Network Planning Methods Example PERT & CPM

Terms Used in Project Management Activity : A certain amount of work or task required in the project Activity duration: In CPM the best estimate of time to complete an activity . In PERT the expected time or average time to complete an activity Critical activity : An activity that has no room for schedule slippages : if it slips the entire the entire project completion will slip. An activity with zero slack

Critical path: The chain of critical activities for the project .The longest path through the network Dummy activity :An activity that consumes no time but shows precedence among activities Earliest finish (EF): The earliest that an activity can finish from the beginning of the project Earliest start ( ES): The earliest that an activity can start from the beginning of the project

Event :A beginning , a completion point ,or a milestone accomplishment within the project . An activity begins and ends with events Latest finish (LF) : The latest that an activity can finish from the beginning of the project Latest start (LS) :The latest that an activity can start from the beginning of the project Most likely time ( t m) : The time for completing the activity that is is the consensus best estimate, used in PERT

Optimistic Time (to): The time for completing an activity if all goes well : used in PERTPessimistic Time (tp): The time for completing an activity if bad luck is encountered : used in PERTPredecessor activity : An activity that must occur before another activity .Slack : The amount of time that an activity or group of activities can slip without causing a delay in the completion of the project Successor activity : An activity that must occur after another activity

Conventions used in drawing network diagrams (Arrows & Circles ) Activity on Arrow (AOA) : The activities are denoted by Arrows and events are denoted by circles

Activity on Node(AON) : Activities are denoted by circles(or nodes) and the precedence relation ships between activities are indicated by arrows

AOA Project Network for HouseAON Project Network for House

Situations in network diagramA must finish before either B or C can startboth A and B must finish before C can startboth A and C must finish before either of B or D can startA must finish before B can startboth A and C must finish before D can start

Forward PassEarliest Start Time (ES)earliest time an activity can start ES = maximum EF of immediate predecessorsEarliest finish time (EF)earliest time an activity can finishearliest start time plus activity timeEF= ES + tLatest Start Time (LS)Latest time an activity can start without delaying critical path time LS= LF - tLatest finish time (LF)latest time an activity can be completed without delaying critical path timeLS = minimum LS of immediate predecessorsBackward Pass

CPM analysisDraw the CPM networkAnalyze the paths through the networkDetermine the float for each activityCompute the activitys float float = LS - ES = LF - EFFloat is the maximum amount of time that this activity can be delay in its completion before it becomes a critical activity, i.e., delays completion of the projectFind the critical path is that the sequence of activities and events where there is no slack i.e.. Zero slackLongest path through a networkFind the project duration is minimum project completion time

Relationship between activities Project durationCritical pathSlack for non critical activitiesCrashing (cost / time trade-offs) Resource usagePERT / CPMNetwork planning methods that generate:

St. Pauls Hospital ImmediateActivity Description Predecessor(s)ASelect administrative and medical staff.BSelect site and do site survey.CSelect equipment.DPrepare final construction plans and layout.EBring utilities to the site.FInterview applicants and fill positions in nursing,support staff, maintenance, and security.GPurchase and take delivery of equipment.HConstruct the hospital.IDevelop an information system.JInstall the equipment.KTrain nurses and support staff.ABB

ACDAE,G,HF,I,J

St. Pauls Hospital ImmediateActivity Description Predecessor(s)ASelect administrative and medical staff.BSelect site and do site survey.CSelect equipment.DPrepare final construction plans and layout.EBring utilities to the site.FInterview applicants and fill positions in nursing,support staff, maintenance, and security.GPurchase and take delivery of equipment.HConstruct the hospital.IDevelop an information system.JInstall the equipment.KTrain nurses and support staff.ABB

ACDAE,G,HF,I,J

St. Pauls Hospital ImmediateActivity Description Predecessor(s)ASelect administrative and medical staff.BSelect site and do site survey.CSelect equipment.DPrepare final construction plans and layout.EBring utilities to the site.FInterview applicants and fill positions in nursing,support staff, maintenance, and security.GPurchase and take delivery of equipment.HConstruct the hospital.IDevelop an information system.JInstall the equipment.KTrain nurses and support staff.ABB

ACDAE,G,HF,I,J

St. Pauls Hospital ImmediateActivity Description Predecessor(s)ASelect administrative and medical staff.BSelect site and do site survey.CSelect equipment.DPrepare final construction plans and layout.EBring utilities to the site.FInterview applicants and fill positions in nursing,support staff, maintenance, and security.GPurchase and take delivery of equipment.HConstruct the hospital.IDevelop an information system.JInstall the equipment.KTrain nurses and support staff.ABB

ACDAE,G,HF,I,JCritical Path

Critical Path

Earliest Start and Earliest FinishBegin at starting event and work forwardES is earliest startES = 0 for starting activitiesES = Maximum EF of all predecessors for non-starting activitiesEF is earliest finishEF = ES + Activity time

A

12K

9C

10G

35J

4H

40B

9D

10E

24I

15F

10FinishStartEarliest Start / Earliest Finish

Earliest Start / Earliest FinishFinishEarliest start timeEarliest finish timeA

12K

9C

10G

35J

4H

40B

9D

10E

240 12I

15F

1012 2712 2263 7222 5759 6319 599 330 99 1912 22Critical pathStart

Latest Start and Latest FinishBegin at ending event and work backwardLF is latest finishLF = Maximum EF for ending activitiesLF = Minimum LS of all successors for non-ending activitiesLS is latest startLS = LF Activity timeESLSEFLFActivity NameActivity Duration

Latest Start / Latest FinishA

12K

9C

10G

35J

4H

40B

9D

10E

240 12I

15F

1012 2712 2263 7222 5759 6319 599 330 99 1912 2248 632 1453 6363 7214 2424 590 99 1919 5935 5959 63Latest start timeLatest finish timeCritical pathFinishStart

What do you notice about ES/LS & EF/LF?For Activity AES = 0LS = 2Meaning: Due to some reason of if activity A is not started at 0 weeks but 1, 2 or 3 weeks, even then completion of project is not delayed

For Activity BES = 0LS = 0Meaning Any delay in start would delay project completion.

Activity Slack AnalysisA

12K

9C

10G

35J

4H

40B

9D

10E

240 12I

15F

1012 2712 2263 7222 5759 6319 599 330 99 1912 2248 632 1453 6363 7214 2424 590 99 1919 5935 5959 63Latest start timeLatest finish timeCritical pathFinishStartSlackK = 63 63 = 0

or

SlackK = 72 72 = 0Slack = LS ES

or

Slack = LF EF

Activity Slack AnalysisA

12K

9C

10G

35J

4H

40B

9D

10E

240 12I

15F

1012 2712 2263 7222 5759 6319 599 330 99 1912 2248 632 1453 6363 7214 2424 590 99 1919 5935 5959 63Latest start timeLatest finish timeCritical pathFinishStart

Activity SlackHow much would we like to reduce the time for activity B?

PERT PERT is based on the assumption that an activitys duration follows a probability distribution instead of being a single valueThree time estimates are required to compute the parameters of an activitys duration distribution:pessimistic time (tp ) - the time the activity would take if things did not go wellmost likely time (tm ) - the consensus best estimate of the activitys durationoptimistic time (to ) - the time the activity would take if things did go well

PERT analysisDraw the network.Analyze the paths through the network and find the critical path.The length of the critical path is the mean of the project duration probability distribution which is assumed to be normalThe standard deviation of the project duration probability distribution is computed by adding the variances of the critical activities (all of the activities that make up the critical path) and taking the square root of that sumProbability computations can now be made using the normal distribution table.

Probability computationDetermine probability that project is completed within specified timewhere = tp = project mean time = project standard mean timex = (proposed ) specified time

Normal Distribution of Project Time

PERT Example Immed. Optimistic Most Likely PessimisticActivity Predec. Time (Hr.) Time (Hr.) Time (Hr.) A -- 4 6 8B -- 1 4.5 5C A 3 3 3 D A 4 5 6 E A 0.5 1 1.5 F B,C 3 4 5 G B,C 1 1.5 5 H E,F 5 6 7 I E,F 2 5 8 J D,H 2.5 2.75 4.5 K G,I 3 5 7

PERT Example ADCBFEGIHKJ PERT Network

PERT Example Activity Expected Time Variance A 6 4/9 B 4 4/9 C 3 0 D 5 1/9 E 1 1/36 F 4 1/9 G 2 4/9 H 6 1/9 I 5 1 J 3 1/9 K 5 4/9

PERT Example Activity ES EF LS LF Slack A 0 6 0 6 0 *critical B 0 4 5 9 5 C 6 9 6 9 0 * D 6 11 15 20 9 E 6 7 12 13 6 F 9 13 9 13 0 * G 9 11 16 18 7 H 13 19 14 20 1 I 13 18 13 18 0 * J 19 22 20 23 1 K 18 23 18 23 0 *

PERT ExampleVpath = VA + VC + VF + VI + VK = 4/9 + 0 + 1/9 + 1 + 4/9 = 2path = 1.414 z = (24 - 23)/(24-23)/1.414 = .71 From the Standard Normal Distribution table: P(z < .71) = .5 + .2612 = .7612

PROJECT COST

Cost consideration in projectProject managers may have the option or requirement to crash the project, or accelerate the completion of the project.

This is accomplished by reducing the length of the critical path(s).

The length of the critical path is reduced by reducing the duration of the activities on the critical path.

If each activity requires the expenditure of an amount of money to reduce its duration by one unit of time, then the project manager selects the least cost critical activity, reduces it by one time unit, and traces that change through the remainder of the network.

When there is more than one critical path, each of the critical paths must be reduced.

If the length of the project needs to be reduced further, the process is repeated.

Project CrashingCrashingreducing project time by expending additional resourcesReduction in activity duration by any change in its resources, resource use, method or material is referred to as crashing of the activityCrash timean amount of time an activity is reducedCrash costcost of reducing activity timeGoalreduce project duration at minimum cost

Activity crashingSlope = crash cost per unit time

Time-Cost RelationshipCrashing costs increase as project duration decreasesIndirect costs increase as project duration increasesReduce project length as long as crashing costs are less than indirect costsTime-Cost Tradeoff

Project Crashing example

Time Cost data

ActivityNormal timeNormal cost RsCrash timeCrash cost RsAllowable crash timeslope1234567128412444300020004000500005005001500753911328003500600071000110011002100053133314007002000800011001100700075000

From..To..

GANTT CHART

Gantt ChartGantt Chart was developed byHenry Laurence Gantt (1861-1919) was a mechanical engineer and management consultant who is most famous for developing the Gantt chart in the 1910s. These Gantt charts were employed on major infrastructure projects including the Hoover Dam and Interstate highway system. He refined production control and cost control techniques.

Example of Gantt Chart

Gantt ChartActivities in Buy a House

Sheet1

BuyHouse WBS2/24/01

`BUY A HOUSE

TASKPREDECESSOR

LOCATIONFINANCINGFIND HOUSEDOWN PAYMENT13

21

1- Criteria3- Determine affordability6- Type of House11- Track financial Market3

43

2- Visit Locations4- Determine mortgage provider7- Find Real Estate Agent12- Get down payment54

61

5- Lockup mortgage commitment8- Look for House13- $ in the Bank72, 6

87

9- Make Offer, P&S Agreem't95, 8

109

10- Closing

TASKPREDECESSOR

13

21

3

43

54

61

72, 6

87

95, 8

109

TASKPREDECESSOR

13

21

3

43

54

61

72, 6

87

95, 8, 13

109

11

1211

1312

Sheet2

Sheet3

Sheet1

BuyHouse WBS2/24/01

`BUY A HOUSE

TASKPREDECESSOR

LOCATIONFINANCINGFIND HOUSEDOWN PAYMENT13

21

1- Criteria3- Determine affordability6- Type of House11- Track financial Market3

43

2- Visit Locations4- Determine mortgage provider7- Find Real Estate Agent12- Get down payment54

61

5- Lockup mortgage commitment8- Look for House14- $ in the Bank72, 6

87

9- Make Offer, P&S Agreem't95, 8

109

10- Closing

TASKPREDECESSOR

1-criteria3

2-visit loc.1

3-affordability

4-mortgage co3

5-mortg lock4

6-type of hse1

7-real est agent2, 6

8-look for hse7

9-offer, P&S5, 8

10-closing9

Sheet2

Sheet3