الفهرس 
ContentsOnly 14 pages are availabe for public view
 |  | from | 94 |  |  |
| | | from | 94 | | |
Abstract
Activity networks have been used to model complex projects. The
critical path method (CPM), program evaluation and review technique
(PERT), and stochastic activity networks(SAN s) are the most widely used
techniques for project management. They are enjoying exceptionally broad
applications in industrial and military activities. These techniques and their
applications have without doubt contributed significantly to better
planning, control, and general organization of many programs. Each of the
above three techniques required different forms of the activity duration
information: fixed time, three time estimates, and an priori distribution
function respectively. The main problem in the analysis of stochastic
activity networks is to evaluate the distribution function, or parameters
such as: the’ mean and the variance, of the project duration. Our concern
will be devoted to the most important one which is the SANs•
A great deal of research has been carried out on methodologies for
estimating project time distributions. The methods can be broadly grouped
into four main approaches: exact analysis, analytical approximation,
analytical bounding, and simulation. The main problem in stochastic
activity networks (longest and shortest path) is divided into two categories.
The first category is to find the distribution of
Zm =maxrT, , T2 , ... ,Tm) and Wm =minf’T, , T2 , ... ,Tm)
That is, finding Hm(t)=P(Zm~t) and Lm(t)=P(W m~t) or finding the r th
moments of Zm and W m or approximating them, where T J , T 2 , ... , T m be
random variables (not necessarily independent identically distributed)
represent the times of the project activities.
The second category is to find the distribution of T=T J + T 2 + ... + T m. This
sum is known as convolution operation.
The first category is concerned with order statistics and has been
tabulated quite extensively in the case of independent identically
distributed random variables. The case of independent but not identical has
been discussed by many authors for some especial distributions. A
contribution of a recent vintage in order statistics is due to Balakrishnan
(1994 a&b). He has developed some recurrence relations to compute all
moments of order statistics in a simple recursive manner when the random
variables are independent exponentially distributed in the untruncated.