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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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]

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

Cumulative Distribution Function

of CITB

Resource Arrival Dates

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

Cumulative Distribution Function

of CITC

Resource Arrival Dates

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

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

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

Un

itA 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

Un

it

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

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

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

Av

era

ge

Idle

Tim

e 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

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

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

A

B

C

D

E

F

G

SQS1 SQS2 SQS3 SQS4

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

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

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?

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

Determine Work Breaks

KEY QUESTIONS

In which activity?

Between which repetitive units?

How long is work break duration?

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

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

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

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

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

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

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

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

Example of a Repetitive Project with

Work Breaks

A B

C

E

D

F

G

H

J

SQS1 SQS2 SQS3 SQS4 SQS5

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

Un

it

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

Un

it

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

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.

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

Examples of Repetitive Projects with

Resource-Sharing Activities

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

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

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

Flowchart of ChaStrobe

See Supplementary Presentation VI for more detail

ChaStrobe’s Automation

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

Flowchart of ChaStrobe’s Optimization

See Supplementary Presentation VII for more detail

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

Results: An unusual up-and-down

pattern in project duration and idle Time

Results in Production Diagram

Search Input and Dynamic Input Code

for Optimization

Decision Variable Cells

Domain Value Cells

Referencing Cells

Objective Function

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

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.

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

THE SEQUENCE STEP

ALGORITHM (SQS-AL)

Q / A