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 Burglary You 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 Office Safe Jewelry Safe Legend Protected by alarm system Locked safe
Disarm the exterior alarm system Disarm the office alarm system Crack & clean out the office safe D. Crack the jewelry safe E. Clean out the jewelry safe F. Pick up the loot & exit 20 minutes 7 minutes 7 minutes 14 minutes 4 minutes 10 minutes 62 total time Necessary Activities and Times
Disarm Exterior Disarm Office Crack Office Crack Jewelry Clean Jewelry Exit Gantt Chart Schedule of the Project 48 minutes to complete the project 20 25 30 35 40 45 50
B C 7 7 F A 20 10 End Start D E 14 4 PERT/CPM Planning of Single Project ES=20 EF=27 ES=27 EF=34 LS=24 LF=31 LS=31 LF=38 ES=0 EF=20 ES=38 EF=48 LS=0 LF=20 LS=38 LF=48 ES=34 EF=38 ES=20 EF=34 LS=34 LF=38 LS=20 LF=34 Legend: Activity = A, B, C, D, E, F Time = 20, 7, 7, 14, 4, 10
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 Opt ML Pess. Var. 15 21 21 1.00 5 7 9 0.45 5 7 9 0.45 13 13.5 17 0.45 4 4 4 0.00 8 10 12 0.45 Mean Disarm the ext. alarm system 20 Disarm the office alarm system 7 Crack & clean out office safe 7 Crack the jewelry safe 14 Clean out the jewelry safe 4 Pick up the loot & exit 10
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.)
B C 7 7 F A 20 10 Start D E 14 4 Critical Chain Planningof Single Project ES=20 EF=27 ES=34 EF=41 LS=27 LF=34 LS=34 LF=41 End ES=0 EF=20 ES=41 EF=51 LS=0 LF=20 LS=41 LF=51 ES=34 EF=38 ES=20 EF=34 LS=37 LF=41 LS=20 LF=34 Note that activities C and D simultaneously require the 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. Legend: Activity = A, B, C, D, E, F Time = 20, 7, 7, 14, 4, 10
Alarm Expert Safe Expert Carry Expert Load Chart of the Project 51 minutes to complete the project 20 25 30 35 40 45 50
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.
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 Activity Crashing Options
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 variability The 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.
B C 7 6 F A 18 10 End Start D E 14 4 Strategic Buffering of a Project Convergence Buffer Project Completion Buffer Resource Contention Buffer 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. Legend: Activity = A, B, C, D, E, F Time = 20, 7, 7, 14, 4, 10
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.