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# Fuzzy Dominant Path Method (F-DPM) for Activity Networks with Ill-know Durations

Author: ZhuoZhiYong
Tutor: LiuZhiJie
School: Dalian University of Technology
Course: Project Management
Keywords: activity networks Activity times Fuzzy numbers Fuzzy Dominant Path Method Degree of criticality.
CLC: F224
Type: Master's thesis
Year: 2004
Quote: 8

### Executive Summary

 First an overview of some approaches to activity networks with ill-know durations is proposed. They all base on probability theory. However, the activity durations and their distributions are subjectively determined, so the premise of probability distributions of activity times is not always applicable.Therefore, we replace probabilistic considerations in the project network analysis by possibilitic ones, to reduce the difficulty arising from the inexact and insufficient information of activity times. So we use triangular fuzzy numbers (TFNs) to simulate the activity times and the fuzzy Delphi method to estimate the TFNs of each activity. Base on these time estimates, we then propose a new fuzzy project-network analysis method -Fuzzy Dominant Path Method (F-DPM) for calculating the fuzzy project completion time, the possibility of meeting certain project completion times, the degree of criticality for each path and other important parameters.Finally, the solution procedure will be described in detail conjunction with an example to illustrate the analysis, algorithm and computation of the proposed method.

### Full-text Catalog

 Chapter Introduction     8-12 1.1 topics background     8-10 the 1.2 topics raised     10-11 1.3 thesis research significance     11 1.4 of this thesis the main work     11-12 fuzzy the advantage line method theory     12-29 2.1 Network Program Basics     12-24 2.1.1 Critical Path Method CPM   the   12-16 2.1.2 Program Evaluation and Review Act PERT     16-20 2.1.3 Monte Carlo (MCM)     20-21 2.1.4 advantage line method (DPM) [25]     21-24 2.2 Fuzzy math basic knowledge     24 -29 2.2.1 fuzzy sets (Zadeh, [15])     24 2.2.2 Convex fuzzy sets and fuzzy number     24-25 2.2.3 LR fuzzy numbers (Dubois and Prade [13])     25-26 2.2.4 triangular fuzzy numbers [20]     26 2.2.5 Fuzzy Sets   nbsp triangular fuzzy number arithmetic; 26-28 2.2.6     28-29 Chapter fuzzy the advantage line method basic principle     29-42 3.1 Basic assumptions     29 3.2 basic definition     29-32 3.2.1 define a fuzzy weighted average value [14]     29-31 3.2.2 defined two Fuzzy variance and standard deviation of fuzzy [14]     31-32 defined in 3.2.3 fuzzy advantages path     32 3.2.4 defined three extended     32 3.3 Fundamental Theorem     32-35 3.3.1 Theorem a [14]     32-33 3.3.2 theorems, two [14]     33 3.3.3 Theorem fuzzy advantages Theorem     33-35 3.4 The basic algorithm of the F-DPM     35-42 3.4.1 using the Delphi method to determine each work lasted the fuzzy number     35-37 3.4.2 project risk coefficient λ and weight coefficient r determine     37-38 3.4.3 to determine the relationship between the advantages path     38-39 3.4.4 the line calculation steps fuzzy advantages     39 3.4.5 results analysis     39-42 Chapter Fuzzy advantage line law F-DPM program design and implementation     42-48 4.1 F-DPM program design principle     42 4.2 F-the DPM program design diagram     42-44 < br /> 4.3 F-DPM program application introduced     44-48 4.3.1 Input data window     44-45 4.3.2 input parameters window     45 - 46 the 4.3.3 results output window     46-47 the 4.3.4 data table output window     47-48 Chapter example     48 -59 5.1 expert review of each work lasted fuzzy numbers are found;   48 5.2 determine project risk coefficient λ and weight coefficient r     48-49 5.3 determine the relationship between the advantages path     49-51 5.4 results     51-52 5.5 parameter characteristics     52-57 5.5. a risk coefficient λ change calculations     52-55 5.5.2 weighting coefficient r change calculations     55-57 5.6 F-DPM PERT law     57-59 Chapter VI Conclusion and Outlook   the   59-62 6.1 the practical value of the F-DPM algorithms analyze     59 6.2 The paper has not been involved in some of     59-62 Reference     62-65 Acknowledgements     65-67

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