Project Scheduling What are the best or most popular software for PERT/CPM project on the market? Can you give one or two examples of how companies can use these software in real

An Introduction to Management Science, 15e Quantitative Approaches to Decision Making

Anderson Sweeney Williams Camm Cochran Fry Ohlmann

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

Chapter 9: Project Scheduling: PERT/CPM

9.1 – Project Scheduling Based on Expected Activity Times

9.2 – Project Scheduling Considering Uncertain Activity Times

9.3 – Considering Time-Cost Trade-Offs

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

PERT/CPM (1 of 3)

PERT – Program Evaluation and Review Technique

Developed by U.S. Navy for Polaris missile project

Developed to handle uncertain activity times

CPM – Critical Path Method

Developed by DuPont & Remington Rand

Developed for industrial projects for which activity times generally were known

Today’s project management software packages have combined the best features of both approaches.

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

PERT/CPM (2 of 3)

PERT and CPM have been used to plan, schedule, and control a wide variety of projects:

R&D of new products and processes

Construction of buildings and highways

Maintenance of large and complex equipment

Design and installation of new systems

PERT/CPM is used to plan the scheduling of individual activities that make up a project.

Projects may have as many as several thousand activities.

A complicating factor in carrying out the activities is that some activities depend on the completion of other activities before they can be started.

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

PERT/CPM (3 of 3)

Project managers rely on PERT/CPM to help them answer questions such as:

What is the total time to complete the project?

What are the scheduled start and finish dates for each specific activity?

Which activities are critical and must be completed exactly as scheduled to keep the project on schedule?

How long can noncritical activities be delayed before they cause an increase in the project completion time?

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

Project Scheduling Based on Expected Activity Times (1 of 21)

A project network can be constructed to model the precedence of the activities.

The nodes of the network represent the activities.

The arcs of the network reflect the precedence relationships of the activities.

A critical path for the network is a path consisting of activities with zero slack.

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

Project Scheduling Based on Expected Activity Times (2 of 21)

The owner of the Western Hills Shopping Center plans to modernize and expand the current 32-business shopping center complex. The project is expected to provide room for 8 to 10 new businesses. Financing has been arranged through a private investor. All that remains is for the owner of the shopping center to plan, schedule, and complete the expansion project.

Let us show how PERT/CPM can help.

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

Project Scheduling Based on Expected Activity Times (3 of 21)

The first step in the PERT/CPM scheduling process is to develop a list of the activities that make up the project.

The immediate predecessor column identifies the activities that must be completed immediately prior to the start of that activity.

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

Project Scheduling Based on Expected Activity Times (4 of 21)

Using the activity information, we can construct a graphical representation of the project, or the project network.

Project Scheduling Based on Expected Activity Times (5 of 21)

A path is a sequence of connected nodes that leads from the Start node to the Finish node. For instance, one path for the network is defined by the sequence of nodes A-E-F-G-I.

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

Project Scheduling Based on Expected Activity Times (6 of 21)

To facilitate the PERT/CPM computations, we modified the project network. The upper left-hand corner of each node contains the corresponding activity letter. The activity time appears immediately below the letter.

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

Project Scheduling Based on Expected Activity Times (7 of 21)

All paths in the network must be traversed in order to complete the project, so we will look for the path that requires the greatest time. Because all other paths are shorter in duration, this longest path determines the total time required to complete the project. If activities on the longest path are delayed, the entire project will be delayed. Thus, the longest path is the critical path. Activities on the critical path are referred to as the critical activities for the project.

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

Project Scheduling Based on Expected Activity Times (8 of 21)

We begin by finding the earliest start time and the latest start time for all activities in the network. Let

ES = earliest start time for an activity

EF = earliest finish time for an activity

t = expected activity time

The earliest finish time for any activity is

EF = ES + t

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

Project Scheduling Based on Expected Activity Times (9 of 21)

Activity A can start as soon as the project starts, so we set the earliest start time for activity A equal to 0. With an expected activity time of 5 weeks, the earliest finish time for activity A

is EF = ES + t = 0 + 5 = 5.

We will write the earliest start and earliest finish times in the node to the right of the activity letter. Using activity A as an example, we have

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

Project Scheduling Based on Expected Activity Times (10 of 21)

Because an activity cannot be started until all immediately preceding activities have been finished, the following rule can be used to determine the earliest start time for each activity:

The earliest start time for an activity is equal to the largest (i.e., latest) of the earliest finish times for all its immediate predecessors.

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

Project Scheduling Based on Expected Activity Times (11 of 21)

Let us apply the earliest start time rule to the portion of the network involving nodes A, B, and C. With an earliest start time of 0 and an activity time of 6 for activity B, we show ES = 0 and EF = 6 in the node for activity B. Activity A

is the only immediate

Predecessor for activity

C. EF for activity A is 5,

so ES for activity C

must be 5. Thus, with

An activity time of 4,

the earliest finish time

for activity C is EF = 9.

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

Project Scheduling Based on Expected Activity Times (12 of 21)

With activities B and C as immediate predecessors, the earliest start time for activity H must be equal to the largest of the earliest finish times for activities B and C. Thus, with EF = 6 for activity B and EF = 9 for activity C, 9 is the earliest start time for activity H (ES = 9). With an activity time of 12 as shown in the node for activity H, the earliest finish time is EF = 21.

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

Project Scheduling Based on Expected Activity Times (13 of 21)

Continuing with this forward pass through the network, we can establish the earliest start time and the earliest finish time for each activity in the network. Therefore, we now know that the expected completion time for the entire project is 26 weeks.

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

Project Scheduling Based on Expected Activity Times (14 of 21)

We now continue finding the critical path by making a backward pass through the network. Because the expected completion time for the entire project is 26 weeks, we begin the backward pass with a latest finish time of 26 for activity I.

Once the latest finish time for an activity is known, the latest start time for an activity can be computed as follows. Let

LS = latest start time for an activity

LF = latest finish time for an activity

Then

LS = LF – t

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

Project Scheduling Based on Expected Activity Times (15 of 21)

Beginning the backward pass with activity I, we know that the latest finish time is LF = 26 and that the activity time is t = 2. Thus, the latest start time for activity I is LS = 24. We will write the LS and LF values in the node directly below the earliest start (ES) and earliest finish (EF) times. Thus, for node I, we have

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

Project Scheduling Based on Expected Activity Times (16 of 21)

The following rule can be used to determine the latest finish time for each activity in the network:

The latest finish time for an activity is the smallest (earliest) of the latest start times for all activities that immediately follow the activity.

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

Project Scheduling Based on Expected Activity Times (17 of 21)

After we complete the forward and backward passes, we can determine the amount of slack associated with each activity.

Slack is the length of time an activity can be delayed without increasing the project completion time.

The amount of slack for an activity is computed as follows:

Slack = LS – ES = LF – EF

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

Project Scheduling Based on Expected Activity Times (18 of 21)

The slack associated with activity C is LS – ES = 8 – 5 = 3 weeks. Hence, activity C can be delayed up to 3 weeks, and the entire project can still be completed in 26 weeks. In this sense, activity C is not critical to the completion of the entire project in 26 weeks.

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

Project Scheduling Based on Expected Activity Times (19 of 21)

Putting this information in tabular form provides the activity schedule shown

Activity	Earliest Start (ES)	Latest Start (LS)	Earliest Finish (FS)	Latest Finish (LF)	Slack (LS–ES)	Critical Path?
A	0	0	5	5	0	Yes
B	0	6	6	12	6
C	5	8	9	12	3
D	5	7	8	10	2
E	5	5	6	6	0	Yes
F	6	6	10	10	0	Yes
G	10	10	24	24	0	Yes
H	9	12	21	24	3
I	24	24	26	26	0	Yes

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

Project Scheduling Based on Expected Activity Times (20 of 21)

We previously stated that project managers look for procedures that will help answer important questions regarding the planning, scheduling, and controlling of projects. Here are the answers:

1. How long will the project take to complete?

Answer: The project can be completed in 26 weeks if each activity is completed on schedule.

2. What are the scheduled start and completion times for each activity?

Answer: The activity schedule shows the earliest start, latest start, earliest finish, and latest finish times for each activity.

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

Project Scheduling Based on Expected Activity Times (21 of 21)

3. Which activities are critical and must be completed exactly as scheduled to keep the project on schedule?

Answer: A, E, F, G, and I are the critical activities.

4. How long can noncritical activities be delayed before they cause an increase in the completion time for the project?

Answer: The activity schedule shows the slack associated with each activity.

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

Summary of the PERT/CPM Critical Path Procedure

Step 1. Develop a list of the activities that make up the project.

Step 2. Determine the immediate predecessor(s) for each activity in the project.

Step 3. Estimate the completion time for each activity.

Step 4. Draw a project network depicting the activities and immediate predecessors listed in steps 1 and 2.

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

Critical Path Procedure (1 of 2)

Step 5. Use the project network and the activity time estimates to determine the earliest start and the earliest finish time for each activity by making a forward pass through the network. The earliest finish time for the last activity in the project identifies the total time required to complete the project.

Step 6. Use the project completion time identified in Step 5 as the latest finish time for the last activity and make a backward pass through the network to identify the latest start and latest finish time for each activity.

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

Critical Path Procedure (2 of 2)

Step 7. Use the difference between the latest start time and the earliest start time for each activity to determine the slack for each activity.

Step 8. Find the activities with zero slack; these are the critical activities.

Step 9. Use the information from steps 5 and 6 to develop the activity schedule for the project.

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

Project Scheduling Considering Uncertain Activity Times

In the three-time estimate approach, the time to complete an activity is assumed to follow a Beta distribution.

An activity’s mean completion time is:

t = (a + 4m + b) / 6

a = the optimistic completion time estimate

b = the pessimistic completion time estimate

m = the most likely completion time estimate

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

Uncertain Activity Times (1 of 2)

An activity’s completion time variance is:

a = the optimistic completion time estimate

b = the pessimistic completion time estimate

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

Uncertain Activity Times (2 of 2)

In the three-time estimate approach, the critical path is determined as if the mean times for the activities were fixed times.

The overall project completion time is assumed to have a normal distribution with mean equal to the sum of the means along the critical path and variance equal to the sum of the variances along the critical path.

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

‹#›

Crashing Activity Times (1 of 2)

To determine just where and how much to crash activity times, we need information on how much each activity can be crashed and how much the crashing process costs. Hence, we must ask for the following information:

Activity cost under the normal or expected activity time

Time to complete the activity under maximum crashing (i.e., the shortest possible activity time)

Activity cost under maximum crashing

‹#›

© 2019 Cengage. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use.

Crashing Activity Times (2 of 2)

When determining the time estimates for activities in a project, the project manager bases these estimates on the amount of resources (workers, equipment, etc.) that will be assigned to an activity.

Th

Collepals.com Plagiarism Free Papers

Are you looking for custom essay writing service or even dissertation writing services? Just request for our write my paper service, and we'll match you with the best essay writer in your subject! With an exceptional team of professional academic experts in a wide range of subjects, we can guarantee you an unrivaled quality of custom-written papers.

Get ZERO PLAGIARISM, HUMAN WRITTEN ESSAYS

Why Hire Collepals.com writers to do your paper?

Quality- We are experienced and have access to ample research materials.

We write plagiarism Free Content

Confidential- We never share or sell your personal information to third parties.

Support-Chat with us today! We are always waiting to answer all your questions.