The Sequence Step Algorithm (SQS-AL) is a general scheduling algorithm for minimizing the duration of repetitive projects with probabilistic activity durations while achieving continuous resource utilization. SQS-AL consists of two main nested loops: the sequence step loop and the replication loop. For each sequence step, each replication loop is a simulation run that collects crew idle time for activities in that sequence step. The collected crew idle times are, then, used to determine resource arrival dates for user-specified confidence levels, i.e., probabilities of having zero idle time in corresponding activities. The process of collecting the crew idle times and determining crew arrival times for activities on a considered sequence step is repeated from the first to the last sequence step. The effect of scheduling activities on the crew idle times for following activities is revealed step by step prior to scheduling the following activities. As a result, SQS-AL can guarantee continuous resource utilization for the user-specified confidence levels.

1. The Sequence Step Algorithm
Doctoral Committee
Prof. Photios G. Ioannou, Chair
Prof. John G. Everett
Prof. Vineet R. Kamat
Prof. Mark P. Van Oyen
A Simulation-Based Scheduling Algorithm
for Repetitive Projects with Probabilistic Activity Durations
Presented by
Chachrist Srisuwanrat
2008

2. MOVITATION
1) Repetitive projects are commonly found in
construction.
2) Using CPM to scheduling repetitive projects results in:
- idle time in resource utilization
- unrealistic presentation for construction activities
3) Activity durations are non-deterministic.
4) Existing scheduling techniques cannot effectively
eliminate idle time and realistically model activities and
resources in repetitive construction projects.

3. OBJECTIVES
 To control idle time in repetitive projects
 To model the realistic nature of activities and
resources in repetitive projects
 To analyze the tradeoff between eliminating idle
time and increasing project duration
 To optimize projects in terms of cost and duration

4. Introduction
Repetitive projects consist of similar units requiring
repetitive work from unit to unit. For examples,
high-rise buildings, housing projects, and highways.
1st floor
2nd floor
3rd floor
A B C
A B C
A B C

5. Constraints in Repetitive Projects
 Technical Constraints
 Resource Availability Constraints
A1 B1 C1
A2 B2 C2
A3 B3 C3
A1
A2
A3 B3
B1
B2
1 2 3 4 5 6 7 8 9 10
3
2
1
Unit
C3
C3
C2
Idle Time
Month
 Resource Continuity Constraints
(a) Precedence Diagram (b) Production Diagram

6. Eliminating Idle Time and Reducing
Hiring Period
Month
1 2 3 4 5 6 7 8 9 10
Unit
3
2
1
A3
A1
A2
B3
B1
B2
C1
C2
C3
A1
A2
A3 B3
B1
B2
1 2 3 4 5 6 7 8 9 10
3
2
1
Unit
C3
C1
C2
Idle Time
Hiring period for A = 6 months
Hiring period for B = 5 months
Hiring period for C = 6 months
Hiring period for A = 6 months
Hiring period for B = 3 months
Hiring period for C = 5 months
Month
(a) Without Continuity Constraints (b) With Continuity Constraints
Applying
resource
continuity
constraints

7. Five Characteristics of
Repetitive Activities
1. Deterministic and Non-Deterministic Duration
Activities
2. Typical and Non-Typical Activities
3. Repetitive and Non-Repetitive Activities
4. Resource-Sharing Activities
5. Hard and Soft Logic Dependencies
See Supplementary Presentation I for more detail

8. CHALLENGES
 Modeling activities and their resources
• Five main characteristics of repetitive activities
• Dynamic resource allocation
 Eliminating and Controlling idle time in resource
utilization
• Under variability in production rates
 Reducing the increased project duration
 Automating the solving processes
 Optimizing problems in terms of cost and duration

9. Literature Review
Researcher Year Technique
Non-
Typical
Activities
Non-
repetitive
Activities
Maintaining
Continuity
Non-
Deterministic
Duration
Interruption
options
Soft
Logic
1 Al Sarraj 1990 Graphical No N/A Yes No No No
2 Reda 1990 LP No No Yes No No No
3 Luts 1990 Simulation Yes N/A (Unit) Yes No No
4 Thabet 1992 Object-Oriented No No N/A No Yes No
5 El-Rayes 1993 DP Yes N/A Yes No No No
6 Suhail and Neale 1994 Graphical No No Yes No No No
7 Harmelink 1995 Graphical Yes Yes Yes No No No
8 Chehayep 1995 Simulation Yes Yes (Unit) Yes No No
9 El-Rayes 1997 Object-Oriented Yes Yes Yes No Yes No
10 Hijazi 1998 Simulation Yes No No Yes No No
11 El-Rayes 2001 DP Yes Yes Yes No Yes No
12 Yang 2002 Graphical Yes Yes Yes No No No
Srisuwanrat 2008 Simulation YES YES YES!! YES!! YES!! YES
See Supplementary Presentation II for more detail

10. Using the number of units to delay
activities to reduce idle time
Using 2 units of A
Using 3 units of A
Using time
1 2 3 4 5 6 7 8 9 10
A1
A2
A3
B3
B1
B2
3
2
1
Unit
Month
(a) Original schedule based on CPM
A1
A2
A3
1 2 3 4 5 6 7 8 9 10 11 12
3
2
1
Unit
B3
B1
B2
B3
B1
B2
B3
B1
B2
Month
(b) Modified schedule based on the number
of units and time

11. PROBLEMS
For repetitive projects with probabilistic activity
durations
 How to model the five characteristics of repetitive
activities
 How to achieve continuous resource utilization
 How to control resources’ idle time
 How to relax resource continuity constraints
 How to analyze the tradeoff between idle time and
project duration

12. PROBLEMS OF THE PROBLEMS
 How to realistically model the five characteristics
of repetitive activities
 How to intelligently achieve continuous resource
utilization
 How to systematically control resources’ idle time
 How to effectively relax resource continuity
constraints
 How to automatically analyze the tradeoff between
idle time and project duration or optimize problems
For repetitive projects with probabilistic activity
durations

13. PROPOSED TECHNIQUES AND
DEVELOPED TOOLS
1. The Sequence Step Algorithm (SQS-AL)
2. Two Simulation Model Templates
3. Work Breaks
4. Resource-Sharing Activities
5. The ChaStrobe Application
6. Optimization in ChaStrobe

14. Employed Techniques and Tools
 Repetitive Scheduling Method by Harris and
Ioannou (1998)
 Stroboscope by Martinez (1996)
 Microsoft Visio
 Visual Basic for Applications (VBA)
 Object Linking and Embedding (OLE)
 Microsoft Excel and Microsoft Project
 Genetic Algorithm (GA)
 Exhaustive Search

15. 1. THE SEQUENCE STEP
ALGORITHM (SQS-AL)
• A generalized concept that can be implemented in
most simulation systems to solve scheduling problems of
repetitive projects with probabilistic activity durations.
• Using sequence step to systematically collect idle
times (CIT) in resources and determine resources’
arrival dates (CLT).
• Controlling idle time according to user-specified
confidence levels of continuous resource utilization.

16. A
B
C
D
E
F
G
SQS1 SQS2 SQS3 SQS4Flowchart of the
sequence step
algorithm
Schedule the problem
Collecting Crew Idle Time
(CIT) in the current SQS
Enough
samples
Arrange the collected
CITs in cumulative
frequency table
Last SQS
plus one
Assign the selected CLTs
to resources in the SQS
Select Crew Lead Time (CLT)
according to the user-
specified confidence levels
Start
FINISH
YES
NO
NO
YES
Move to the next SQS
Sequence Step Loops
Replication Loops

17. Example of a repetitive projects
consisting of 3 units requiring 3 activities
Activity Duration
A Uniform[20,2]
B Uniform[10,1]
C Uniform[15,1.5]

18. Collected Crew Idle Time for
Activity B (CITB)
CITB
(days) Hit %Hit
CITB
(days) Hit %Hit
CITB
(days) Hit %Hit
< 2 0 0 < 19 1059 35.3 < 36 2785 92.83
< 3 11 0.37 < 20 1179 39.3 < 37 2831 94.37
< 4 24 0.8 < 21 1302 43.4 < 38 2867 95.57
< 5 39 1.3 < 22 1426 47.53 < 39 2899 96.63
< 6 57 1.9 < 23 1553 51.77 < 40 2931 97.7
< 7 93 3.1 < 24 1680 56 < 41 2950 98.33
< 8 133 4.43 < 25 1790 59.67 < 42 2959 98.63
< 9 180 6 < 26 1893 63.1 < 43 2968 98.93
< 10 229 7.63 < 27 2006 66.87 < 44 2977 99.23
< 11 292 9.73 < 28 2111 70.37 < 45 2988 99.6
< 12 359 11.97 < 29 2248 74.93 < 46 2991 99.7
< 13 431 14.37 < 30 2360 78.67 < 47 2995 99.83
< 14 518 17.27 < 31 2448 81.6 < 48 2996 99.87
< 15 613 20.43 < 32 2535 84.5 < 49 2998 99.93
< 16 719 23.97 < 33 2609 86.97 < 50 2999 99.97
< 17 826 27.53 < 34 2671 89.03 < 51 2999 99.97
< 18 932 31.07 < 35 2735 91.17 < 52 3000 100

19. Cumulative Distribution Function
of CITB

20. Resource Arrival Dates

21. Collected Crew Idle Time for
Activity C (CITC)
CITC
(days) Hit %Hit
CITC
(days) Hit %Hit
CITC
(days) Hit %Hit
23 0 0 36 2574 85.8 49 2990 99.67
24 0 0 37 2669 88.97 50 2993 99.77
25 140 4.67 38 2753 91.77 51 2993 99.77
26 312 10.4 39 2805 93.5 52 2994 99.8
27 519 17.3 40 2854 95.13 53 2997 99.9
28 730 24.33 41 2889 96.3 54 2998 99.93
29 1004 33.47 42 2910 97 55 2998 99.93
30 1257 41.9 43 2924 97.47 56 2998 99.93
31 1549 51.63 44 2947 98.23 57 2998 99.93
32 1881 62.7 45 2962 98.73 58 2998 99.93
33 2206 73.53 46 2969 98.97 59 2999 99.97
34 2329 77.63 47 2974 99.13 60 3000 100
35 2462 82.07 48 2985 99.5 61 3000 100

22. Cumulative Distribution Function
of CITC

23. Resource Arrival Dates

24. Summary
Sum of Idle Time
Between Units (UIT)
Selected Crew Lead Time (CLT) for
50% Confidence Level
Average
Project
Duration
Average
Total
Idle Time
SQS A B C A B C
1 0 23 25 0 0 0 50 47
2 0 23 25 0 0 0 50 47
3 0 3 31 0 23 0 56 34
4 (Final) 0 3 2 0 23 31 58 5

25. EXAMPLE 2
Work Amount (Work Units)
Unit A B C D E F G
1 100 150 200 150 100 150 50
2 250 100 150 200 150 250 200
3 150 200 50 100 50 50 50
4 200 150 200 150 100 100 150
Productivity
(Work Units/Time Units)
Activity Mean SD
A 10 1.0
B 20 2.0
C 15 1.5
D 15 1.5
E 25 2.5
F 15 1.5
G 20 2.0
A
B
C
D
E
F
G
SQS1 SQS2 SQS3 SQS4
For example, A1’s duration on average is 100/10 = 10 time units

26. Results from CPM and SQS-AL
RSM_SQS1_n1
0
1
2
3
4
0 10 20 30 40 50 60 70 80 90 100 110 120 130
Time
Unit
A B C D E F G
RSM_SQS4_n1
0
1
2
3
4
0 10 20 30 40 50 60 70 80 90 100 110 120 130
Time
Unit
A B C D E F G
(a) Results form CPM
Project duration: 102 days
Idle time: 225 days
(b) Results form SQS-AL
Project duration: 123 days
Idle time: 0 days
See Supplementary Presentation III for more detail

27. Results from each Sequence Step
Average Sum of Lags
Between Units
(UIT)
Assigned Crew Lead Time
(CLT)
Average
Project
Duration
Average
Project
Idle Time
SQS B C D E F G B C D E F G
2 38 34 30 48 30 45 0 0 0 0 0 0 102 225
3 0 0 1 11 1 16 55 50 0 0 0 0 113 29
4 0 0 0 0 0 12 55 50 70 80 70 0 119 12
5* 0 0 0 0 0 0 55 50 70 80 70 100 123 0

28. Balancing Between
Idle Time and
Project Duration
Total Idle Time and Project Duration
0
50
100
150
200
250
100 120 140 160 180
Average Project Duration
AverageIdleTime
20%
40%
60%
80%
100%
Confidence
Level SQS
Average Project
Duration
Average Project
Idle Time
100%
2 102 225
3 128 29
4 142 14
5 158 0
80%
2 102 225
3 113 29
4 119 12
5 123 0
60%
2 102 225
3 113 30
4 114 18
5 118 2
40%
2 102 226
3 108 31
4 109 18
5 113 5
20%
2 102 225
3 108 37
4 109 25
5 113 8

29. 2. SIMULATION MODEL
TEMPLATES
1. Work Flow Template
• Non-Typical Activities
• Non-Repetitive Activities
• Non-Deterministic Duration Activities
• Soft Logic Dependent Activities
2. Resource Flow Template
• Dynamic Resource Allocation
• Resource-Sharing Activities
X_WorkRemain
X_WorkDone
X_CrewPerform
X_Work2
X_Work1
X_CrewLeadTime
X_Leave
OrStay
X_CrewOffSite
X_CrewPerform
X_CrewIdle
X_Crew1
X_Crew2
X_Crew3
X_Crew4
X_Crew5
X_Crew6

30. Work Flow (Activity X) and Resource
Flow (Resource X) Sub-Networks
X_WorkRemain
X_CrewLeadTime
X_Leave
OrStay
X_CrewOffSiteX_WorkDone
X_CrewPerform
X_CrewIdle
X_Work2
X_Work1
X_Crew1
X_Crew2
X_Crew3
X_Crew4
X_Crew5
X_Crew6
ACTIVITY RESOURCE
WORK FLOW
X_WorkRemain
X_CrewPerform
X_WorkDone
RESOURCE FLOW
X_CrewOffSite
X_CrewLeadTime
X_CrewIdle
X_LeaveOrStay

31. A
B
C
D
E
F
G
SQS1 SQS2 SQS3 SQS4

32. Tradeoff between eliminating idle
time and increasing project duration
 Delaying resources’ arrival dates eliminates idle time
 Increasing project duration
 How to decrease the prolonged project duration?
• Balancing production rates
• Using lower confidence levels
• Introducing work breaks

33. 3. WORK BREAKS
 Work Breaks are deliberate interruptions, not idle time
 Activities
• Introduced deliberate interruptions
• Split into sub-series, each has its own CIT and CLT
• Start sooner and might allow their successors to
start sooner
 Resources
• Informed in advance
• Leave site and return later
• Do not get paid

34. UNIT
4
3
2
1
Days
10 30 60 70 90 130110 12020 50 80 100400
Eliminating Crew Idle Time
LagB1,B2
LagB2,B3
LagB3,B4
LagC1,C2
LagC2,C3
LagC2,C3
CPM Project Duration = 105 days with idle time of 75 days
RSM Project Duration = 135 days without idle time
How can we reduce project duration without incurring idle time?

35. UNIT
4
3
2
1
Days
10 30 60 70 90 130110 12020 50 80 100400
Work Break
Example of Work Break
CPM Project Duration = 105 days with idle time of 75 days
RSM Project Duration = 135 days without idle time
RSM with work break at B2-B3 Project Duration = 115 days without idle time

36. Determine Work Breaks
KEY QUESTIONS
 In which activity?
 Between which repetitive units?
 How long is work break duration?

37. In Which Activity? And For how long?
Activity to receive a work break
• Must be on the “Controlling Sequence”
• Must have “Converging” relationship with its
predecessor on the controlling sequence
• Must have “Diverging” relationship with its
successor on the controlling sequence
The work break duration
• The sum of idle time after the break position
before postponement

38. UNIT
4
3
2
1
Days
10 30 60 70 90 130110 12020 50 80 100400
Controlling Points & Sequence
CPM Project Duration = 105 days with idle time of 75 days
RSM Project Duration = 135 days without idle time
CPBC
CPAB CPCD

39. UNIT
4
3
2
1
Days
10 30 60 70 90 130110 12020 50 80 100400
Relative Production Rates
CPBC
CPAB CPCD
Activity B, which is on controlling sequence has converging RPR
with its predecessor and diverging RPR with its successor.
Thus, for this example, possible work break positions that could
reduce project duration are: B1-B2, B2-B3, and B3-B4.
Possible
work break
position

40. Work Break Position-Duration?
 Split a repetitive activity into subseries
 Record idle time:
•Before the work break
•After the work break
 Shift each subseries to achieve continuity
 Best split: Work Break Position - Duration

41. UNIT
4
3
2
1
Days
10 30 60 70 90 130110 12020 50 80 100400
Work Break B1-B2
RSM project duration with work break B1-B2 = 120 days
Idle Time=10
Idle Time=10
Idle Time=10
Duration of Work Break B1-B2 = Sum of Idle Time after completing B1
= 10+10+10 = 30 days
Work Break
30 days

42. UNIT
4
3
2
1
Days
10 30 60 70 90 130110 12020 50 80 100400
Work Break B2-B3
RSM project duration with Work Break B2-B3 = 115 days
Idle Time=10
Idle Time=10
Idle Time=10
Postponement duration for activity B1 = Sum of Idle Time BEFORE the break
Duration of Work Break B2-B3 = Sum of Idle Time AFTER the break
Work Break
20 days
Delay

43. Work Break
10 days
UNIT
4
3
2
1
Days
10 30 60 70 90 130110 12020 50 80 100400
Work Break B3-B4
RSM project duration with Work Break B3-B4 = 125 days
Idle Time=10
Idle Time=10
Idle Time=10
Postponement duration for activity B1 = Sum of Idle Time BEFORE the break
Duration of Work Break B3-B4 = Sum of Idle Time AFTER the break
Delay

44. Summary of Work Break Alternatives
Work Break
Location
Initial
Delay
Work Break
Duration
Project
Duration
B1 – B2
B2 – B3
B3 – B4
0
10
20
30
20
10
120
115
125

45. Example of a Repetitive Project with
Work Breaks
A B
C
E
D
F
G
H
J
SQS1 SQS2 SQS3 SQS4 SQS5

46. 0
1
2
3
4
5
6
7
8
9
10
0 30 60 90 120 150 180 210 240 270 300 330 360 390 420 450
Time
Unit
A B C D E F G H J
Average Total Idle Time = 1 day
Average Project Duration = 449 days
Controlling Sequence
0
1
2
3
4
5
6
7
8
9
10
0 30 60 90 120 150 180 210 240 270 300 330 360 390 420 450
Time
Unit
A B C D E F G H J
Average Total Idle Time = 3 days
Average Project Duration = 342 days
Controlling Sequence
Total of 81 possible
positions for work breaks.
Only 27 positions are
tested.
(a) Results from SQS-AL
without work breaks
(b) Results from SQS-AL
with 3 work breaks
Note: using CPM to scheduling this
project results in 277-day of project
duration and 438-day of idle time
Break
Break
Break
See Supplementary Presentation IV for more detail

47. Method Work Break
Positions
Average
Project
Duration
Average
Total Idle
Time
Project Duration
plus
idle time
CPM - 277 438 715
SQS-AL - 449 1 450
SQS-AL* G7-G8 410 3 413
SQS-AL** G7-G8, B5-B6 376 3 379
SQS-AL*** G7-G8, B5-B6,C4-C5 342 3 345
Results from Introducing Work Breaks
• SQS-AL reduces idle time by 22 months, compared to
CPM.
• SQS-AL*** with 3 work breaks reduces project duration
by 5 months, compared to SQS-AL w/o work breaks.

48. 4. RESOURCE-SHARING
ACTIVITIES
 Activities sharing one or more resources, called
“Resource-Sharing Activities”
 “Shared Resources”
 How to model resource-sharing activities and shared
resources?
 What could be the problems when scheduling
repetitive projects with resource-sharing activities?
One resource flow sub-network serving many work flow sub-networks
- Resources’ SQS
- Changes in working sequences, changes in idle time
- Slow production rates, idle time cannot be eliminated

49. Examples of Repetitive Projects with
Resource-Sharing Activities

50. Considerations When Scheduling
Resource-Sharing Activities
 Need to collect CIT and determine CLT
• In which sequence step?
 Need to delay resources’ arrival dates to eliminate
idle time
• Can the idle time in shared resources be eliminated?
 Need to allocate shared resource to activities
• Which resource-sharing activity gets the shared
resource first?
 Assigning CLT might change:
• CIT for the shared resource itself and of other resources
• Working sequences for the shared resource?
See Supplementary Presentation V for more detail

51. Scheduling Resource-Sharing Activities
Schedulers must pay attention to:
• Increasing idle time from SQS to SQS
• Changes in working sequences for shared resources
• Slow production rates of dependents between the
resource-sharing activities
• Precedence relationships between resource-sharing
activities (e.g., direct or indirect)
• Proximity of start dates for resource-sharing activities
• Effect of assigning CLT on their dependents

52. 5. THE CHASTROBE APPLICATION
 Generates simulation models and code
• conforming to SQS-AL
• conforming to the two suggested simulation model
templates
 Presents results in Excel, Visio, and Project
• Includes comparison between CPM, RSM, and
SQS-AL
 Performs optimization
• Modifying simulation models and code automatically

53. Flowchart of ChaStrobe
See Supplementary Presentation VI for more detail

54. ChaStrobe’s Automation

55. 6. OPTIMIZATION IN CHASTROBE
 Three Levels of Simulation Code and Model
Manipulation
• Parameter Manipulation (e.g., confidence levels and the
number of resources of each type)
• Simulation Code Manipulation (e.g., whether to fix work
sequence)
• Simulation Model Manipulation (e.g., model shared
resource with two dedicated resources)
 Two Search Methods
• The Exhaustive Search
• The Genetic Algorithm

56. Flowchart of ChaStrobe’s Optimization
See Supplementary Presentation VII for more detail

57. Example
ACT Variability
Unit
1 2 3 4 5
Duration (days)
A Normal[1,0.1] 40 45 40 40 45
M Normal[1,0.1] 15 15 10 10 10
B Normal[1,0.1] 50 40 50 50 40
X Normal[1,0.1] 20 30 25 20 20
U Normal[1,0.1] 15 20 15 25 20
V Normal[1,0.1] 40 40 45 45 40
C Normal[1,0.1] 15 15 15 15 15
N Normal[1,0.1] 20 25 30 20 25
Y Normal[1,0.1] 20 20 20 20 20
D Normal[1,0.1] 45 35 40 40 30
A Normal[1,0.1] 40 45 40 40 45

58. Results: An unusual up-and-down
pattern in project duration and idle Time

59. Results in Production Diagram

60. Search Input and Dynamic Input Code
for Optimization
Decision Variable Cells
Domain Value Cells
Referencing Cells

61. Objective Function

62. Results from using GA solution
Objective Function Value is derived from:
1200 – Project Duration – Project Idle Time
Method Project
Duration
Project
Idle time
Objective
Function
Value
CPM 416 944 -160
SQS-AL 746 533 -79
SQS-AL* 591 21 588

63. CONTRIBUTIONS
1) The Sequence Step Algorithm (SQS-AL):
 Schedules repetitive projects under uncertainty
 Maintains continuity in resource utilization at a specified
confidence level
2) Simulation model templates:
 Capture the characteristics of repetitive activities and resources
 Differentiate different statuses of activities and resources
 Organizes the simulation models for repetitive projects
3) Means to satisfy and relax resource continuity constraints:
 Using confidence levels
 Introducing work breaks
4) Guidelines to schedule resource-sharing activities.
5) Scheduling system, ChaStrobe, solving the problem of scheduling
probabilistic repetitive project.
6) Optimization system, ChaStrobe, optimizing project cost and
project duration.

64. FUTURE WORKS AND
RECOMMENDATIONS
 Introduce global causal dependencies
• When should SQS-AL repeat the same SQS or go back to
previous SQS?  WEATHER changes productivity, duration,
and, therefore, idle time.
Recommendation: Adding another loop with conditions
 Reduce computing time
• Is it necessary to simulate the entire network or only specific
SQS in each replication loops?
Recommendation: Simulating activities in certain sequence steps
based on the current SQS and confidence levels
Limitations:
 Apply to naturally discrete unit
 How to model linear production activities, e.g., block and bar activities

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THANK YOU
ZERO IDLE TIME
With
100% CONFIDENCE

66. THE SEQUENCE STEP
ALGORITHM (SQS-AL)
Q / A