Project Robust Scheduling Based on the Scattered Buffer Technology
Abstract
:1. Introduction
2. Problem Description
3. Literature Review of the Scattered Buffer Scheduling Algorithms
3.1. RFDFF
3.2. STC
- Calculate all stc(i)
- Sort activities by decreasing stc(i)
- While no improvement found do
- take next activity j from list
- if stc(j) = 0: procedure terminates
- else add buffer in front of j
- update schedule
- if improvement and feasible do
- store schedule
- goto next iteration step
- else
- remove buffer in front of j
- restore schedule
4. Unit activity Slack Algorithm (UAS)
4.1. Metric of the Solution Robustness
4.1.1. Analysis of the Influencing Factors of the Predecessors on the Solution Activity
4.1.2. Three Types of Delay in the Solution Activity
4.1.3. Comprehensive Effect Analysis of the Different Delay Types on the Solution Activity
4.1.4. Metric Calculation of the Solution Robustness
4.2. Resource Allocation Algorithm with Maximum Use of the Precedence Relations (MPRRA)
4.2.1. Principle of Resource Allocation
4.2.2. Resource Allocation Strategy
4.2.3. Resource Allocation Algorithm
Algorithm 1: Maximize the use of precedence relations for resource allocation. |
begin /* process 1 */ Divide stage by activity completion time for ← 1 to stage do ← ← ← for do while = 1 do ← ← ← for do while = 1 do ← ← ← /* process 2 */ Sort all activities in ascending order according to activity completion time for do ← for do while do ← end |
4.3. Steps of the Scattered Buffer Algorithm
- (1)
- Take the shortest project makespan as the goal using the meta-heuristic algorithm to generate a baseline schedule of the project. The project completion time is determined based on this schedule.
- (2)
- Based on the baseline schedule, the resource allocation algorithm with the maximum use of precedence relations is used to generate the resource flow network.
- (3)
- Calculate the value of in all solution activities in the current schedule, the value of (the completion time of the project in the current schedule) and the measure value of of the solution robustness. Then, the activity is arranged in descending order according to the value of .
- (4)
- Insert a unit of time buffer in front of the activity in which the value of is the greatest, and set the corresponding value of as 0. At the same time, the start time of this activity and subsequent activities is postponed for a unit of time, and the schedule is modified.
- (5)
- Calculate the value of of all solution activities in this modified schedule, as well as the completion time () of this modified schedule and the measure value () of the solution robustness.
- (6)
- If the completion time () of this modified schedule does not exceed the due date () of the project, and the measure value () of the solution robustness is lower than the previous one (), then this modified schedule is feasible, and is used as the current schedule of the next iteration, and , are replaced by the current value. If the measure value () of the solution robustness is larger than the previous one (), and , then the algorithm should be terminated, the current schedule should be output and used as a robust scheduling. Otherwise, go to Step (8).
- (7)
- If the completion time () of this modified schedule exceeds the due date () of the project, and , then the algorithm should be terminated, and the current schedule should be output and used as a robust scheduling. Otherwise, go to Step (8).
- (8)
- Remove a unit of time buffer that is inserted in front of the activity, and modify the starting time of this activity and its follow-up activities.
- (9)
- Select the activity that has the greatest value of in the sequence, insert a unit of buffer time in front of this activity and modify the starting time of this activity and the subsequent activities to get an modified schedule. Then, go to Step (5).
5. Experimental Analysis
5.1. Experimental Design
5.1.1. Parameter Setting
5.1.2. Evaluation Index
5.2. Analysis of Experimental Results
5.2.1. Impact of Scheduled Due Date on the Robust Schedule
5.2.2. Impact of Activity Duration Randomness on the Robust Schedule
6. Conclusions
Author Contributions
Conflicts of Interest
References
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Problem | Robustness Metrics | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
RFDFF | STC | UAS | RFDFF | STC | UAS | RFDFF | STC | UAS | ||
J10 | SP | 0.7449 | 0.7730 | 0.7977 | 0.8117 | 0.8165 | 0.8401 | 0.8968 | 0.8675 | 0.9017 |
SC | 24.8486 | 24.2272 | 19.2713 | 19.5327 | 18.6960 | 14.0884 | 10.1944 | 14.1227 | 7.1140 | |
TPCP | 0.6237 | 0.6281 | 0.6261 | 0.7417 | 0.7454 | 0.7416 | 0.8861 | 0.8886 | 0.8864 | |
APL | 33.1894 | 33.1750 | 33.1526 | 33.1488 | 33.1196 | 33.1661 | 33.1488 | 33.1555 | 33.1587 | |
SP | 0.6756 | 0.7006 | 0.7104 | 0.7502 | 0.7654 | 0.7709 | 0.8592 | 0.8365 | 0.8546 | |
J20 | SC | 110.7461 | 103.0997 | 89.5769 | 78.7674 | 72.5052 | 64.5783 | 39.8592 | 48.3712 | 35.2247 |
TPCP | 0.5080 | 0.5030 | 0.5124 | 0.6698 | 0.6776 | 0.6678 | 0.8830 | 0.8801 | 0.8833 | |
APL | 54.5441 | 54.5768 | 54.4076 | 54.5441 | 54.3327 | 54.4847 | 54.5441 | 54.4815 | 54.4659 | |
J30 | SP | 0.6461 | 0.6855 | 0.6622 | 0.7416 | 0.7752 | 0.7465 | 0.8730 | 0.8769 | 0.8581 |
SC | 205.3720 | 153.3981 | 154.0193 | 145.3222 | 114.7046 | 115.1642 | 72.6573 | 70.4379 | 67.3279 | |
TPCP | 0.4012 | 0.4149 | 0.3956 | 0.6064 | 0.6151 | 0.6021 | 0.8846 | 0.8857 | 0.8790 | |
APL | 69.9003 | 69.8646 | 69.8022 | 69.9003 | 69.9853 | 69.9593 | 69.9003 | 69.8613 | 69.9458 |
Problem | Robustness Metrics | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
RFDFF | STC | UAS | RFDFF | STC | UAS | RFDFF | STC | UAS | ||
J10 | SP | 0.8117 | 0.8165 | 0.8401 | 0.7640 | 0.7590 | 0.7776 | 0.7657 | 0.7585 | 0.7733 |
SC | 19.5327 | 18.6960 | 14.0884 | 48.2386 | 52.3158 | 43.8052 | 83.7207 | 88.8957 | 79.7710 | |
TPCP | 0.7417 | 0.7454 | 0.7416 | 0.6152 | 0.6154 | 0.6162 | 0.5977 | 0.5963 | 0.5980 | |
APL | 33.1488 | 33.1196 | 33.1661 | 34.6062 | 34.6046 | 34.5928 | 36.2456 | 36.2775 | 36.2419 | |
SP | 0.7502 | 0.7654 | 0.7709 | 0.6967 | 0.6989 | 0.7016 | 0.7010 | 0.7018 | 0.7041 | |
J20 | SC | 78.7674 | 72.5052 | 64.5783 | 191.2419 | 196.3070 | 181.9613 | 336.7798 | 342.1054 | 330.9924 |
TPCP | 0.6698 | 0.6776 | 0.6678 | 0.5175 | 0.5158 | 0.5134 | 0.4826 | 0.4850 | 0.4828 | |
APL | 54.5441 | 54.3327 | 54.4847 | 57.7925 | 57.6623 | 57.7660 | 61.7850 | 61.7099 | 61.8216 | |
J30 | SP | 0.7416 | 0.7752 | 0.7465 | 0.6970 | 0.7081 | 0.6938 | 0.7019 | 0.7063 | 0.6924 |
SC | 145.3222 | 114.7046 | 115.1642 | 249.4382 | 240.4390 | 233.2613 | 392.4993 | 397.3236 | 400.9541 | |
TPCP | 0.6064 | 0.6151 | 0.6021 | 0.4543 | 0.4613 | 0.4607 | 0.4210 | 0.4232 | 0.4190 | |
APL | 69.9003 | 69.9853 | 69.9593 | 74.0973 | 74.2202 | 73.9554 | 79.7130 | 79.7725 | 79.9574 |
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Pang, N.; Su, H.; Shi, Y. Project Robust Scheduling Based on the Scattered Buffer Technology. Appl. Sci. 2018, 8, 541. https://doi.org/10.3390/app8040541
Pang N, Su H, Shi Y. Project Robust Scheduling Based on the Scattered Buffer Technology. Applied Sciences. 2018; 8(4):541. https://doi.org/10.3390/app8040541
Chicago/Turabian StylePang, Nansheng, Huifang Su, and Yingling Shi. 2018. "Project Robust Scheduling Based on the Scattered Buffer Technology" Applied Sciences 8, no. 4: 541. https://doi.org/10.3390/app8040541