TOC – Critical chain I
J.Skorkovský
ESF-MU, KPH

TOC concisely I (see PWP presentation about TOC)
•origin: E.M.Goldratt, Jerusalem
•cost world<->throughput world
•analogy weight of the chain – solidity of the chain
•how to find a bottleneck?
•tools of TOC – tree structures
•CRT – EC – TT – PT – FRT  meaning:
•Current Reality Tree  - Evaporating Cloud Tree– Transition Tree  -
•   - Prerequisite Tree – Future Reality Tree

TOC concisely I (see PWP presentation about TOC)
•bottleneck in project management is critical path
•finding (assessment) of bottleneck is not easy and often it is not explicit (uncompromising)
•everybody knows something about TOC  and nobody knows how to implement it to the real world- and
this is again another bottleneck (tendon of Achilles from the heel to the scruff)
•

TOC-five steps (revision)
•Five steps process:
•            Step 0.   Identify the Goal of the System/Organization
Step 0.5 Establish a way to measure progress to Goal
•
•Step 1.  Identify the system’s constraint.
•Step 2.  Exploit the system’s constraint.
•Step 3.  Subordinate everything else to the above decision.
•Step 4.  Elevate the system’s constraint.
•Step 5.  If a constraint is broken (that is, relieved or improved), go back to  Step 1. But don’t
allow inertia to become a constraint.
•

Linear image of the project
•activities – abscissas – Gantt graph
•constantly changing conditions (Parkinson low, Murphy low, Student syndrome, customer changes -
„fancies “,“caprices“.. ….  ),
•
•
Solvina z Austrálie
Trouble
Trouble
Ajtík z Autsralie 20020416

Parallel image of the  project



Project and its budget
•price of the whole project
•project length (time)
•project stages and length of each activity
•assigned resources to every activity and their capacities (time per defined period)
•time reserves (buffers) and their estimation
•unfavourable influences (see Murphy´s lows - http://murphy.euweb.cz, etc.)
•
•
•
•

Selected Murphy´s laws
•If your attack is going well, you have walked into an ambush (trap)
•Planner is alerted about modification of the plan exactly in the moment, when the plan is finally
adjusted
•To carry out  n+1 trivialities you need two times more time than time necessary to carry out n
trivialities (law 99 %)
•If anything can go wrong, it will
•Any given program, when running, is obsolete
•No matter how many resources you have, it is never enough
•Brains x Beauty x Availability = Constant.
This constant is always zero.

Project Pyramid – principle (not necessary pro MPH_AOMA)
Project Budget Cost Volume
Stage 1 ->Workshop->approval->Correction
(2nd stage set out)
Quality
Management
Stage 2 ->Workshop->approval->Correction
(3rd stage set out)
Quality
Management
And Credit Notes
(Return Management)
Financial Management
1st part
e.g. Initial work on Finite Capacity
Planning integration
Basically all the scope
of the project framed
by e.g. your clauses 2-7
Stage 3 ->Workshop->approval->Correction
(4th stage set out)
180 hours for Allocations 1st stage
All budgeted
hours for allocations
All budgeted
hours for quality..
Total volume of hours
suggested for the 1st stage corresponds
to the volume of the smaller triangle,
which represents 430 hours

Example of the real budget- data is modified
 (not necessary pro MPH_AOMA)


Capacity assignment
 (not necessary pro MPH_AOMA- only example of capacity plan¨


Resources and orders
Matrix structure of multi-project environment – responsibility
of project managers and responsibility of department managers are in conflict
time
capacity
Order 1
Order 2
Project manager 1
Project manager 2
Chief 1
Chief 2
overload
0789209039

Probability– median an element of statistical file,
 which is after sorting in the middle .Median of the set (1,5,2,2,1)  is 2

5 min        15min                                               45min
100 „5-miniutes meeting happened.
How many times it took 5 minutes only ?
Variability of the real time assigned to activity

Colleague ask for a quick rendez-vous: „Do not worry, it will take maximum 5 minutes!“.
How long it takes on average?
Partial time of any activity in the project

Probability of finishing tasks A to E  in time  is 50%. (50*50*….*50=3,125 %)
What is a probability, that task F will start in time ?
A
B
C
D
E
F
50%
3%
50%
50%
50%
50%
      How the timely finishing of the tasks A,B,C and D will influence the integration point ?
a)saving are fully wasted
b)delay in one task will be immediately transferred to the next project task (activity) see +10
-2
-5
-1
-7
+10
+10
Project environment is very complicated because of integration linkages and their dependencies

Project environment is very complicated because of integration linkages and their dependencies
G
G
G
B
B
B
In order to start  B in the upper branch, you have to finish G and also B in the lower
branch. The probability, that B start in time is  50 % worse, than it was shown
on the previous slide.

The project must be protected against influences of breakdowns (troubles)
activity 1
activity 2
activity 3
B
B
B
B
= buffer
Standard estimation with protecting buffers for every activity
activity 1
activity 2
activity 3
buffer
1st step   :  every activity is shorten to 50 % of  its original time size.
2nd step :  critical path buffer at the end of the project
will have size of 50 % of the total sum of saved time
created by shortening all partial activities
istockphoto_245312-steam-train-buffer-close-up

Critical path,  adjoining branches of the project and adjoining buffers (AB)
Project buffer
Critical path
activity X
activity Y
AB
Adjoining project branch
Buffer serves as a safety tool to accumulate reasons
of expected and unexpected delays
activity 1
activity 2
activity 3

Critical Path (CP)
• Critical path is defined as the longest way   (meaning time) from the starting point of the
project graph to the ending point.
• Every project has at least one critical path

The rules of CP:
• Every delayed task on CP will essentially  delay the whole project
•
• Truncation of duration of any task on CP will shorten whole project

CP definition (more in detail)
  Critical path is defined as the longest way   (meaning time)
  from the starting point of the project graph to the ending point
Critical path represents technological dependencies and given
times of every task on Critical path  inclusive of necessary
condition for fulfilment of foregoing  tasks (activities)
framed by integration points.

Critical chain definition
•   In TOC the Critical chain is defined as the longest way  (meaning time)  from the starting
point of the project graph (Gantt) to the ending point which takes into account technological
dependencies  as well as time of the tasks and moreover, capacities of assigned resources.
•    With infinite capacities of resources you can consider Critical path=Critical chain

Multi-project management and critical resources (CCR) used in more that one project branch
X
X
X
X
AB
AB
AB
AB


Project buffer
X
Disadvantageous variant
Critical chain
Critical path
CCR = Capacity Constrained Resource = X

Multi-project management and critical resources (CCR) used in more that one project branch
X
X
X
X
AB
AB
AB
AB


X
After transformation
of activities
Project buffer
Critical chain

Project management based on remainimg time in buffers – Buffer Management
•Buffers are used for timely warning and that is to say predicting  and avoiding future problems
related to project deadlines (milestones)
•
•It is also used as a guideline for corrective actions

Basic metrics showing the project status
•The partial size of Critical chain (CC) fulfilled in days (in  %)
•How much of buffer size was used to fulfil above mentioned partial size of CC ?
•Trend of  project (buffer consumption graph- see next slide)
•Consumption of the financial buffer
•Priorities – bigger buffer penetration- bigger priority
•Adjoining branches have always lower priorities
•It is not allowed to create bad multitasking
•

Trends of the project
%  use of the buffer
% consumption of the critical chain
Dangerous zone
Warning zone
Safety zone
peril print_guardian_angel_watching_over_children_bridge_litho pompier_009

Planning  - principles
•We are working with plan , which takes into account different times of tasks   :
•- start of the tasks are changed based on termination of preceding  tasks
- you have to react in project in such a way , that handover is done as a baton pass during races
A1
B1
C1
D1
B
Buffer
Plan with sharp deadlines with buffers 50% (2+3+3=8 8+4=12)
2
4
6
8
10
Planned start
12
Critical chain completion
8 days
0
100%
100%
Zdroj MPM systems

      Buffer
Planning  - principles
•A1 did not started yet , because this A1 resource is still working on another order (task), which
may be part of another project
•B1 already started an for completion will need another two days
A1
C1
D1
r
2
4
6
8
10
Planned start
12
B1
0
100%
100%
Zdroj MPM systems
Plan with sharp deadlines with buffers 50% (2+3+3=8 8+4=12)
Critical chain completion
8 days
1


Plan 2nd day after start
•A1 started and will be finished (completed) tomorrow.
•B1 will be finished (completed) tomorrow
A1
C1
D1
r
B1
0
100%
100%
2
4
6
8
10
Planned start
Plan with sharp deadlines with buffers 50% (2+3+3=8 8+4=12)
Critical chain completion
8 days
Buffer
12
Zdroj MPM systems


Plan 3rd day after start
•A1 despite all efforts resource A1 needs another day to complete.
•B1 has completed his work with 2 days delay
A1
C1
D1
r
B1
0
100%
100%
Plan with sharp deadlines with buffers 50% (2+3+3=8 8+4=12)
Planned start
2
4
6
8
10
Critical chain completion
8 days
12
3
Buffer
Zdroj MPM systems


 Plan 6 day after start
•A1 completed his task with 2 days delay
•B1 completed his task with 2 days delay
•C1 completed his task 1 day earlier than expected (planned)
•D1 will start to work tomorrow
A1
C1
D1
r
B1
0
100%
100%
Plan with sharp deadlines with buffers 50% (2+3+3=8 8+4=12)
Planned start
Critical chain completion
8 days
Zdroj MPM systems
2
4
6
8
10
12
Buffer


 Plan 8 day after start
•A1 completed his task with 2 days delay
•B1 completed his task with 2 days delay
•C1 completed his task 1 day earlier than expected (planned)
•D1 needs one day more to complete
A1
C1
D1
r
B1
0
100%
100%
Plan with sharp deadlines with buffers 50% (2+3+3=8 8+4=12)
Planned start
Critical chain completion
8 days
2
4
6
8
10
12
Buffer
Zdroj MPM systems

rezerva
Plan 11 day after start
•A1 completed his task with 2 days delay
•B1 completed his task with 2 days delay
•C1 completed his task 1 day earlier than expected (planned)
•D1 completed his task with 2 days delay
A1
C1
D1
r
0
B1
Plan with sharp deadlines with buffers 50% (2+3+3=8 8+4=12)
Planned start
100%
100%
Critical chain completion
8 days
2
4
6
8
10
12
11
Zdroj MPM systems

Critical Path (CP)
•Critical Path Method, abbreviated CPM, or Critical Path Analysis, is a mathematically based
algorithm for scheduling a set of project activities. It is an important tool for effective project
management.

Critical Path (CP)
Milestones
Activity

Critical Path (CP)
Building a diagram 1


Critical Path (CP)
Building a diagram 2


Critical Path (CP)
Building a diagram 3


Critical Path (CP)
Building a diagram 4 – calculating the FORWARD PASS
Early Starts and Early finishes dates are calculated by means of Forward Pass
ES
EF
13-7=6
16=7+6+3

Critical Path (CP)
Building a diagram 5 – calculating the BACKWARD PASS
Late Starts and Late Finishes dates are calculated by means of Backward Pass
LS
LF
18-2=16
16-3=13
13-3=10
13-2=11
10-3=7
16-3=13
13-3=10
Difference
Forward-Backward :
you can start
7 minutes later and the time
of the project (duration)
 is the same
Planüberhang,
Slip, Scivolo,
Regresso,
загрузочный

Critical Path (CP)
Building a diagram 6 – calculating the FLOAT(SLACK)/CP
 Free Float: Amount of time a single task can be delayed
 without delaying the early start of any successor task =LS-ES or LF-EF

Critical Path (CP)
•Project Planning and control.
•Time-cost trade-offs.
•Cost-benefit analysis.
• Reducing risk.
CPM is helpful in :

Critical Path (CP)
Limitation of CPM :
•Does not consider resource capacities.
•Less efficient use of buffer time.
•Less focus on non critical tasks that can cause risk.
•Based on only deterministic task duration.
•Critical Path can change during execution.

Multi-project Management
w1
w2
w3
w4
w5
w6
w7
w8
w9
w10
w11
w12
w13
w14
DAP
Project 1














12
Project 2














12
Project 3














12

36
K1
K2
K3
w1
w2
w3
w4
w5
w6
w7
w8
w9
w10
w11
w12


DAP
Project 1














6
Project 2














6
Project 3














6
18
Bad multitasking  causes, that one project will be significantly longer
and no other project will be shorter

Multitasking characterization
•people always overestimate the length of their tasks
•salesman  offers impracticable terms (dates)
•The fight for reserves (capacities) causes, that all saved time is fully wasted (Student´s
syndrome)
•Reserves (if any) are used badly
•Bad use of reserves causes lack of transparent assignment
•Non transparent priorities are parents of bad multitasking
•Bad multitasking causes longer duration of all activities (tasks) and thus all the projects
•

Project Quick, resources A-E and activities X,Z,X,W, and V
Resource and activity
Activity=Task
A-Y
Median of the required
 time
10 days
You can say, that 50 % of any activities finish earlier, and other 50 %
will be delayed, meaning, that 10 days represents 50 % of the estimated time
for chosen activity
Project managers decided, that activity ends if 90 % of estimated time
will be consumed. It means, that they add a time buffer of 8 days
(for the safety reasons). 10 d= 50%, 20d=100%, 2d=10%, 20d-2d=18d, 18d-10d=8d
A-Y
B-Z
C-X
D-W
E-V
5 x 10 days=50 days

Time distribution
 Time
10 days
18 days

Five activities (tasks)
 and applied modifications
•If we consider for every activity time buffer 8 days we will get :
A-Y
B-Z
C-X
D-W
E-V
5 x 10 days= 50 days
A-Y
 8
B-Z
 8
C-X
 8
D-W
 8
E-V
 8
5 x 18 days= 90 days

Vložte obrázek některého z významných geografických úkazů země.

Five activities and modifications (added buffers) and four types of troubles
A-Y
 8
B-Z
 8
C-X
 8
D-W
 8
E-V
 8
A-Y
B-Z
C-X
D-W
E-V
Delayed
„reporting“
We wait for resource D
 (even if C finished earlier)
Parkinson
Real delay
No one trouble causes project delay taking into consideration
planned delivery date  (agreed date  of the project).
Dissipation of acquired time reserves was caused by company strategy saying
strictly stick to the planned project schedule (example of rigid management)

Five projects after modification (buffers united to one and placed to the  end of the project)
A-Y
B-Z
C-X
D-W
E-V
 8
 8
 8
 8
 8
A-Y
B-Z
C-X
D-W
Parkinson
Little bit longer than 20 days median
but shorter than 18 days
 Earlier end of
activity A
 8
 8
 8
 8
 8
= CPB=current project buffer = 40 days
 8
 8
 4
= new buffer = 50 % out of CPB, which makes CPB/2
E-V

Critical path- Critical chain
START
Activity V
14 days, resource A
Activity W
6 days, resource B
Activity X
6 days, resource C
Activity Y
10 days,
 resource A
Activity Z
4 days,
 resource D
END
Critical path
Critical Chain

Gantt graph for X,Z,V,W a Z
1
2
3
4
5
6
7
8
9
1
0
1
1
1
2
1
3
4
1
2
3
4
5
6


1
2
3
4
1
2
3
4
5
6
1
2
3
4
5
6
7
8
9
1
0

1
2
3
4
5
6
7
8
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
2
1
2
2
2
3
2
4
2
5
2
6
2
7
2
8

Critical chain
Critical path
Project is considered as successful if is finished in expected time
 and financial budget is not exceeded

Critical chain with buffers
START
Activity V
7 days=14/2, RES  A
Activity W
3=6/2 days, RES B
Activity X
3=6/2 days, RES C
Activity Y
5=10/2 days, RES A
Activity Z
2=4/2 days, RES D
END
>
Adjoining
buffer
1,5 days
>
Project
buffer
7 days
7=(7+5+2)/2
Length of the Critical Chain:
7+5+2+7=21
and  originally it was all in all 24 days
>
Adjoining
buffer
1,5 days

Multitasking – sequential order of resources
1
2
3
4
5
6
7
8
9




Time




1A
PB1

AB1
AB-Adjoining Buffer
2 B
PB2
AB 2A
AB2
2 A

PB3

AB3
3 A
Project 1
Project 2
Project 3
Framed by those three projects we could see collision in utilization of some resources. GREEN
RESOURCE  at the
end of projects  P1 and P2 and the same by YELLOW RESOURCE at the beginning of P1 and P2.
In the adjoining branches we could see collision due to the bad resources allocation in P1 and P3
and in all three
projects we have collision of BROWN and RED RESOURCES.
This is caused by matrix organisation scheme of the company
PB-Project  Buffer

Matrix scheme
1
2
3
4
5
6
7
8
9




TIME




1A
PB 1

AB 1
2 B
PB2
AB 2A
AB 2
2 A

PB 3

AB 3
3 A

Project manager 1
Project manager 2
Project manager 3
Manager commanding RED RESOURCE
Project 1
Project 2
Project 3
AB-Adjoining Buffer
PB-Project  Buffer

Collisions among project and department managers (DMi) (those who control resources)





DM1
DM2
DM3
DM4
DM5
Project Manager 1

Resources
PM always persuade Department managers to assign their resources
to their project and department managers want have all projects finished as soon as possible
with maximum parallel processing possible
Project Manager 2

Project Manager 3

Collisions among project and department managers (DMi) (those who control resources)
•The synchronization of the starts of the projects is based on most utilized (overloaded) resource,
which is the cause of prevailing quantity of conflicts
•
•The above mention statement means, that all your started projects are covered by all most critical
capacity resources (CCR) of the organization and due to this fact you will have less started
projects.
•
•Less started projects results in less quantity of conflicts among project managers and department
managers
boxing_giant

Multitasking – modified schedule-stage  1
1
2
3
4
5
6
7
8
9




Time




1A
PB 1

AB 1
2 B
  PB2
AB 2A
     AB 2
2 A

PB 3

PB 3
3 A
Project 1
Project 2
Project 3
We have to protect critical  (DRUM) resource – in our case  RED RESOURCE. At the first sight it
looks like
all the scheduled projects will last longer. On the other hand, these reshuffling will result in
higher probability,
that they end in planned time and that is the reason of less conflicts among PM and DM.
conflict
conflict
We should
push it
AB-Adjoining Buffer
PB-Project  Buffer

Collisions among project and department managers (DMi) (those who control resources)
•To all three projects we have inserted buffers protecting the critical chain
•
•
•On the other hand, after reshuffling of the schedule in order to decrease  quantity of conflicts
we did nothing to protect critical capacity resource (drum, CCR)
•
•Above mentioned statement is the reason to insert additional protecting buffer before drum
resource (Drum-Feeding Buffer) = DFB =
DFB 1
See next slide
c%3Fq%3D1826fa62fa51dd54_large

Multitasking – modified schedule-stage  2
1
2
3
4
5
6
7
8
9




TIME




        1A
PB 1

AB 1
2 B
PB 2
AB 2A
      AB 2
2 A

PB 3

AB 3
            3 A
Project 1
Project 2
Project 3
Conflict
DFB 1
DFB 3
Conflict
AB-Adjoining Buffer
PB-Project  Buffer
We should
push it forward
We have to protect critical  (DRUM) resource – in our case  RED RESOURCE. At the first sight it
looks like
all the scheduled projects will last longer. On the other hand, these reshuffling will results in
higher probability,
that they end in planned time and that is the reason of less conflicts among PM and DM.

 Project
    Buffer (10)
Buffer consumption - variant A
Activity A(10)
Activity B(10)
Project
    Buffer (10)
Activity A(5+8)
Activity B(10)
Buffer penetration  = 3 days
10=(10+10)/2
Rate of penetration is used to assign priorities to the partial activities

Project Buffer 2
Priorities assigned to resources
•If one resource have to be assigned to two activities starting in the same moment so the first
activity which will start is the one belonging to the project with bigger project buffer
penetration
•If none of all project buffers were penetrated with previous activities, so the first starts this
activity which belongs to the critical chain.
A 1

AB 1


AB 2
A 2
A2 starts first because PB 2 is partially consumed (penetrated)
AB-Adjoining Buffer
PB-Project  Buffer

Project Buffer 1

Priorities assigned to resources
A 1
    Project
     Buffer 1

AB  1


AB 3
           A 2
A 2
DFB 3
AB 2
Critical chain
 This activity starts first because it is a part of the Critical chain
and Project Buffer 1 is penetrated

AB-Adjoining Buffer
PB-Project  Buffer
Project Buffer 2

Main benefits of the Critical Chain (CC) usage
•Every single project ends significantly earlier, than projects where other project management
methods than CC were applied
•
•Total time needed to end more project than one is markedly shorter
•
•Promised delivery times are fulfilled with higher rate of credibility
•
•You will have more free capacity of all used resources

Main benefits of the Critical Chain (CC) usage
•Better initial estimation about project timing and thus bore accurate planning
•
•During starting of the projects you did not meet any problem taking into consideration drum
resource
•
•Decrease of unfavourable effects such  as  Student syndrome, Murphy attacks and impacts of
Parkinson´s laws by redeployment and integration of all buffers to one and only one project buffer
at the end of the project
•
•Utilization of benefits caused by earlier ended activities
•
•Use of reporting system which provides you with valuable information of buffer penetration , the
extent of time reserves and thus  better helping system for assigning priorities

project-manager-attributes



Thanks for Your Attention
Wave_Surfing_At_Pipeline,_Hawaii