- 學位論文
高低標準完工機率下趕工時間的擬定
The Estimation of Project Crash Time under High and Low Probability Benchmark
摘要
本研究的重點放在計劃評核術中的作業時間分配與預期時間下其專案完工機率。在研究中，我們首先將常見的作業時間分配與其機率密度函數整理出來，而後，我們考慮在高標準與低標準的情況下，其專案應該在什麼時間完工，才能符合我們所訂的標準。在本研究中，我們將低標準設為25%；高標準設為75%，希望所擬定之時間，需符合我們所訂定標準。 本研究建立一套方法，在考慮低標準或高標準時，找出其最少的趕工時間，讓專案在預期時間下的完工機率能符合我們所訂的標準。主要是利用中央極限定理，將專案的路徑視為常態分配，去推估專案在預期時間下的完工機率，而由於要徑支配專案的完工時間，所以，專案在預期時間下的完工機率往往是以要徑在預期時間下的完工機率做代表。 本研究發現當趕工過後，有新的要徑產生時，由於要徑間變異數的大小不同，需評估是否需要進一步趕工，特別的是，當我們是採取低標準時，當新的要徑是變異數較小，我們必需再進一步趕工；但若是採取高標準時，當新的要徑是變異數較大時，我們才需要再進一步的趕工。 本研究將以兩個例子去說明這個方法是如何進行的，及高低標準會對要徑選擇上的影響。
並列摘要
The study of PERT has concentrated in the areas of activity time distributions and the probability that a project can be completed within a specified duration. In this research, we first examine several activity time distributions and their probability density functions. We then consider the situation when a project is to be completed within desired time duration with both low and high expectations. In this research we use 25% chance of project completion before the desired time as low expectation. On the other hand, we use 75% chance of project completion before the desired time as high expectation. By Using the Central Limit Theorem and by tracing the occurrence of critical paths, we develop an approach that will allow us to determine the minimum amount of crash time that will meet project completion time with either low expectation or high expectation. It is noted that the occurrence of new critical paths that have different variance often requires repeated evaluation leading to more crashing time. Specifically, while using the low expectation, new critical path with lower variance will lead to more crash time. On the other hand, when high expectation is adopted, new critical path with higher variance will lead to more crash time. Two numerical examples are used to illustrate this developed approach and the effects of low expectation and high expectation.