. 17 - The new director of special events at a large...Ch. 17 - PRINTED BY: 92248ddb24ccbc6@placeholder.10274.edu....Ch. 17 - The project described in the following table is...Ch. 17 - The following precedence diagram reflects three...Ch. 17 - A project manager has compiled a list of major...Ch. 17 - Here is a list of activity times for a project as...Ch. 17 - The project manager of a task force planning the...Ch. 17 - PRINTED BY: 92248ddb24ccbc6@placeholder.10274.edu....Ch. 17 - Chucks Custom Boats (CCB) builds luxury yachts to...Ch. 17 - Prob. 17PCh. 17 - Create a risk matrix in the style of Figure 17.13...Ch. 17 - Create a risk matrix for this project: Explain...Ch. 17 - CASE: The Case of the Mexican crazy quilt 1. The...Ch. 17 - CASE: The Case of the Mexican crazy quilt 2. The...Ch. 17 - CASE: The Case of the Mexican crazy quilt 3. The...Ch. 17 - CASE: The Case of the Mexican crazy quilt 4. The...Ch. 17 - CASE: The Case of the Mexican crazy quilt 5. The...Ch. 17 - B. Smitty Smith is a project manager for a large...
Knowledge Booster
Background pattern image
Operations Management
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, operations-management and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Practical Management Science
Operations Management
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:Cengage,
Text book image
Operations Management
Operations Management
ISBN:9781259667473
Author:William J Stevenson
Publisher:McGraw-Hill Education
Text book image
Operations and Supply Chain Management (Mcgraw-hi...
Operations Management
ISBN:9781259666100
Author:F. Robert Jacobs, Richard B Chase
Publisher:McGraw-Hill Education
Text book image
Business in Action
Operations Management
ISBN:9780135198100
Author:BOVEE
Publisher:PEARSON CO
Text book image
Purchasing and Supply Chain Management
Operations Management
ISBN:9781285869681
Author:Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson
Publisher:Cengage Learning
Text book image
Production and Operations Analysis, Seventh Editi...
Operations Management
ISBN:9781478623069
Author:Steven Nahmias, Tava Lennon Olsen
Publisher:Waveland Press, Inc.
Inventory Management | Concepts, Examples and Solved Problems; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=2n9NLZTIlz8;License: Standard YouTube License, CC-BY