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研究生：	王彥欽 Wang, Yan-Cin
論文名稱：	應用模糊層級分析法與模糊品質機能展開於含資源限制之專案排程 Applications of FAHP and FQFD for Project Scheduling with Resource Constraints
指導教授：	楊世銘 Yang, Shih-Ming
共同指導教授:	劉育釧 Liu, Yu-Chuan
學位類別：	碩士 Master
系所名稱：	工學院 - 航空太空工程學系 Department of Aeronautics & Astronautics
論文出版年：	2011
畢業學年度：	99
語文別：	中文
論文頁數：	103
中文關鍵詞：	模糊層級分析法、模糊甘特圖、關鍵鏈、資源限制、基因演算法
外文關鍵詞：	FQFD, FAHP, Fuzzy Gantt chart, Fuzzy critical chain, Resource constraint, Genetic algorithm
相關次數：	點閱：97 下載：4
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本論文主要探討在資源限制情況的專案排程管理，專案的不確定性因素總是造成專案時程以及成本的增加；因此，專案排程的首要任務為定義專案中各作業的模糊度。模糊度可用來衡量專案中個別作業的不確定性指標。本論文基於模糊度，發展出模糊結束時間評估及模糊甘特圖，可以有效呈現各作業模糊特性。基於模糊度而發展出來的模糊結束時間評估方法，在面對專案之中的不確定性因素時，可以提供專案管理者有效地管理資源，並作為一個有效率的專案管理工具。模糊結束時間評估的方法並和基因演算法結合應用於含資源限制的專案排程。為了縮短作業時程，在不違反資源限制的情況之下，藉由適當的資源分配可以將作業區間考慮為可變動性的。透過基因演算法排除資源衝突，並找到最佳化結果。

The project scheduling with resource constraint is studied in this thesis. As the uncertainties can always happen to raise project duration and/or cost, the degree of fuzziness for every project activity is firstly developed. The degree of fuzziness can be considered as the relative index to measure the uncertainty for every project activity. The fuzzy Gantt chart based on the degree of fuzziness that keeps is proposed for more effective project management. The proposed fuzzy finish time estimation by degree of fuzziness is further applied with fuzzy critical chain method and genetic algorithm for resource constrained project scheduling. The activity duration is considered a variable by properly arranging the resource input to shorten the activity duration while without violating the resource constraints. Because the resource conflict is strongly related to the activity duration, the optimization result based on the proposed fuzzy finish time estimation according to the degree of fuzziness can provide an effective and efficient management tool for project managers to manage the resource effectively in facing uncertainties.

CONTENTS
ABSTRACT…………………………………………i
CONTENTS………………………………………ii
LIST OF TABLES…………………………iii
LIST OF FIGURES……………………v
CHAPTER
I	INTRODUCTION
1 Motivation…………………………………………………………………	1
2 Literature Review…………………………………………………2
3 Outline………………………………………………………………….6
II	CRITICAL CHAIN, FQFD – FAHP, AND GENETIC ALGORITHM
1 Critical Chain Project Management………………………………7
2 Fuzzy Set Theory……………………………………………………………….10
3 FQFD and FAHP..……………………………………………………………14
4 Genetic Algorithm…………………………………………………………23
III 	FUZZY GANTT CHART SCHEDULING
1 Introduction………………………………………………………………………41
2 Degree of Fuzziness by FQFD and FAHP……………………41
3 Fuzzy Gantt Chart……………………….……………….………43
4 FGC application in FCC…………………………………………….………45
5 Summary…………………………………………………………….…………….....47
IV	APPLICATIONS OF FGC AND GA FOR RESOURCE CONSTRAINTS
1 Introduction………………………………………………………………………	74
2 FGC with GA for Project Scheduling under Resource Constraints...………74
3 Summary.......................................	.79
V	SUMMARY AND CONCLUSIONS…………………………………………	…..97
REFERENCES……………………………………………………………………….......99
 
LIST OF TABLES
Table	Page
1 	The fundamental scale for pair - wise matrix………………27
2 	Random index (R.I.)……………………………………….... ………27
3 	The definition of triangular fuzzy numbers for FAHP judgmental matrix.. ………….	27
3 	Calculated result of fuzzy scheduling after using different algorithm for case 1 to case 3…………... 49
2 	The project’s fuzzy trapezoidal model for every activity………….………………….	50
3 	Definition of the fuzzy numbers………………. …………	51
4 	The calculated data in relationship matrix of each PC towards one another by FAHP technique.. ………………........51
5 	Calculated result of relationship matrices after using FAHP for   to  .……...	52
6 	The buffer time for FQFD + FAHP model compared with the traditional critical chain ones…………….......55
1 	Properties of fuzzy scheduling with resource constraint for case 1 to case 4 and its schematic demonstration…………….......…………..………………..81
2 	Results of the original and optimized duration for every activity from the fuzzy finish time estimation…………….......…………..……………………..…………	82
3 	Results of the original and optimized activity duration and buffer time for every activity from the  -cut method………………..……………………..……...…….....	83
4 	Results of the original and optimized crisp duration and buffer time for every activity from the fuzzy finish time estimation………...………………..………….....	84
5 	Calculated result of fuzzy scheduling with resource constraint after using different algorithm for case 1 to case 4……………….………...………………..………….....	85
6 	Calculated result of fuzzy scheduling considers different resource constraint for case 1 to case 4 in different algorithm………………...………………..………….....	86

 
LIST OF FIGURES
Figure	Page
1 	Critical chain methodologies--building a critical path …..............…........	.…………...28
2 	Critical chain methodologies--monitor the buffer……29
3 	The difference of the membership functions between a crisp value and a fuzzy set…	30
4 	Four main types of fuzzy membership function: (1) triangular fuzzy membership function, (2) trapezoidal fuzzy membership function, (3) Gaussian fuzzy membership function, and (4) LR fuzzy membership function…….........31	
5 	Operations on fuzzy sets: (a) two fuzzy sets A and B, (b) , (c)  and (d)  ..........................32
6 	The example of (a) triangular fuzzy set and (b) trapezoidal fuzzy set.…………….....	.33
7 	4-phase system of QFD…………………..…………34
8 	The structure of House of Quality (HOQ)……........35
9 	The example of fuzzy QFD with five triangular fuzzy linguistic spaces {VL, L, M, H, VH}…………….......……………36
10 	The membership function of triangular fuzzy numders……………………	37
11 	Typical hierarchy structure: (a) a complete hierarchy for priorities of alternatives and, (b) an incomplete hierarchy structure……………………...................................	38
12 	The integration model by (a) AHP with (b) House of Quality (HOQ) structure……..	39
13 	Flow chart of the genetic algorithm…………………..……………………................	40
1 	The integration model by (a) AHP with, (b) House of Quality (HOQ) structure….	…56
2 	FQFD with five fuzzy linguistic spaces [ VL, L, M, H, VH ] applied in project scheduling…………………………………………………………………….……....	57
3 	Scheduling for evalution of relationship matrix and importance of PC from FAHP	…58
4 	The activity network of the example project…...……...........................................…..	59
5 	Fuzzy trapezoidal model………………………………...………….…………….......	60
6 	The fuzzy relative relationship matrix of each PC towards one another……………..	61
7 	The relationship matrix of all activities in terms of project time limit...……………..	62
8 	The relationship matrix of all activities in terms of project activity begin time……...	63
9 	The relationship matrix of all activities in terms of project budget…………………..	64
10 	The relationship matrix of all activities in terms of manpower………..……………..	65
11 	The relationship matrix of all activities in terms of technology difficulty…………..	66
12 	The relationship matrix of all activities in terms of facility requirement………….....	67
13 	The activity finish time point on the fuzzy trapezoidal model………...……………..	68
14 	The example of Fuzzy Gantt Chart………...…………………………………………	69
15 	The fuzzy Gantt chart of the project case………...…………………………………..	70
16 	Fuzzy Gantt chart in FCC………...…………………………………………………..	71
17 	The  -cut method for determining buffer time of  activity………….…………….	72
18 	Fuzzy Gantt chart in FCC with buffer based on  - cut method…………….……….	73
1 	The duration time of every project and the resource required......................................	87
2 	Description of the variable duration by GA in step…..............................................…	88
3 	Binary representation of chromosome for the variable duration and priority of activities. ……………………………………………………………………..............	89
4 	Results of scheduling and resource analysis from the fuzzy finish time estimation, (a) project scheduling, (b) corresponding resource requirement..................................	90
5 	Results of scheduling and resource analysis with the constraint of workers ≦ 40, (a) project scheduling and (b) corresponding resource leveling........................................	91
6 	Results of scheduling and resource analysis with the constraint of workers ≦ 40 and variable duration consideration, (a) project scheduling and (b) corresponding resource leveling…………………………………………….......................................	92
7 	Results of scheduling and resource analysis with the constraint of workers ≦ 40 and variable duration by cutting duration half based on FGC and  -cut buffer time consideration, (a) project scheduling and (b) corresponding resource leveling………...…………………………………………….......................................	93
8 	The crisp (target) and fuzzy (buffer) part of activity duration time.............................	94
9 	Results of scheduling and resource analysis with the constraint of workers ≦ 40 and variable crisp duration and buffer time consideration, (a) project scheduling and (b) corresponding resource leveling……………………………..................................	95
10 	The example of resource constraint problem considers three circumstances to explain the total duration changes …………………………........................................	96

                                    

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