Project Planning & Scheduling

Yousaf Ali KhanDepartment of Management Sciences and HumanitiesGIK Institute of Engineering Sciences and Technology

What is a ―Project‖?― An individual or collaborative enterprise that is

carefully planned and designed to achieve a

particular aim‖

EXAMPLES:

• constructing a new road

• building a ship

• designing and marketing a new product

• moving to a new office block

• installation of a computer system.

Objectives and Tradeoffs

Meet the

specifications

Meet the

Deadline--schedule

Due Date!

Stay within

the budget

Management of Projects

Planning - goal setting, defining the project, team

organization

Scheduling - relates people, money, and supplies to

specific activities and activities to each other

Controlling - monitors resources, costs, quality, and

budgets; revises plans and shifts resources to meet

time and cost demands

Planning

Objectives

Resources

Work break-down schedule

Organization

Scheduling

Project activities

Start & end times

Network

Controlling

Monitor, compare, revise, action

Project Management Activities

Establishing objectives

Defining project

Creating work breakdown structure

Determining resources

Forming organization

Project Planning

Often temporary structure

Uses specialists from entire company

Headed by project manager

Coordinates activities

Monitors scheduleand costs

Permanent structure called ‗matrix organization‘

Project Organization

A Sample Project Organization

TestEngineer

MechanicalEngineer

Project 1 ProjectManager

Technician

Technician

Project 2 ProjectManager

ElectricalEngineer

Computer Engineer

Marketing FinanceHuman

Resources DesignQuality

MgtProduction

President

The Role ofthe Project Manager

Highly visibleResponsible for making sure that:

All necessary activities are finished in order and on time

The project comes in within budget

The project meets quality goals

The people assigned to the project receive motivation, direction, and information

Project Life Cycle

Concept

Feasibility

Planning

Execution

Closure

Man

agem

en

t

Work Breakdown Structure (WBS)

Level

1. Project

2. Major tasks in the project

3. Subtasks in the major tasks

4. Activities (or work packages)to be completed

Example Of WBS For Building a

House

Identifying precedence relationships

Sequencing activities

Determining activity times & costs

Estimating material and worker requirements

Determining critical activities

Project Scheduling

1. Shows the relationship of each activity to others and to the whole project

2. Identifies the precedence relationships among activities

3. Encourages the setting of realistic time and cost estimates for each activity

4. Helps make better use of people, money, and material resources by identifying critical bottlenecks in the project

Purposes of Project Scheduling

Gantt chart

Critical Path Method (CPM)

Program Evaluation and Review Technique (PERT)

Project Scheduling Techniques

• Gantt Charts– Shown as a bar charts

– Do not show precedence relations

– Visual & easy to understand

• Network Methods– Shown as a graphs or networks

– Show precedence relations

– More complex, difficult to understand and costly than Gantt charts

PERT and CPM

Network techniques

Developed in 1950‘s

CPM by DuPont for chemical plants (1957)

PERT by Booz, Allen & Hamilton with the U.S. Navy, for Polaris missile (1958)

Consider precedence relationships and interdependencies

Each uses a different estimate of activity times

Six Steps PERT & CPM

1. Define the project and prepare the work breakdown structure

2. Develop relationships among the activities -decide which activities must precede and which must follow others

3. Draw the network connecting all of the activities

4. Assign time and/or cost estimates to each activity

5. Compute the longest time path through the network – this is called the critical path

6. Use the network to help plan, schedule, monitor, and control the project

Questions PERT & CPM Can Answer

1. When will the entire project be completed?

2. What are the critical activities or tasks in the project?

3. Which are the noncritical activities?

4. What is the probability the project will be completed by a specific date?

5. Is the project on schedule, behind schedule, or ahead of schedule?

6. Is the money spent equal to, less than, or greater than the budget?

7. Are there enough resources available to finish the project on time?

8. If the project must be finished in a shorter time, what is the way to accomplish this at least cost?

Constant-Time Networks

Activity times are assumed to be constant

Activities are represented by Arcs in the network

Nodes show the events

Notations used in calculating start and finish times:

– ES(a) = Early Start of activity a

– EF(a) = Early Finish of activity a

– LS(a) = Late Start of activity a

– LF(a) = Late Finish of activity a

A Comparison of AON and AOA Network Conventions

Activity on Activity Activity onNode (AON) Meaning Arrow (AOA)

A comes before B, which comes before C

(a) A B CBA C

A and B must both be completed before C can start

(b)

A

CC

B

A

B

B and C cannot begin until A is completed

(c)

B

A

CA

B

C

Rules

1. One node has no arc entering and defines the starting

event.

2. One node has no arc leaving and defines the finishing

event.

3. Each activity should appear exactly once as an arc of

the network, and lies on a path from the starting event

to the finishing event. Dummy activities can also be

used.

4. There should be a path passing successively through

any two activities if and only if the first is a pre-

requisite for the second.

5. There should be at most one arc between each pair of

nodes of a network.

Drawing Project Networks

We consider an activity-on-arc approach.

We need a list of activities (constituent elements of a

project) and their prerequisites.

Example. Planting a tree

Description Activity Prerequisites

Dig hole A -

Position tree B A

Fill in hole C B

A B C1 2 3 4

Analysing Project Networks

Number the nodes so that each arc is directed

from a node i to a node j where i < j.

Let A be the set of activities

dij be the duration of activity (i, j)n be the number of nodes.

Compute earliest event times, assuming that the

project starts at time zero and all activities are

scheduled as early as possible.

EET1 = 0EETj = max{EETi + dij} j=2,…,n

(i,j)A

Analysing Project NetworksNote that EETj is the length of a longest path from

node 1 to node j.

The project duration is EETn.

Compute latest event times, assuming that the

project finishes at time EETn and all activities are

scheduled as late as possible.

LETn = EETn

LETi = min{LETj - dij} i=n-1,…,1(i,j)A

Note that LETn - LETi is the length of a longest path

from node i to node n.

Determining the Project Schedule

Perform a Critical Path Analysis

The critical path is the longest path through the network

The critical path is the shortest time in which the project can be completed

Any delay in critical path activities delays the project

Critical path activities have no slack time

Slack is the length of time an activity can be delayed without delaying the entire project

Slack = LS – ES or Slack = LF – EF

Example

Activity DescriptionImmediate

Predecessors

A Lease the site —

B Hire the workers —

C Arrange for the Furnishings A

D Install the furnishings A, B

E Arrange for the phones C

F Install the phones C

G Move into the Office D, E

H Inspect and test F, G

Precedence and times for Opening a New Office

Determining the Project Schedule

Perform a Critical Path Analysis

Activity Description Time (weeks)

A Lease the site 2

B Hire the workers 3

C Arrange for the furnishings 2

D Install the furnishings 4

E Arrange for the phones 4

F Install the phones 3

G Move into the office 5

H Inspect and test 2

Total Time (weeks) 25

AOA Network For

Opening a New Office

H

(Inspect/ Test)

7Dummy Activity

6

5D

(Install the furnishings)

4C

(Arrange for the

furnishings)

1

3

2

Determining the Project Schedule

Perform a Critical Path Analysis

A

Activity Name or Symbol

Earliest Start ES

Earliest FinishEF

Latest Start

LS Latest Finish

LF

Activity Duration

2

ES/EF Network for Opening a New Office

Start

0

0

ES

0

EF = ES + Activity time

A

2

EF of A = ES of A + 2

2

ESof A

0

ES/EF Network for Opening a New Office

E

4

F

3

G

5

H

2

4 8 13 15

4

8 13

7

D

4

3 7

C

2

2 4

B

3

0 3

Start0

0

0

A

2

20

LS/LF Network for Opening a New Office

E

4

F

3

G

5

H

2

4 8 13 15

4

8 13

7

D

4

3 7

C

2

2 4

B

3

0 3

Start0

0

0

A

2

20

LF = EF of Project

1513

LS = LF – Activity time

LF = Min(LS of following activity)

10 13

Computing Slack Time

After computing the ES, EF, LS, and LF times for all activities, compute the slack or free time for each activity

Slack is the length of time an activity can be delayed without delaying the entire project

Slack = LS – ES or Slack = LF – EF

Computing Slack Time

Earliest Earliest Latest Latest OnStart Finish Start Finish Slack Critical

Activity ES EF LS LF LS – ES Path

A 0 2 0 2 0 YesB 0 3 1 4 1 NoC 2 4 2 4 0 YesD 3 7 4 8 1 NoE 4 8 4 8 0 YesF 4 7 10 13 6 NoG 8 13 8 13 0 YesH 13 15 13 15 0 Yes

Critical Path for Opening a New Office

E

4

F

3

G

5

H

2

4 8 13 15

4

8 13

7

13 15

10 13

8 13

4 8

D

4

3 7

C

2

2 4

B

3

0 3

Start0

0

0

A

2

20

42

84

20

41

00

ES – EF Gantt Chartfor Opening a New Office

A Lease the site

B Hire the workers

C Arrange for the furnishings

D Install the furnishings

E Arrange for the phones

F Install the phones

G Move into the office

H Inspect and test

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

A

B

C

D

E

F

G

H

CPM assumes we know a fixed time estimate for each activity and there is no variability in activity times

PERT uses a probability distribution for activity times to allow for variability

Variability in Activity Times

Three time estimates are required

Optimistic time (a) – if everything goes

according to plan

Most–likely time (m) – most realistic estimate

Pessimistic time (b) – assuming very

unfavorable conditions

Probabilistic Time Estimates

• Optimistic time

– Time required under optimal conditions

• Pessimistic time

– Time required under worst conditions

• Most likely time

– Most probable length of time that will be

required

Probabilistic Estimates

Activitystart

Optimistictime

Most likelytime (mode)

Pessimistictime

to tptm te

Beta Distribution

Expected Time

te =to + 4tm +tp

6

te = expected time

to = optimistic time

tm = most likely time

tp = pessimistic time

Variance

2 =(tp – to)

2

36

2 = variance

to = optimistic time

tp = pessimistic time

1-2-3

(H)7Dummy

Activity6

52-4-6

(D)

41-2-3

(C)

1

3

2

Optimistic

timeMost likely

time

Pessimistic

time

Computing Variance

Most ExpectedOptimistic Likely Pessimistic Time Variance

Activity a m b t = (a + 4m + b)/6 [(b – a)/6]2

A 1 2 3 2 .11

B 2 3 4 3 .11

C 1 2 3 2 .11

D 2 4 6 4 .44

E 1 4 7 4 1.00

F 1 2 9 3 1.78

G 3 4 11 5 1.78

H 1 2 3 2 .11

Probability of Project Completion

Project variance is computed by summing the variances of critical activities

s2 = Project variance

= (variances of activities on critical path)

p

Probability of Project Completion

Project variance is computed by summing the variances of critical activities

Project variance

2 = .11 + .11 + 1.00 + 1.78 + .11 = 3.11

Project standard deviation

p = Project variance

= 3.11 = 1.76 weeks

p

Probability of Project Completion

Standard deviation = 1.76 weeks

15 Weeks

(Expected Completion Time)

Probability of Project Completion

What is the probability this project can be completed on or before the 16 week deadline?

Z = – /p

= (16 wks – 15 wks)/1.76

= 0.57

due expected datedate of completion

Where Z is the number of standard deviations the due date or target date lies from the

mean or expected date

Probability of Project Completion

What is the probability this project can be completed on or before the 16 week deadline?

Z= − /sp

= (16 wks − 15 wks)/1.76

= 0.57

due expected datedate of completion

Where Z is the number of standard deviations the due date or target date lies

from the mean or expected date

.00 .01 .07 .08

.1 .50000 .50399 .52790 .53188

.2 .53983 .54380 .56749 .57142

.5 .69146 .69497 .71566 .71904

.6 .72575 .72907 .74857 .75175

From Appendix I

Probability of Project Completion

Time

Probability(T ≤ 16 weeks)is 71.57%

0.57 Standard deviations

15 16Weeks Weeks

What Project Management Has Provided So Far

The project‘s expected completion time is 15 weeks

There is a 71.57% chance the equipment will be in place by the 16 week deadline

Five activities (A, C, E, G, and H) are on the critical path

Three activities (B, D, F) are not on the critical path and have slack time

A detailed schedule is available

Advantages of PERT/CPM

1. Especially useful when scheduling and controlling large projects

2. Straightforward concept and not mathematically complex

3. Graphical networks help highlight relationships among project activities

4. Critical path and slack time analyses help pinpoint activities that need to be closely watched

5. Project documentation and graphics point out who is responsible for various activities

6. Applicable to a wide variety of projects

7. Useful in monitoring not only schedules but costs as well

Trade-Offs And Project Crashing

The project is behind schedule

The completion time has been moved forward

It is not uncommon to face the following situations:

Shortening the duration of the project is called project crashing

Factors to Consider When Crashing A Project

The amount by which an activity is crashed is, in fact, permissible

Taken together, the shortened activity durations will enable us to finish the project by the due date

The total cost of crashing is as small as possible

Steps in Project Crashing

1. Compute the crash cost per time period. If crash costs are linear over time:

Crash costper period =

(Crash cost – Normal cost)

(Normal time – Crash time)

2. Using current activity times, find the critical path and identify the critical activities

Steps in Project Crashing

3. If there is only one critical path, then select the activity on this critical path that (a) can still be crashed, and (b) has the smallest crash cost per period. If there is more than one critical path, then select one activity from each critical path such that (a) each selected activity can still be crashed, and (b) the total crash cost of all selected activities is the smallest. Note that the same activity may be common to more than one critical path.

4. Update all activity times. If the desired due date has been reached, stop. If not, return to Step 2.

Crashing The Project

Time (Wks) Cost ($) Crash Cost CriticalActivity Normal Crash Normal Crash Per Wk ($) Path?

A 2 1 22,000 22,750 750 Yes

B 3 1 30,000 34,000 2,000 No

C 2 1 26,000 27,000 1,000 Yes

D 4 2 48,000 49,000 1,000 No

E 4 2 56,000 58,000 1,000 Yes

F 3 2 30,000 30,500 500 No

G 5 2 80,000 84,500 1,500 Yes

H 2 1 16,000 19,000 3,000 Yes

Crash and Normal Times and Costs for Activity B

| | |

1 2 3 Time (Weeks)

$34,000 —

$33,000 —

$32,000 —

$31,000 —

$30,000 —

—

Activity Cost

Crash

Normal

Crash Time Normal Time

Crash Cost

Normal Cost

Crash Cost/Wk =Crash Cost – Normal Cost

Normal Time – Crash Time

=$34,000 – $30,000

3 – 1

= = $2,000/Wk$4,000

2 Wks

Figure 3.16