Sequence step algorithm repetitive project scheduling for project with probabilistic activity durations using simulation
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The document presents a simulation-based scheduling algorithm for repetitive construction projects characterized by probabilistic activity durations, aiming to minimize idle time while balancing project duration. It discusses various constraints and challenges associated with modeling activities and resource utilization, highlighting the proposed Sequence Step Algorithm (SQS-AL) to optimize project scheduling. The paper also reviews existing scheduling techniques and demonstrates the effectiveness of the proposed methods through various examples and results.
![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]](https://image.slidesharecdn.com/sequencestepalgorithmrepetitiveprojectschedulingforprojectwithprobabilisticactivitydurationsusingsim-140819092747-phpapp01/85/Sequence-step-algorithm-repetitive-project-scheduling-for-project-with-probabilistic-activity-durations-using-simulation-17-320.jpg)
![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](https://image.slidesharecdn.com/sequencestepalgorithmrepetitiveprojectschedulingforprojectwithprobabilisticactivitydurationsusingsim-140819092747-phpapp01/85/Sequence-step-algorithm-repetitive-project-scheduling-for-project-with-probabilistic-activity-durations-using-simulation-57-320.jpg)
Sequence step algorithm repetitive project scheduling for project with probabilistic activity durations using simulation
- 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
- 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
- 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
- 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
- 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
- 66. THE SEQUENCE STEP ALGORITHM (SQS-AL) Q / A