Production and Operations Management Systems

Chapter 7: Project Management

Sushil K. Gupta

Martin K. Starr

2014

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After reading this chapter, you should be able to (continued):

Draw project network diagrams.

Find critical paths and project durations.

Calculate early start, early finish, late start and late finish

times of activities.

Explain how to use forward-pass calculations to determine the

shortest feasible time for project completion.

Explain how to use backward-pass calculations to determine

which project activities are on the critical path.

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After reading this chapter, you should be able to (continued):

Describe what slack means; explain how to derive it.

Crash activities (including multiple paths) to reduce project duration;

perform time-cost tradeoff analysis.

Analyze probabilistic projects; explain when deterministic and

probabilistic estimates for activity times apply.

Show how to use optimistic and pessimistic activity time estimates to

obtain a variance measure for activity times.

Identify implications of limited resources.

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Introduction

Projects consist of a set of goal-oriented activities that end when the goal is achieved.

Such undertakings are time-based endeavors and have a finite planning horizon.

Projects are special work configurations designed to accomplish singular or nearly singular goals.

Examples include: putting on one play, writing new software, constructing a building, launching a new product, redesigning an established traditional hotel, and developing a new service etc.

In this presentation we discuss management of projects.

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Classification of Projects

Projects can be classified according to the following criteria:

Degree of simplicity to change things.  

Degree of complexity reflecting the number of people, teams,

components and activities.

Frequency of repetition.

Number of new activities involved.

. .

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Managing Projects

Competent project management methods keep track of what is required at start up, what has been done as it progresses and what still needs to be done.

Good project methods point to activities that are critical for completion.

Project managers expedite important activities that seem to be slipping.

These points are part of the five project life cycle stages (below):

1.Begin by describing goals which requires developing and specifying the desired project outcomes.  

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Managing Projects (continued)

1. On prior page

2. Planning the project requires specifying (in detail) the activities that are essential to accomplish the goals. It involves planning the management of the project including the timing of the activities.

3. Carrying out the project requires doing the activities as scheduled.

4. Completing the project can mean disbanding work groups and closing down the project-management team.

5. The use of continuous project teams is an increasingly attractive option.

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Project Management Origins

Starting about 1957, two similar approaches to large-scale project network planning and tracking were begun at separate locations and for different reasons. These were:

PERT—program evaluation review techniqueCPM—critical path method

PERT was developed by the U.S. Navy Special Projects Office in conjunction with Booz Allen Hamilton for the Polaris submarine launched missile project.

There were about 100,000 activities divided amongst thousands of suppliers.  

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Project Management Origins (continued)

CPM was a similar method developed by DuPont and Remington Rand, which later became Unisys. It was used to design and coordinate chemical plant operations.

The essential difference between PERT and CPM is in specifying the times for performing various activities.

PERT was used for projects where the activity times were not certain because project managers were unfamiliar with the activities.

On the other hand the projects and activities were familiar to the project managers in the case of CPM.

These days the distinction between PERT and CPM seems to be disappearing and together these are called PERT/CPM or simply network techniques. These two methods share the notion of a critical path as discussed later in the chapter.

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Project Network

The following steps are required to utilize these network models.

Make a list of all activities that are required to complete the project.

Establish the precedence relationships among activities and document the rationale for these relationships.

Estimate the time to perform each task or activity using one of the following two options.Option 1: deterministic estimates for activity times. Option 2: probabilistic estimates for activity times.

Draw the precedence diagram (of project activities).Develop a project schedule.

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Project Management Example

ActivityImmediate

PredecessorsImmediate Followers

Time (Weeks)

A None D 9B None E,F 5C None G 7D A H 12E B H 8F B I 6G C I 11H D,E I 5I F,G,H J 4J I None 10

Note: Either Immediate Predecessors or Immediate Followers need to be specified.

Activity on Node (AON) Diagram

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Finding Critical Path and Project Duration

A

C

B

D

E

F

I

G

H

J

LengthA D H I J 40 Critical Path

B E H I J 32B F I J 25

C G I J 32

Paths

ActivityTime

(Weeks)

A 9

B 5C 7D 12E 8F 6G 11H 5I 4J 10

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Early Start and Early Finish Times

A

C

B

D

E

F

I

G

H

J

ActivityTime

(Weeks)

Early Start Time

(Weeks)

Early Finish Time

(Weeks)

A 9 0 9

B 5 0 5C 7 0 7D 12 9 21E 8 5 13F 6 5 11G 11 7 18H 5 21 26I 4 26 30J 10 30 40

Early Finish Time = Early Start Time + Activity Time

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Late Start and Late Finish Times

A

C

B

D

E

F

I

G

H

J

Late Start Time = Late Finish Time - Activity Time

ActivityTime

(Weeks)

Late Start Time

(Weeks)

Late Finish Time

(Weeks)

A 9 0 9

B 5 8 13C 7 8 15D 12 9 21E 8 13 21F 6 20 26G 11 15 26H 5 21 26I 4 26 30J 10 30 40

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Slack Time

ActivityTime

(Weeks)

Early Start Time

(Weeks)

Early Finish Time

(Weeks)

Late Start Time

(Weeks)

Late Finish Time

(Weeks)

Slack Time

(Weeks)

A 9 0 9 0 9 0B 5 0 5 8 13 8C 7 0 7 8 15 8D 12 9 21 9 21 0E 8 5 13 13 21 8F 6 5 11 20 26 15G 11 7 18 15 26 8H 5 21 26 21 26 0I 4 26 30 26 30 0J 10 30 40 30 40 0

Slack Time = Late Finish - Early Finish = Late Start - Early Start

Paths LengthA D H I J 40 Critical Path

B E H I J 32

B F I J   25

C G I J   3215

Reducing Project Duration: Crashing of Activities

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Data for Crashing

ActivityImmediate

Predecessor (s)

Normal Time

(weeks)

Crash Time (weeks)

Normal Cost ($)

Crash Cost ($)

Cost of Crashing/

Week

Maximum Crashing Possible

A None 9 6 $13,000 $15,550 $850 3

B None 5 4 $7,000 $7,900 $900 1

C None 7 5 $15,000 $15,800 $400 2

D A 12 8 $12,000 $14,800 $700 4

E B 8 5 $9,000 $10,500 $500 3

F B 6 4 $5,000 $6,200 $600 2

G C 11 9 $13,000 $14,000 $500 2

H D,E 5 4 $8,000 $9,000 $1,000 1

I F,G,H 4 3 $3,000 $3,500 $500 1

J I 10 8 $12,000 $15,000 $1,500 2

        $97,000 $112,250    

Cost of Crashing per week = (Crash Cost - Normal Cost)/(Normal Time - Crash Time)Critical Path

A-D-H-I-JMaximum Crashing Possible = Normal Time - Crash Time

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Crashing Process

  Schedule 1 Schedule 2 Schedule 3 Schedule 4 Schedule 5 Schedule 6

PATHNormal

ScheduleCrash (I) by

1 weekkCrash (D) by 4 weeks

Crash (A) by 3 weeks

Crash (H) by 1 week

Crash (J) by 2 weeks

A-D-H-I-J 40 39 35 32 31 29

B-E-H-I-J 32 31 31 31 30 28

B-F-I-J 25 24 24 24 24 22

C-G-I-J 32 31 31 31 31 29

Activity Cost 97,000

97,500

100,300

102,850

103,850

106,850

Crashing Cost  

500

2,800

2,550

1,000

3,000

Cost of Crashing   500=700*4 (2800)

=850*3 (2550) 1000

=1500*2 (3000)

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Time Cost Trade-offProject Time Activity Cost Fixed Cost Total Cost

29 106,850 23,200 130,050

30 105,350 24,000 129,350

31 103,850 24,800 128,650

32 102,850 25,600 128,450

33 102,000 26,400 128,400

34 101,150 27,200 128,350

35 100,300 28,000 128,300

36 99,600 28,800 128,400

37 98,900 29,600 128,500

38 98,200 30,400 128,600

39 97,500 31,200 128,700

40 97,000 32,000 129,000

       

Fixed Cost/Week 800    

A project time of 35 weeks minimizes the total cost.

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Project Management - Probabilistic

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Probabilistic PERT

Expected Activity Time = (Optimistic Time + 4* Most Likely Time + Pessimistic Time)/6

Variance of Activity Times = Square of {(Pessimistic Time - Optimistic Time)/6}

ActivityImmediate

Predecessor (s)Optimistic

Time

Most Likely Time

Pessimistic Time

Expected Activity

Time

Variance of Activity Times

A None 5.00 8.00 11.00 8.00 1.000B None 2.00 6.00 10.00 6.00 1.778C None 3.00 3.00 3.00 3.00 0.000D A 8.00 9.00 10.00 9.00 0.111E B 3.00 5.00 10.00 5.50 1.361F B 2.00 4.00 7.00 4.17 0.694G C 3.00 5.00 10.00 5.50 1.361H D,E 3.00 4.00 5.00 4.00 0.111I F,G,H 6.00 9.00 11.00 8.83 0.694J I 2.00 5.00 8.00 5.00 1.000

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AON Diagram

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Probability of Project Completion

z-Value = (Project Due Date - Expected Time of the Path)/Standard Deviation

For a given value of z, the Excel function "=NORMSDIST(z)" can be used to find probability or z tables (included in the appendix) can be used.

The probability of completing the project by the due date is assumed to be the probability of completing the critical path by the due date.

Project Due Date 36  

PathsExpected

Time of the Path

Variance of the Path

Standard Deviation

of the Path z-Value

Probability of completing the path

by due date

A-D-H-I-J 34.83 2.92 1.71 0.683 0.7527B-E-H-I-J 29.33 4.94 2.22 2.998 0.9986

B-F-I-J 24.00 4.17 2.04 5.879 1.0000C-G-I-J 22.33 3.06 1.75 7.818 1.0000

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Resource Management

Resource management switches extra resources from places where they are not essential to places where they could be used immediately, that is, balance resource assignments across activities over time.

Resource management has two functions – resource leveling and resource scheduling.

In resource leveling the goal is to minimize the fluctuations in resources required from one period to another over the life of the project.

In resource scheduling it is assumed that there is an upper limit on the resources available and all activities are to be scheduled within the resource constraints.

 

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Thank you

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