An Introduction to Critical Chain Project Management

Ed D. Walker II, Ph.D.Valdosta State University

Characteristics of Projects• The project consists of a well-defined collection of jobs,

or activities, which when completed marks the end of the project.

• The activities may be started and stopped independently of each other, within a given sequence (thus eliminating continuous flow processes.)

• The activities are ordered; that is, they must be performed in technological sequence.

• Difficult production planning and inventory control• General purpose equipment• High labor skills

Cat BurglaryYou and two business partners have decided to

rob a local jewelry store. You plan to do this at night because the police have a longer response time and because the night patrolman comes by every 50 minutes. The store has an external alarm; a jewelry safe; an office alarm; and a safe full of securities in the office. The scheme requires split-second timing but you feel that you and your partners in crime can get away with it.

Layout of the Jewelry Store

Display Area Office Area

Protected by alarm systemLegend

Jewelry Safe

Office Safe

Locked safe

Necessary Activities and Times

A. Disarm the exterior alarm system B. Disarm the office alarm systemC. Crack & clean out the office safeD. Crack the jewelry safeE. Clean out the jewelry safeF. Pick up the loot & exit

20 minutes 7 minutes 7 minutes14 minutes 4 minutes10 minutes62 total time

Gantt Chart Schedule of the Project

20 25 30 35 40 45 50

Disarm ExteriorDisarm OfficeCrack OfficeCrack Jewelry

Clean Jewelry

Exit

48 minutes to complete the project

PERT/CPM Planning of Single Project

Start End

ES=0

A

20

B

7

C

7

D

14

E

4

ES=20 ES=27

ES=20 ES=34

ES=38

F

10

Legend:Activity = A, B, C, D, E, FTime = 20, 7, 7, 14, 4, 10

EF=20LS=0 LF=20

EF=27LS=24 LF=31

EF=34LF=38LS=31

EF=34LS=20 LF=34

EF=38LF=38LS=34

LF=48EF=48

LS=38

A Word on Activity Times• Most activities do not take some EXACT amount of time,

but rather have some associated variability. • PERT/CPM activities are assumed to follow a Beta

distribution.• Pessimistic (P)• Most likely (ML)• Optimistic (O)• The mean of the Beta distribution is given by:

(P+4*ML+O)/6• The variance is given by: ((O-P)/6)2

Variability of Project Activities Mean

Disarm the ext. alarm system 20Disarm the office alarm system 7Crack & clean out office safe 7Crack the jewelry safe 14Clean out the jewelry safe 4Pick up the loot & exit 10

Opt ML Pess. Var. 15 21 21 1.00 5 7 9 0.45 5 7 9 0.4513 13.5 17 0.45 4 4 4 0.00 8 10 12 0.45

Probability of Critical Path On-Time Completion

• Critical path = 48 minutes• Allowable time = 50 minutes• Variance on critical path =

1+.45+0+.45 = 1.90• Z = (50-48)/1.378 = 1.45• 92.6% chance of completion on or before

50 minutes.

Cat Burglary

• In this case, the project is being performed by you and two accomplices selected for their special abilities. You know about and can defeat any alarm system. Your first accomplice can crack open any safe, and your second accomplice can carry the great weight of the loot. As you are all in this together, you decide that all of you must exit at the same time (no one leaves early.)

Critical Chain Planningof Single Project

Start End

ES=0

A

20

B

7

C

7

D

14

E

4

ES=20 ES=34

ES=20 ES=34

ES=41

F

10

Legend:Activity = A, B, C, D, E, FTime = 20, 7, 7, 14, 4, 10

EF=20LS=0 LF=20

EF=27LS=27 LF=34

EF=41LF=41LS=34

EF=34LS=20 LF=34

EF=38LF=41LS=37

LF=51EF=51

LS=41

Note that activities C and D simultaneously requirethe use of a common resource (resource 2).

The Weist and Levy heuristic schedules D then C on Resource 2 as D is on the PERT/CPM critical path.

Load Chart of the Project

20 25 30 35 40 45 50

Alarm Expert

Safe Expert

Carry Expert

51 minutes to complete the project

Probability of Critical Chain On-Time Completion

• Critical chain = 51 minutes• Allowable time = 50 minutes• Variance on critical chain =

1+.45+.45+.45 = 2.35• Z = (50-51)/1.533 = .65• 25.8% chance of completion on or before

50 minutes.

Activity Crashing Options

  

 

Equipment option

Total Cost

Cost / minute crashed

Affected Activity Mean O ML P σ2

#1 $1000 $1000 A – Exterior alarm 19 14 20 20 1.00

#2 $2000 $1000 A – Exterior alarm 18 13 19 19 1.00

#3 $500 $500 B - Office alarm 6 4 6 8 0.45

#4 $750 $750 C - Office safe 6 4 6 8 0.45

#5 $1500 $1500 D - Jewelry safe 13 12 12.5 16 0.45

#6 $3000 $1500 D - Jewelry safe 12 11 11.5 15 0.45

Which Activities should be Crashed?

• Crashing Activity B (office alarm) is the cheapest ($500) but would not affect project duration.

• Crashing Activity C (office safe) is the next cheapest at $750 and would reduce project duration to 50 minutes (a 50-50 shot at getting away).

• Crashing Activity A (exterior alarm) is the next cheapest at $1000 per minute crashed.

• If we were to spend $2750 on equipment, we could reduce the Critical Chain to 48 minutes and increase our probability of getting away from ~25% to ~92%.

Probability of Critical Chain On-Time Completion with Crashing

• Critical chain = 48 minutes• Allowable time = 50 minutes• Variance on critical chain =

1+.45+.45+.45 = 2.35• Z = (50-48)/1.533 = 1.305• 91.15% chance of completion on or before

50 minutes.

Strategic Buffering of a Project

Buffering the critical chain against variabilityThe first buffer that should be considered is

some amount of time added to the end of the project – the project completion buffer.

A second type of buffer is the convergence buffer.

A third type of buffer is the resource contention buffer.

Strategic Buffering of a Project

Start End

A

18

B

7

C

6

D

14

E

4

F

10

Legend:Activity = A, B, C, D, E, FTime = 20, 7, 7, 14, 4, 10

There are three buffers placed into the project network to assure 100% execution of the critical chain.

Project Completion Buffer -- placed between the last activity on the critical chain and the end node of the network.

Convergence Buffer -- placed where a non-critical chain intersects the critical chain (between the last activity on the non-critical chain and the critical chain.)

Resource Contention Buffer -- special type of convergence buffer, placed before a common resource is used on two PERT/CPM paths.

Project Completion Buffer

Resource Contention Buffer

Convergence Buffer

Controlling the project• There are eight problems which can be classified as one of three

types:– Convergence– Resource contention– Management practice of PERT/CPM

• The strategic buffers “take care of” convergence and resource contention.

• Though strategic buffers “take care of” management practice to some extent, the project manager must ensure that the activity managers provide reasonable estimates of activity duration. Additionally, the project manager must not plan to start critical chain activities based on time in order to take advantage of optimistic completion times.