Flow Time 2-Critical Path Method Based on the book: Managing Business Process Flows

4. Flow-Time Analysis

Flow Time

2-Critical Path Method

Based on the book: Managing Business Process Flows


Flow Time Example: Activity Times

A1 A3

A4 A6

A5A2

4

3

6

4

2

3

E

S

What is the Theoretical Flow Time Critical Path method 2Ardavan Asef-Vaziri, June, 2015


Critical Path Method: Paths

A1 A3

A4 A6

A5A2

4

3

6

4

2

3

E

S

Critical Path is the longest Path

How many paths?

Critical Path method 3Ardavan Asef-Vaziri, June, 2015

10 11 8


Critical Path Example of Flow Time

a) The Critical Path is A1-A4-

A6. The theoretical flow time

of the process is 4+4+3= 11.

b) What will happen if

activity A5 is increased from

2 to 4?

A5 is not on critical path. Increasing its time by 2

increases the length of the path A2-A5-A6 from 8 to 10.

It does not become a critical path. The flow time is still

11.

c) What will happen if activity A5 is increased from 2 to

5?


10 1

1 8


Critical Path Example of Flow Time

The length of the path A2-A5-A6

becomes 11.

Both A1-A4-A6 and A2-A5-A6

are critical path. The flow time

is still 11.

d) What will happen if activity A1 is increased from 4 to

5?

Path A1-A4-A6 is still critical and the flow time increases

to 12.

e) What will happen if activity A3 is increased from 6 to

8?

Now path A1-A3 becomes critical and the flow time

increases to 4+8 =12.


10 1

1 8


Theoretical Critical Path vs. Critical Path

A1 A3

A4 A6

A5A2

4

3

6

4

2

3

E

S

W1

W2

W4

W3

W6

W7

W5

W9

W8

The time of the critical path differs from the time of the theoretical critical path. Why?

The critical path itself also may differ from the theoretical critical path. Why?



Critical Path Methos: Forward Path; Earliest Starts

A1 A3

A4 A6

A5A2

4

3

6

4

2

3

E

S0

0

0

0

0

0

4

3

3

4

4

3

4

4

3

4

4 10

8

5

5

5

8 8

10

10

8 11

11

11

11



Forward Path; Earliest Starts

10

3020

Max = 30

5

35

35

35



Backward Path; Latest Starts

A1 A3

A4 A6

A5A2

4

3

6

4

2

3

E

S0

0

0

0

0

0

4

3

3

4

4

3

4

4

3

4

4 10

8

5

5

5

8 8

10

10

8 11

11

11

111

111

11

11

11

555

88

8

8

8

8

8

4

6

4

4

66

633

3

40

0

0 11

11



30

3030

Min = 35

5

35

45

30

Backward Path; Latest Starts



Activity Slack

Slack, or float: The amount of time a noncritical

task can be delayed without delaying the project

Slack—LFT – EFT or LST – EST

EST—Earliest Start Time; Largest EFT of all predecessors

EFT—Earliest Finish Time; EST + duration for this

task

LFT—Latest Finish Time; Smallest LST of following tasks

LST—Latest Start Time; LFT – duration for this task



Critical Path, Slacks

A1 A3

A4 A6

A5A2

4

3

6

4

2

3

E

S

0 4

3

4

4 10

8 8 11

11

11

11

5

88

8

4

663

40

11



A Key Problem: The Impact Converging Activities

15Activity

215Activity

1

15Activity

15Activity

2

15Activity

1

Which process has a longer flow time?.

In a deterministic world they both have a flow time of 30 mins. The situation differs in real world where nothing is deterministic.Suppose instead of an exact number of 15, the activity time is uniformly distributed in the range of 10 to 20. The average is still 15.



Activity time = 10+10rand()rand() is a random number between 0 and 1. If it is ranch = 0, the duration of the activity is 10, if rand() = 1, 1, the duration of the activity is 20. For all possible rand() 10 ≤ Activity Time ≤ 20For the fist project, the project duration is computed as the duration of Activity 1 + duration of Activity 2. That is10+10rand()+10+10rand()We can generate 1000 instance of each activity in excel and compute project duration.



Activity 1 Activity 2 Project 111.49 17.18 28.6718.24 10.55 28.7810.11 12.32 22.4312.87 14.05 26.9115.52 15.58 31.1119.19 16.92 36.1111.18 13.78 24.9712.55 12.12 24.6616.97 19.19 36.1618.11 11.54 29.6511.82 11.87 23.6814.11 16.55 30.6617.40 16.71 34.1111.35 17.84 29.1913.80 14.27 28.0610.17 17.33 27.5015.51 11.22 26.73

Average 30.02


For project 2, still duration of all the activities are computed as 10 ≤ 10+10rand() ≤ 20However, the the project duration is computed as the MAX duration of (Activity 1, Activity 2) + duration of Activity 3. Max duration of (Activity 1, Activity 2) > 10+10rand(). That is the significance of convergence points.



Not even in a single instance the duration of Project 1 was greater that that of Prject 2.

Act1 Act2 Act 1&2 Act 3 Project 2 d(p2)>=d(P1)11.49 15.63 15.63 17.18 32.81 118.24 15.98 18.24 10.55 28.78 110.11 15.66 15.66 12.32 27.98 112.87 15.68 15.68 14.05 29.73 115.52 19.11 19.11 15.58 34.69 119.19 12.84 19.19 16.92 36.11 111.18 15.49 15.49 13.78 29.27 112.55 16.59 16.59 12.12 28.70 116.97 16.41 16.97 19.19 36.16 118.11 18.55 18.55 11.54 30.09 111.82 19.03 19.03 11.87 30.90 114.11 16.35 16.35 16.55 32.90 117.40 10.33 17.40 16.71 34.11 111.35 15.00 15.00 17.84 32.84 113.80 15.08 15.08 14.27 29.34 110.17 15.03 15.03 17.33 32.35 115.51 17.66 17.66 11.22 28.88 1

Average= 31.71 1000


Key Problem Flow time: 10,000 Instances


Activity 1 Activity 2 Project 111.49 17.18 28.6718.24 10.55 28.7810.11 12.32 22.4312.87 14.05 26.9115.52 15.58 31.1119.19 16.92 36.1111.18 13.78 24.9712.55 12.12 24.6616.97 19.19 36.1618.11 11.54 29.6511.82 11.87 23.6814.11 16.55 30.6617.40 16.71 34.1111.35 17.84 29.1913.80 14.27 28.0610.17 17.33 27.5015.51 11.22 26.73

Average 30.02

Act1 Act2 Act 1&2 Act 3 Project 2 d(p2)>=d(P1)11.49 15.63 15.63 17.18 32.81 118.24 15.98 18.24 10.55 28.78 110.11 15.66 15.66 12.32 27.98 112.87 15.68 15.68 14.05 29.73 115.52 19.11 19.11 15.58 34.69 119.19 12.84 19.19 16.92 36.11 111.18 15.49 15.49 13.78 29.27 112.55 16.59 16.59 12.12 28.70 116.97 16.41 16.97 19.19 36.16 118.11 18.55 18.55 11.54 30.09 111.82 19.03 19.03 11.87 30.90 114.11 16.35 16.35 16.55 32.90 117.40 10.33 17.40 16.71 34.11 111.35 15.00 15.00 17.84 32.84 113.80 15.08 15.08 14.27 29.34 110.17 15.03 15.03 17.33 32.35 115.51 17.66 17.66 11.22 28.88 1

Average= 31.71 1000


Converging Activities + Common Resources

Activity R2

Activity B2

Activity B1

Activity R1

Activity G

All activities are [10,20] minutes. 10+10RAND(). Average 15. One Recourse Red, One Resource Blue, One Resource Green.Project Duration >> 45


Microsoft Excel Worksheet


Activity B1 Activity R1 Max B1, R1 Activity R2 Activity B2 Upper Path Lower Pth Both Paths Activity G Project13.54 11.37 13.54 15.92 11.20 29.46 24.74 29.46 13.47 42.93 32.036514.11 18.92 18.92 17.78 16.42 36.70 35.34 36.70 12.43 49.13 34.1599217.06 18.57 18.57 10.49 19.18 29.06 37.75 37.75 11.58 49.33 36.179913.28 18.62 18.62 13.49 19.53 32.11 38.15 38.15 12.16 50.31 36.5076910.56 18.23 18.23 19.88 18.24 38.10 36.47 38.10 17.12 55.23 37.0730710.93 18.17 18.17 16.59 17.90 34.75 36.07 36.07 19.82 55.89 57.337716.27 12.90 16.27 14.08 15.20 30.35 31.48 31.48 11.48 42.96 57.3493716.61 14.26 16.61 19.68 16.76 36.29 33.37 36.29 10.42 46.71 57.3967312.75 19.72 19.72 11.70 19.96 31.42 39.68 39.68 14.55 54.23 57.4039811.41 17.03 17.03 19.08 12.91 36.11 29.94 36.11 13.37 49.48 57.4271613.82 10.23 13.82 18.60 10.44 32.42 24.26 32.42 14.39 46.81 57.6928512.45 18.87 18.87 15.98 16.83 34.85 35.70 35.70 10.39 46.09 57.7263811.54 10.69 11.54 16.92 11.90 28.46 23.45 28.46 15.78 44.24 57.8893616.32 19.50 19.50 16.63 17.89 36.13 37.38 37.38 18.75 56.13 57.9690517.21 15.19 17.21 15.61 13.87 32.83 31.08 32.83 13.91 46.74 58.167210.40 10.16 10.40 10.96 11.14 21.36 21.54 21.54 17.04 38.58 58.2273518.00 16.74 18.00 13.57 15.93 31.57 33.93 33.93 16.51 50.44 58.4555215.08 15.10 16.74 14.86 15.15 31.59 31.88 33.38 15.16 48.54


1 23 45 67 89 11113315517719922124326528730933135337539741944146348550752955157359561763966168370572774977179381583785988190392594796999130

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Flow Time 2-Critical Path Method Based on the book: Managing Business Process Flows

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Transcript of Flow Time 2-Critical Path Method Based on the book: Managing Business Process Flows