department of industrial...

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Islamic University of Gaza - Palestine

Engineering Project Management

Presented ByDr. Abed Schokry

Department of Industrial Engineering

Chapter 12: Network Scheduling Techniques


Learning Outcomes:After completing this chapter, you should be able to:1. Describe the role and application of PERT/CPM for

project scheduling.2. Explain the benefits and limitations of PERT and CPM3. Define a project in terms of activities such that a

network representation can be developed.4. Develop a complete project schedule.5. Compute the critical path, the project completion time

and its variance.

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Learning Outcomes (cont.):

After completing this chapter, you should be able to:6. Convert optimistic, most likely, and pessimistic time

estimates into expected activity time estimates.7. Compute the probability of the project being

completed by a specific time.8. Compare between CPM & PERT9. Find the least expensive way to shorten the duration

of a project to meet a target completion date.


Learning Outcomes (cont. ):

After completing this chapter, you should be able to:

(Will NOT be discussed)!!!

1. Explain and formulate the crashing problem as a linearprogramming (LP) model.

2. Know some of the specialized software available in the marketfor scheduling and tracking project activities.

3


Key Terms

– Critical Path: The longest time path through thetask network.

– The series of tasks (or even a single task) thatdictates the calculated finish date of the project(That is, when the last task in the critical path iscompleted, the project is completed).

– The "longest" path (in terms of time) to thecompletion of a project.

– If shortened, it would shorten the time it takes tocomplete the project.

– Activities off the critical path would not affectcompletion time even if they were done morequickly.


Crashing

Shifting resources to reduce slack time so the criticalpath is as short as possible. Always raises projectcosts and is typically disruptive – a project should becrashed with caution.

Milestone

A significant task which represents a key accomplishmentwithin the project. Typically requires special attention andcontrol.

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THE PM Concept Assumption A Critical Path Exists

• A small set of activities, which make up the longestpath through the activity network control the entireproject.

• If these "critical" activities could be identified &assigned to responsible persons, managementresources could be optimally used by concentratingon the few activities which determine the fate of theentire project.

• Others can be re-planned, rescheduled & resourcesfor them can be reallocated, without affecting theproject.


Scheduling Techniques

• Gantt or bar charts• Milestone charts• Line of balance• Networks

– Program Evaluation and Review Technique (PERT)– Arrow Diagram Method (ADM) [Sometimes called the

Critical Path Method (CPM)]– Graphical Evaluation and Review Technique (GERT)– Precedence Diagram Method (PDM)

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Bar (Gantt) Chart

TASKS 1 2 3 4 5

4

MONTHS AFTER GO-AHEAD

3

2

1

5


Milestone Chart

ACTIVITY

TESTINGANALYSISREPORTPRESENTATION

TIME

6


Standard PERT Nomenclature

6 3

COMPLETE TESTING COMPLETE FINAL REPORT

3 WEEKS

LEGENDLEGEND

EVENT

ACTIVITY


Benefits of CPM/PERT

• Useful at many stages of project management• Mathematically simple• Give critical path and slack time• Provide project documentation• Useful in monitoring costs

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Dependencies

7

26 18

31

7

18

31

26

BURST POINT SINK


Conversion From Bar To PERT

4

2

3

1

5

6 7

3

2 2221

11

4

1 2

3 4 5

6 7

TIME

BAR CHART

PERT CHART

8


Simplified PERT Network

1 9

3

42 8765

LEGEND: (TIME = WEEKS)EVENTACTIVITYCRITICAL PATH ACTIVITY


Dummy activityAn imaginary activity with no duration, used to show

either an indirect relationship between 2 tasks or toclarify the identities of the tasks .

In CPM, each activity must be uniquely defined by itsbeginning and ending point.

When two activities begin and end at the same time, adummy activity (an activity which begins and ends atthe same time) is inserted into the model todistinguish the two activities.

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Dummy Activities

A

B

C

D

DUMMYACTIVITY

PRECEDINGACTIVITY

A -B -C BD A,B


Slack TimeThe amount of time a task can be delayed before the

project finish date is delayed.Total slack can be positive or negative. If total slack is

a positive it indicates the amount of time that thetask can be delayed without delaying the projectfinish date.

If negative, it indicates the amount of time that mustbe saved so that the project finish date is notdelayed. Total Slack = Latest Start - Earliest Start.

By default and by definition, a task with 0 slack isconsidered a critical task. If a critical task is delayed,the project finish date is also delayed. (Also knownas float time)

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Slack Identification

C (8,10)2 (15,17)

EARLIEST START TIME

EARLIEST FINISH TIME

LATEST FINISH TIME

LATEST START TIME

ACTIVITY

TIME


Types Of Slack

[ 20, 26 ]

[ 24, 30 ]

[ 30, 36 ]

[ 24, 30 ]

POSITIVE SLACK NEGATIVE SLACK

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Negative Slack

FORWARD PASS

BACKWARD PASS

CUSTOMER’S CUSTOMER’SSTART DATE FINISH DATE

3

2

4

1


Replace FS (Finish to start) with SS (start to Start)dependencies

Replace a team member with a more skilled person

Add resources From non-critical path tasks to critical path tasks From other projects To where

critical path tasks high-risk tasks tasks with large duration variances

Schedule Compression Techniques

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Reducing Project Completion Time

• Project completion times may need to be shortenedbecause:– Different deadlines– Penalty clauses– Need to put resources on a new project– Promised completion dates

• Reduced project completion time is “crashing”


Reducing Project Completion Time – (cont.)

• Crashing a project needs to balance– Shorten a project duration– Cost to shorten the project duration

• Crashing a project requires you to know– Crash time of each activity– Crash cost of each activity

Crash cost/duration = (crash cost-normal cost)/(normal time– crash time)

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Schedule Compression

• Elimination of some parts of the project• Addition of more resources• Substitution of less time-consuming components or

activities• Parallelization of activities• Shortening critical path activities• Shortening early activities• Shortening longest activities


Schedule Compression (Cont.)

• Shortening easiest activities• Shortening activities that are least costly to speed up• Shortening activities for which you have more

resources• Increasing the number of work hours per day

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Resource Leveling

• Resource leveling is an attempt to eliminate themanpower peaks and valleys by smoothing out theperiod-to-period resource requirements. The idealsituation is to do this without changing the end date.However, in reality, the end date moves out andadditional costs are incurred.


Resource Allocation

• Resource allocation (or resource limited planning) isan attempt to find the shortest possible critical pathbased upon the available or fixed resources. Theproblem with this approach is that the employeesmay not be qualified technically to perform work onmore than one activity in a network.

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Planning Objectives (Primary)

• Best time• Least cost• Least risk


Planning Objectives (Secondary)

• Studying alternatives• Optimum schedules• Effective use of resources• Communications• Refinement of the estimating process• Ease of project control• Ease of time or cost revisions

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Planning Objectives (Limitations)

• Calendar completion• Cash or cash flow restrictions• Limited resources• Management approvals


Program Crashing

• Project duration can be reduced by assigning moreresources to project activities.

• Doing this however increases project cost.

• Decision is based on analysis of trade-off betweentime and cost.

• Crashing achieved by devoting more resources tocrashed activities.

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Time & Costs: Normal vs. Crash

• For the time-only CPM project schedule, we typicallyassume that activity duration is fixed at its NORMALTIME, or the duration with the lowest direct activitycost (i.e., NORMAL COST).

• However, some activities may be expedited if higherresource levels are available. The shortest activityduration is called CRASH TIME. The cost to completean activity in that amount of time is called CRASHCOST.


Program Crashing

Project crashing is a method for shortening projectduration by reducing one or more critical activities toa time less than normal activity time.

We attempt to “crash” some “critical” events byallocating more resources to them, so that the time ofone or more critical activities is reduced to a time thatis less than the normal activity time.

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Crashing Activity Times

• In the Critical Path Method (CPM) approach to projectscheduling, it is assumed that the normal time to complete anactivity, tj , which can be met at a normal cost, cj , can becrashed to a reduced time, tj’, under maximum crashing for anincreased cost, cj’.

• It is assumed that its cost per unit reduction, Kj , is linear andcan be calculated by:

Kj = (cj' - cj)/(tj - tj').

• E.g.: in the example on the right,

• Kj = total crash cost/total crash time

• = $2000/5 = $400/wk


Which Activities are the Best Candidates for Crashing?

• Any activity that is on the critical path

• Activities with relatively long durations

• Bottleneck activities (that appear on multiple critical paths)

• Activities with relatively low costs to crash

• Activities that are not likely to cause quality problems if crashed

• Activities that occur relatively early in the schedule and are

labor intensive

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Options for Crashing Activities

• Adding Resources

• Outsourcing Project Work

• Overtime

• Establishing Core Project Team

• Temporary Fixes

• Fast-Tracking

• Critical Chain PM

• Brainstorming

• Reducing Scope

• Phasing Project Deliverables


Potential Problems with Crashing

• Reduced flexibility and less margin for error• Increased risk of failure to complete project on time• Raises potential for poor quality• Increases potential for staff burnout, stress, and

turnover• Raises activity-based costs• May negatively affect other projects• May create unrealistic expectations for future

projects• Hard to know true indirect costs

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Program Crashing Costs

110,000

120,000

130,000

140,000

150,000

160,000

PRO

GR

AM C

OST

, $

10 12 14 16 18 20 22 24PROGRAM COMPLETION TIME, WEEKS

CRASH B

CRASH FCRASH A

CRASH E

NORMAL OPERATIONS

ALL ACTIVITIES CRASHED

MINIMUM COST

TOTAL CRASH


Precedence Network

TASKS 1 2 3 4 5

4

MONTHS AFTER GO-AHEAD

3

2

1

5

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Types Of Precedence Charts

ACTIVITY 1

ACTIVITY 1

ACTIVITY 2

ACTIVITY 2FINISH-TO-START

START-TO-START

FINISH START

START

START


Types Of Precedence Charts

ACTIVITY 1

ACTIVITY 1

ACTIVITY 2

ACTIVITY 2

FINISH-TO-FINISH

PERCENT COMPLETE

FINISHFINISH

20 %

50 %

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Time Estimates

o Optimistic time (to) – It is the shortest time inwhich the activity can be completed.

o Most likely time (tm or tml) – It is the probable timerequired to perform the activity.

o Pessimistic time (tp) – It is the longest estimatedtime required to perform an activity.

o Expected time (te)te = to + 4tm + tp

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Steps in CPM/ PERT

1. Identify the specific activities.

2. Determine proper sequence of the activities.

3. Construct the network diagram.

4. Estimate the time required for each activity.

5. Determine the critical path.

6. Update the PERT chart.

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PERT Calculations• Step 1: Define tasks• Step 2: Place Tasks in a logical order, find the critical

path– The longest time path through the task network. The series of

tasks (or even a single task) that dictates the calculated finishdate

• Step 3: Generate estimates– Optimistic, pessimistic, likely and PERT- expected– Standard Deviation and variance

• Step 4: Determine earliest and latest dates• Step 5:Determine probability of meeting expected

date• Steps 1 and 2 are logic and legwork, not calculation –

these require a clear goal


• Assuming steps 1 and 2 have been completed begincalculations – use a table to organize your calculations

• Simple calculations to estimate project durations• Based on input of 3 estimated durations per task

– Most Optimistic (TO) – best case scenario– Most Likely (TL) “normal” scenario– Most Pessimistic (TP) Worst case scenario

• Formula derives a probability-based expected duration(TE)– (TO x 1 + TL x 4 + TP x 1) / 6 = TE

– Read this formula as the sum of (optimistic x 1 + likely x 4 +pessimistic x 1) divided by 6 = expected task duration

• Complete this calculation for all tasks

PERT Calculations –Step 3

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• Standard deviation and variance– Standard deviation (SD) is the average deviation from

the estimated time• SD=(TP-T0)/6 {read as (pessimistic-optimistic)/6}• As a general rule, the higher the standard deviation the

greater the amount of uncertainty

– Variance (V) reflects the spread of a value over anormal distribution

• V=SD² (Standard deviation squared)

PERT Calculations – Step 3


PERT Calculations – Step 3• When doing manual PERT Calculations it is helpful

to construct a table to stay organized• Consider the sample project– planting trees and

flowers, set up using a list– Rough estimates and no risk analysis

• No Range, simply rough estimates - unreliable?– PERT Analysis will better refine estimates

• Start by setting up a table to organize data

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Activity Description Precedence Optimistictime

Most Likelytime

Pessimistictime

Expectedtime

A Initial design - 12 16 26 17

B Survey market A 6 9 18 10

C Build prototype A 8 10 18 11

D Test prototype C 2 3 4 3

E Redesigning B,D 3 4 11 5

F Market testing E 6 8 10 8

G Set upproduction

F 15 20 25 20


Advantages of PERT

• Expected project completion time.

• Probability of completion before a specified date.

• The critical path activities that directly impact thecompletion time.

• The activities that have slack time and that can lendresources to critical path activities.

• Activity start and end dates.

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Limitations• The PERT Formula Requires Too Much Work.

• The network charts tend to be large and unwieldy.

• Calculating the time estimates is very complex for all theactivities.

• Updating of the project is time consuming and requireshigh costs.

• Emphasis is laid only on time factors and cost factors areneglected.

• Clearly defined, independent and stable activities• Specified precedence relationships• Over emphasis on critical paths


Difference between CPM & PERT

CPM PERT• CPM works with fixed deterministictime

• PERT works with probabilistic time

• CPM is useful for repetitive and noncomplex projects with a certaindegree of time estimates.

• PERT is useful for non repetitive andcomplex projects with uncertain timeestimates.

• CPM includes time-cost trade off. • PERT is restricted to time variable.

• CPM- for construction projects. • PERT- used for R&D programs.

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PERT & CPM

• PERT (Program Evaluation and Review Technique) –introduced by US military (Navy) in 1958

• US Navy : control costs & schedules for Polaris Submarineconstruction

• CPM (Critical Path Method) – introduced by US industryin 1958 (DuPont Corporation and Remington-Rand)

• Industry: control costs and schedules in manufacturing– Common weakness to both: ignores most dependencies

• Considers only completion of a preceding required task• Both rely on a logical sequence of tasks

– Organized visually (Charts), tabular or simple lists


Step 1-Define the Project: C and BU is bringing a new product on lineto be manufactured in their current facility in existing space. Theowners have identified 11 activities and their precedencerelationships. Draw the net work diagram for the project.

Activity Description ImmediatePredecessor

Duration(weeks)

A Develop product specifications None 4B Design manufacturing process A 6C Source & purchase materials A 3D Source & purchase tooling & equipment B 6E Receive & install tooling & equipment D 14F Receive materials C 5G Pilot production run E & F 2H Evaluate product design G 2I Evaluate process performance G 3J Write documentation report H & I 4K Transition to manufacturing J 2

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Revisiting C and BU Using Probabilistic Time Estimates

Activity Description Optimistictime

Most likelytime

Pessimistictime

A Develop product specifications 2 4 6B Design manufacturing process 3 7 10C Source & purchase materials 2 3 5D Source & purchase tooling & equipment 4 7 9E Receive & install tooling & equipment 12 16 20F Receive materials 2 5 8G Pilot production run 2 2 2H Evaluate product design 2 3 4I Evaluate process performance 2 3 5J Write documentation report 2 4 6K Transition to manufacturing 2 2 2


Calculating Expected Task Times

Activity Optimistictime

Most likelytime

Pessimistictime

Expectedtime

A 2 4 6 4B 3 7 10 6.83C 2 3 5 3.17D 4 7 9 6.83E 12 16 20 16F 2 5 8 5G 2 2 2 2H 2 3 4 3I 2 3 5 3.17J 2 4 6 4K 2 2 2 2

6

4 cpessimistilikelymostoptimistictimeExpected

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Estimating the Probability of Completion Dates

• Using probabilistic time estimates offers the advantage ofpredicting the probability of project completion dates

• We have already calculated the expected time for each activityby making three time estimates

• Now we need to calculate the variance for each activity• The variance of the beta probability distribution is:

– where p=pessimistic activity time estimateo=optimistic activity time estimate

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6opσ


© Wiley 2007

Project Activity VarianceActivity Optimistic Most

LikelyPessimistic Variance

A 2 4 6 0.44

B 3 7 10 1.36

C 2 3 5 0.25

D 4 7 9 0.69

E 12 16 20 1.78

F 2 5 8 1.00

G 2 2 2 0.00

H 2 3 4 0.11

I 2 3 5 0.25

J 2 4 6 0.44

K 2 2 2 0.00

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Variances of Each Path through the Network

PathNumber

Activities onPath

Path Variance(weeks)

1 A,B,D,E,G,H,J,k 4.82

2 A,B,D,E,G,I,J,K 4.96

3 A,C,F,G,H,J,K 2.24

4 A,C,F,G,I,J,K 2.38


Calculating the Probability of Completing the Project inLess Than a Specified Time

• When you know:– The expected completion time– Its variance

• You can calculate the probability of completing the project in“X” weeks with the following formula:

Where DT = the specified completion dateEFPath = the expected completion time of the path

2PσEFD

timestandardpathtimeexpectedpathtimespecifiedz PT

pathofvarianceσ 2Path

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Example: Calculating the probability of finishing theproject in 48 weeks

• Use the z values in Appendix B to determine probabilities• e.g. probability for path 1 is

PathNumber

Activities on Path Path Variance(weeks)

z-value Probability ofCompletion

1 A,B,D,E,G,H,J,k 4.82 1.5216 0.9357

2 A,B,D,E,G,I,J,K 4.96 1.4215 0.9222

3 A,C,F,G,H,J,K 2.24 16.5898 1.000

4 A,C,F,G,I,J,K 2.38 15.9847 1.000

1.524.82

weeks44.66weeks48z


Example:

Activity Description Predecessors Immediate Time (days)

A Initial Paperwork --- 3

B Build Body A 3

C Build Frame A 2

D Finish Body B 3

E Finish Frame C 7

F Final Paperwork B,C 3

G Mount Body to Frame D,E 6

H Install Skirt on Frame C 2

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Example

Start Finish

3 66 9

B

36 99 12

D

3

0 30 3

A

3

3 53 5

C

2

12 1812 18

G

66 915 18

F

3

5 716 18

H

2

5 125 12

E

7

Latest Start and Finish Times


Example:

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ACTIVITY INFORMATION

EARLY START01/06/97

TIME DURATION2 WORK-WEEKS

EARLY FINISH14/06/97

ACTIVITY 4

TOTALSLACK(TS)

$250,000

LATE START15/06/97

COST/PROFITCENTER 2810

LATE FINISH28/06/97

FREE SLACK(FS)


End of Chapter 12

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