營建工程專案的執行過程存在有許多無法預期且不可
避免的不確定性因素，使專案常有進度落後而需趕工之現
象。此外，專案亦可能為因應特殊之目的而需將排程壓縮
並進行趕工。上述兩種情形，均將使專案管理人員面對趕
工方案的決策問題。
然而，以往關於專案排程趕工問題的研究，大多將作
業之工期或成本視為確定值進行時間成本權衡分析，且多
僅以求解位於最佳時間成本權衡曲線上的最佳解為目的，
乃缺乏趕工方案的決策機制。
本研究旨在建立標準化之專案排程趕工決策模式，包
含有:(1)灰預測專案進度、(2)模糊專案排程、(3)模糊時
間與模糊成本權衡、(4)最適趕工方案決策等四個子模式。
首先，藉由灰預測專案進度趨勢之結果，用以確認專案是
否有進行趕工之必要。若專案需進行趕工，則將作業之工
期與成本均視為模糊值進行模糊專案排程，並運用α截集
將模糊專案排程結果量化為明確區間值，從而結合基因演
算法進行模糊時間與模糊成本權衡分析，求解位於最佳時
間成本權衡曲線上的最佳趕工方案集合。最後，在可符合
完工時間限制的最佳趕工方案中，搜尋可滿足總成本可能
為最低與總成本變異區間為最小等兩個目標的方案，作為
完工時間限制下的最適趕工方案。本研究亦根據所建立之
模式，開發一專案排程趕工決策系統(Project Schedule
Acceleration Optimizer, PSAO)。
經由案例之應用與驗證結果顯示:(1)利用灰預測方法
進行專案進度趨勢之短期預測具適用性與不錯之準確率。
(2)根據決策者持有之風險態度，PSAO可在合理的演算時間
內正確地求解各最佳趕工方案之總工期與總成本變異間，
並輸出完工時間限制下的最適趕工方案決策結果。因此，
藉由本研究提出之模式與PSAO應用系統，確可將專案所在
環境之不確定性風險納入考量，從而完成完工時間限制下
的最適趕工方案決策。

The environment of the construction project is
usually filled with uncertainties. Consequently
accelerating the project schedule became the common
and important issue for the project manager to meet
client's demand in time. There are two main reasons
for compressing the project schedule. One is the
schedule delay that may result from executing
project activities, such as misestimating the
activity duration. The other is the specific
purpose for early completing the project, such as
completing a shopping mall for entering the market
earlier in the competitive department business.
The project schedule accelerating process can
be transferred to the typical time-cost trade-off
analysis since minimizing time and cost are both
preferred by the project manager. However, the
traditional time-cost tradeoff problem assumes the
time and cost of the activity are deterministic. In
addition, previous research mainly focuses on
finding the optimal or near-optimal solutions along
the time-cost trade-off curve; no decision-making
mechanism has been proposed to decide the best
strategies in terms of accelerating the project
schedule. Therefore, it is necessary to develop a
decision model that can determine if accelerating
project schedule is needed and then decides best
strategies for achieving it under uncertainties.
This research presents a model that combines
grey prediction method, fuzzy set theory, and
genetic algorithms to solve the problem of deciding
the best strategies in accelerating the project
schedule under uncertainty. At first the grey
prediction method is used to forecast the project
progress and decide that whether the project
schedule needs to be accelerated or not. Next, if
the project schedule needs to be accelerated, the
fuzzy set theory is applied to model the activity
duration and cost. Furthermore, the α-cut is
employed to transfer the fuzzy project duration and
direct cost into crisp values according to decision
maker's risk attitude. Finally, genetic algorithms
are adopted to solve the fuzzy time-cost trade-off
problem to find best strategies which not only
minimize the project cost but also minimize the
variance in project cost under the time limit.
Results showed that this new project schedule
accelerating model can provide more realistic
solutions for the construction time-cost trade-off
problem based on the different risk attitudes
of the decision maker. In addition, a user-friendly
program is built to provide a practical tool for
construction managers.

1. AbouRizk, S. M., and Wales, R. J. (1997). “Combined discrete-event/continuous
simulation for project planning.” J. Constr. Engrg. and Mgmt., ASCE, 123(1),
11-20.

2. Ahuja, H. N., and Nandakumar, V. (1985). “Simulation model to forecast
project completion time.” J. Constr. Engrg. and Mgmt., ASCE, 111(4), 325-342.

3. An, S., Yan, J., and Yu, X. (1996). “Grey-system studies on agricultural
ecoengineering in the Taihu Lake area, Jiangsu, China.” Ecological
Engineering., 7, 235-245.

4. Ang, A. (1975). “Analysis of activity network under uncertainly.” J. of
Engrg. Mech., ASCE, 101(4), 373-387.

5. Arikan, F., and Gungor, Z. (2001). “An application of fuzzy goal programming
to a multiobjective project network problem.” Fuzzy sets and Sys., 119,49-58.

6. Ayyub, B. M., and Halder, A. (1984). “Project scheduling using fuzzy set
concepts.” J. Constr. Engrg. and Mgmt., ASCE, 110(2), 189-203.

7. Bandemer, H., and Nather, W. (1992). Fuzzy data analysis. Kluwer Academic
Publishers, Dordrecht.

8. Barraza, G. A., Back, W. E., and Mata, F. (2000). “Probalistic monitoring of
project performance using SS-curves.” J. Constr. Engrg. And Mgmt., ASCE,
126(2), 142-148.

9. Burns, S. A., Liu, L., and Feng, C.W. (1996). “The LP/IP hybrid method for
construction time-cost trade-off analysis.” Constr. Mgmt. and Economics, 14,
265-276.

10. Carr, R. I. (1979). “Simulation of construction project duration.” J.
Constr. Div., ASCE, 105(2), 415-423.

11. Chanas, S., and Kamburowski, J. (1981). “The use of fuzzy variables in
PERT.” Fuzzy sets and Sys., 5, 11-19.

12. Chang, A. S. T. (2001). “Defining cost/schedule performance indices and
their ranges for design projects.” J. Mgmt. in Engrg., ASCE, 17(2), 122-130.

13. Chehayeb, N. N., and AbouRizk, S. M. (1998). “Simulation-based scheduling
with continuous activity relationships.” J. Constr. Engrg. and Mgmt., ASCE,
124(2), 107-115.

14. Chen, S. J., and Hwang, C. L. (1992). Fuzzy multiple attribute decision
making, New York：Springer-Verlag Press.

15. Chen, S. M., and Chang, T. H. (2001). “Finding multiple possible critical
paths using Fuzzy PERT.” IEEE Trans. on Sys., Man, and Cyb. Part B, 31(6),
930-937.

16. Construction Industry Institute (CII). (1988). Project control for
engineering, Publ. No. 6-1, Bureau of Engineering Research, University of
Texas at Austin, Austin, Tex.

17. Coskunoglu, O. (1984). “Optimal probabilistic compression of PERT
networks.” J. Constr. Engrg. and Mgmt., ASCE, 110(4), 437-446.

18. Crandall, K. C. (1976). “Probabilistic time scheduling.” J. Constr. Div.,
ASCE, 102(3), 415-423.

19. De, P., Dunne, E. J., and Wells, C. E. (1995). “The discrete time-cost
tradeoff problem revisited.” Eur. J. Operational Res., 81, 225-238.

20. Diaz, C. F., and Hadipriono, F. C. (1993). “Nondeterministic networking
methods.” J. Constr. Engrg. and Mgmt., ASCE, 119(1), 40-57.

21. Feng, C. W., Liu, L., and Burns, S. A. (1997). ‘‘Using genetic algorithms
to solve construction time-cost trade-off problems.’’ J. Comp. Civ. Engrg.,
ASCE, 11(3), 184–189.

22. Feng, C. W., Liu, L., and Burns, S. A. (2000). “Stochastic construction
time-cost trade-off analysis.” J. Comp. Civ. Engrg., ASCE, 14(2), 117-126.

23. Gen, M., and Cheng, R. (1997). Genetic algorithms and engineering design., A
Wiley-Interscience Publication, New York.

24. Goldberg, D. E. (1989). Genetic algorithms in search, optimization & machine
learning, Addison-Wesley Publishing Co., Reading, Mass.

25. Harris, R. B. (1978). Precedence and arrow networking techniques for
construction. John Wiley & Sons, Inc., New York, N. Y.

26. Holland, J. H. (1975), Adaptation in natural and artificial systems, Univ. of
Michigan Press, Ann Arbor, Mich.

27. Isidore, L. J. (1999). “Integrated range estimating and probabilistic
scheduling of construction project.” PhD dissertation, Dept. of Civil
Engineering, Texas A&M University, College Station, Tex.

28. Isidore, L. J., and Back, W. E. (2001). “Probabilistic optimal-cost
scheduling.” J. Constr. Engrg. and Mgmt., ASCE, 127(6), 431-437.

29. Jian, H., Wakamatsu, H. and Feng, G. J. (1991). “Snowfall prediction based
on grey system theory.” The Journal of Grey System, 3(2). 121-132.

30. Kaufmann, A., and Gupta, M. M. (1985). Introduction to fuzzy arithmetic -
theory and applications. Van Nostrand Reinhold Company Inc., New York.

31. Kelly, J. E., Jr. (1961). “Critical path planning and scheduling:
mathematical basis.” Operations Res., 9(3), 167-179.

32. Kerridge, A. E. (1986). “Predict project results with trending method.”
Engineering and Construction Project Management, A. E. Kerridge and C. H.
Verralin, eds., Gulf Publishing Co., Houston.

33. Klir, G. J., and Yuan, B. (1995). Fuzzy sets and fuzzy logic-theory and
applications. Prentice-Hall, Englewood Cliffs, N.J.

34. Laslo, Z. (2003). “Activity time–cost tradeoffs under time and cost chance
constraints.” Computers & Ind. Engrg. 44, 365-384.

35. Lee, E. S. and Li, R. J. (1988). “Comparison of fuzzy numbers based on the
probability measure of fuzzy events.” Computers and Mathematics with
Applications, 15, 887-896.

36. Leu, S. S., and Yang, C. H. (1999). “GA-Based multicriteria optimal model
for construction scheduling.” J. Constr. Engrg. and Mgmt., ASCE, 125(6),
420-427.

37. Leu, S. S., Chen, A. T., and Yang, C. H. (1999). “Fuzzy optimal model for
resource-constrained construction scheduling.” J. Comp. Civ. Engrg., ASCE,
13(3), 207-216.

38. Leu, S. S., Chen, A. T., and Yang, C. H. (2001). “A GA-based fuzzy optimal
model for construction time-cost trade-off.” Int. J. Project Mgmt., 19,
47-58.

39. Li, H., and Love, P. E. D. (1997). “Using improved genetic algorithms to
facilitate time-cost optimization.” J. Constr. Engrg. and Mgmt., ASCE,
123(3), 233-237.

40. Li, H., Cao, J. N., and Love, P. E. D. (1999). “Using machine learning and
GA to solve time-cost trade-off problems.” J. Constr. Engrg. and Mgmt.,
ASCE, 125(5), 347-353.

41. Lin, M. (1989). “An application of the GM(1,1) Model : the prediction of
flight safety.” The Journal of Grey System, 1(1).

42. Liu, L., Burns, S. A., and Feng, C. W. (1995). ”Construction time-cost
trade-off analysis using LP/IP hybrid method.” J. Constr. Engrg. And Mgmt.,
ASCE, 121(4), 446-454.

43. Liu, S. T. (2003). “Fuzzy activity times in critical path and project
crashing problems.” Cyb. and Sys., 34, 161-172.

44. Lorterpong, P. and Moselhi, O. (1996). “Project-network analysis using fuzzy
sets theory.” J. Constr. Engrg. and Mgmt., ASCE, 122(4), 308-318.

45. Meyer, W. L., and Shaffer, L.R. (1963). ”Extensions of the critical path
method through the application of integer programming.” Civ. Engrg. Constr.
Res. Ser. 2, University of Illinois, Urbana.

46. Michalewicz, Z. (1996). Genetic Algorithms + Data Structures = Evolution
Programs. 3rd edition. Springer, New York.

47. Mon, D. L., Cheng, C. H., and Lu, H. C. (1995). “Application of fuzzy
distributions on project management.” Fuzzy sets and Sys., 73, 227-234.

48. Moselhi, O. (1993). “Schedule compression using the direct stiffness
method.” Can. J. Civ. Engrg., 20, 65-72.

49. Nasution, S. H. (1994). “Fuzzy critical path method.” IEEE Trans. on Sys.,
Man, and Cyb., 24(1), 48-57.

50. Perera, S. (1980). “Linear programming solution to network compression.” J.
Constr. Div., ASCE, 106(3), 315-326.

51. Que, Bryan, C. (2002). “Incorporating Practicability into Genetic
Algorithm-Based Time-Cost Optimization.” J. Constr. Engrg. and Mgmt., ASCE,
128(2), 139-143.

52. Seiler, J. R. (1983). “Cost and schedule data analysis and forecasting,”
Project Management Institute Seminar/Symposium, Houston,Texas, October,17-19.

53. Siemens, N. (1971). “A simple CPM time-cost tradeoff algorithm.” Mgmt.Sci.,
17(6), B-354-363.

54. Ward, S. A. and Lithfield, T. (1980). Cost control in design and
construction. McGraw-Hill, New York.

55. Woolery, J. C., and Crandall, K. C. (1983). “Stochastic network model for
planning scheduling.” J. Constr. Engrg. and Mgmt., ASCE, 109(3), 342-354.

56. Wu, J. H., and Lau, C. R. (1998). “A study to improve GM(1,1) via heuristic
method.” The Journal of Grey System.

57. Yager, R. R. (1981). “A procedure for ordering fuzzy subsets of the unit
interval.” Information science, 24, 143-161.

58. Yao, J. S., and Lin, F. T. (2000). “Fuzzy critical path method based on
signed distance ranking of fuzzy numbers.” IEEE Trans. on Sys., Man, and
Cyb. Part A, 30(1), 76-82.

59. Yau, C., and Ritchie, E. (1990). “Project compression: A method for speeding
up resource constrained projects which preserve the activity schedule.” Eur.
J. Operational Res., 49(1), 140-152.

60. Yoon, K. P. (1996). “A probabilistic approach to rank complex fuzzy
numbers” Fuzzy sets and Sys., 80, 167-176.

61. Zadeh, L. A. (1965). “Fuzzy sets.” Information Control, 8, 338-353.

62. 安信誠二 (1991)，Fuzzy工學，昭晃堂，東京。

63. 陸海文，模糊數排序法之探討，國立成功大學工業管理科學系博士論文，民國90年。

64. 黃价成，時程管理體系整合做法，國立成功大學土木工程學系碩士論文，民國89年。

65. 溫坤禮、黃宜豐、陳繁雄、李元秉、連志峰、賴家瑞 (2002)，灰預測原理與應用，全華
科技圖書股份有限公司，台北。

66. 廖彬超，以時間序列分析建構工程進度管控模式之研究，國立台灣大學土木工程學研究
所營建管理組碩士論文，民國90年。

67. 鄧聚龍、郭洪 (1996)，灰色原理與應用，全華科技圖書股份有限公司公司，台北。

68. 賴瓊華，完工時間限制下模糊計畫評核術之研究，國立成功大學工業管理科學系碩士論
文，民國90年。