Chap8 Project Scheduling: LaggingProject Scheduling: Lagging, crashing and activity network

9-1Pinto Chapter 10

Lags in Precedence RelationshipsLags in Precedence RelationshipsLags in Precedence RelationshipsLags in Precedence Relationships

lag is The logical relationship between thelag is The logical relationship between the start and finish of one activity and the start and finish of another activity.

Four logical relationships between tasksg p1. Finish to Start2. Finish to Finishs to s3. Start to Start4 Start to Finish4. Start to Finish

Finish to Start LagFinish to Start LagFinish to Start LagFinish to Start Lag

• Most common type of sequencingMost common type of sequencing• Shown on the line joining the modes

– Added during forward passAdded during forward pass– Subtracted during backward pass

0 A 6 6 B 11 15 C 22L 4Spec Design

6Design Check

5Blueprinting

7

Lag 4

Finish to Finish LagFinish to Finish LagFinish to Finish LagFinish to Finish Lag

Two activities share a similar completion pointTwo activities share a similar completion point– The mechanical inspection cannot happen until

wiring, plumbing, and HVAC installation are complete

15 D 21

10 A 16 16 B 21 21 C 22

Wiring6

10 A 16Plumbing

6

16 B 21HVAC

5

21 C 22Inspection

1

Lag 3

Start to Start LagStart to Start LagStart to Start LagStart to Start Lag

30 D 3630 D 36Wiring

6

31 A 3333 B 36

HVAC36 C 37

Inspection

Lag 3

31 A 33Plumbing

65 1

Start to Finish LagStart to Finish LagStart to Finish LagStart to Finish Lag

• L t t f l• Least common type of lag relationship

• Successor’s finish dependent on• Successor s finish dependent on predecessor’s start

30 D 36Wiring

6

28 B 33 33 C 34

6Lag 3

22 A 28Plumbing

28 B 33HVAC

5

33 C 34Inspection

16

TradeTrade--Offs And Project CrashingOffs And Project Crashing

It is not uncommon to face the It is not uncommon to face the following situations:following situations:

The project is behind schedule Th l ti ti h b d The completion time has been moved

forward

Shortening the duration of the project is called project crashingproject is called project crashing

Crashing ProjectsCrashing ProjectsCrashing ProjectsCrashing Projects

Accelerating a project by committing moreAccelerating a project by committing more resources than initially planned

Principal methods for crashing

Improving existing resources’ productivity Improving existing resources productivityChanging work methods Increasing the quantity of resources

Factors to Consider WhenFactors to Consider WhenFactors to Consider When Factors to Consider When Crashing A ProjectCrashing A Project

The amount by which an activity is crashed i i f t i iblis, in fact, permissible

Taken together, the shortened activity d ti ill bl t fi i h th j tdurations will enable us to finish the project by the due date

The total cost of crashing is as small as The total cost of crashing is as small as possible

Steps in Project CrashingSteps in Project CrashingSteps in Project CrashingSteps in Project Crashing

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

Crash costCrash costper periodper period

== (Crash cost (Crash cost –– Normal cost)Normal cost)

(N l ti(N l ti C h ti )C h ti )per periodper period (Normal time (Normal time –– Crash time)Crash time)

2.2. Using current activity times, find the critical Using current activity times, find the critical ffpath and identify the critical activitiespath and identify the critical activities

Steps in Project CrashingSteps in Project CrashingSteps in Project CrashingSteps in Project Crashing

3 If there is only one critical path then select3. If there is only one critical path, then select the activity on this critical path that:

A- can still be crashedA can still be crashedB- 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

1. each selected activity can still be crashed2. the total crash cost of all selected activities is the

smallest. Note that a single activity may be common to more than

one critical path.p

Steps in Project CrashingSteps in Project CrashingSteps in Project CrashingSteps in Project Crashing

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

Crashing The ProjectCrashing The ProjectCrashing The ProjectCrashing The ProjectGiven 13 weeks instead of 16 weeks

Time (Wks) Cost ($) Crash Cost CriticalA ti it N l C h N l C h P Wk ($) P th?Activity Normal Crash Normal Crash Per Wk ($) Path?

A 2 1 22,000 22,750 750 YesB 3 1 30,000 34,000 2,000 No, , ,C 2 1 26,000 27,000 1,000 YesD 4 3 48,000 49,000 1,000 NoE 4 2 56 000 58 000 1 000 YE 4 2 56,000 58,000 1,000 YesF 3 2 30,000 30,500 500 NoG 5 2 80,000 84,500 1,500 YesG 5 2 80,000 84,500 1,500 YesH 2 1 16,000 19,000 3,000 Yes

Critical Path And Slack Times For Critical Path And Slack Times For Milwaukee PaperMilwaukee Paper

F4 7

10 13

C2 4

A20

4220

E

3

H4 8 13 15

2

Start0 0

2

SlackSlack = 0= 0 SlackSlack = 6= 6SlackSlack = 0= 0

4

G

213 154 8

D3

B0 3

0 00

SlackSlack = 0= 0SlackSlack = 0= 0

5

8 13

8 134

3 7

3

0 3

8441

SlackSlack = 1= 1 SlackSlack = 1= 1 SlackSlack = 0= 0

Critical Path And Slack Times For Critical Path And Slack Times For Mil k PMil k P

• Current critical path using normal times is ACEGH

Milwaukee PaperMilwaukee Paperp g

• A has the lowest crass cost/week which is 750 $ /week : crashing A by 1 week

• At this stage the original path starts ACEGH remains critical with a completion time of 14 weeks14 weeks

• However a new path start BDGH is also critical now with a completion of 14 weeks

• Any further crashing must be done to both critical paths • We select C from path 1 and D from the other path however G is better since it is

it i ip p

common even it is more expensive

• Total cost : A+G =750+1500 =2250 $

Managerial ConsiderationsManagerial ConsiderationsManagerial ConsiderationsManagerial Considerations

• Determine activity fixed and variable costs• Determine activity fixed and variable costs• The crash point is the fully expedited activity

• Optimize time-cost tradeoffs• Shorten activities on the critical pathp• Cease crashing when

the target completion time is reached– the target completion time is reached– the crash cost exceeds the penalty cost

What is the lowest cost to complete this project in 53 weeks? Times are in weeksproject in 53 weeks? Times are in weeks and costs in dollars.Activity Pred Normal Min Normal Crash

Time Time Cost CostA -- 14 9 500 1500B A 5 2 1000 1600B A 5 2 1000 1600C A 10 8 2000 2900D B C 8 5 1000 2500D B, C 8 5 1000 2500E D 6 5 1600 1900F D 9 6 1500 3000F D 9 6 1500 3000G E, F 7 4 600 1800H G 15 11 1600 3600

U i Mi ft P j tU i Mi ft P j tUsing Microsoft ProjectUsing Microsoft Project

Program 3.1

U i Mi ft P j tU i Mi ft P j tUsing Microsoft ProjectUsing Microsoft Project

Program 3.2

U i Mi ft P j tU i Mi ft P j tUsing Microsoft ProjectUsing Microsoft Project

Program 3.3

U i Mi ft P j tU i Mi ft P j tUsing Microsoft ProjectUsing Microsoft Project

Program 3.4

U i Mi ft P j tU i Mi ft P j tUsing Microsoft ProjectUsing Microsoft Project

Program 3.5

U i Mi ft P j tU i Mi ft P j tUsing Microsoft ProjectUsing Microsoft Project

Program 3.6

U i Mi ft P j tU i Mi ft P j tUsing Microsoft ProjectUsing Microsoft Project

Program 3.7g