## Activity Networks: Project Planning and Control by Network Models |

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Page 203

Naturally, we are always interested in the procedure that yields the greatest lower

bound, because then the bounds

Unfortunately, such power of discrimination is either not known or not achievable

with reasonable computing effort. Then heuristics are called upon to

" or "tight" lower bounds. Usually, such "tightness" is

increased computing effort, and it may be better to be content with a less powerful

...

Naturally, we are always interested in the procedure that yields the greatest lower

bound, because then the bounds

**obtained**are uniformly the most powerful.Unfortunately, such power of discrimination is either not known or not achievable

with reasonable computing effort. Then heuristics are called upon to

**obtain**"good" or "tight" lower bounds. Usually, such "tightness" is

**obtained**at the expense ofincreased computing effort, and it may be better to be content with a less powerful

...

Page 244

As is almost always the case, the improved result is

of extra computing effort. However, as we see below, under the assumption of

independence of arc durations, the total effort is still well below the effort required

for the calculation of en. §2.2 The Second Approach The second approach is

based on the following (rather obvious) observation: if all arrows in a directed

acyclic network, such as in PERT, are reversed, the average duration of the

project en ...

As is almost always the case, the improved result is

**obtained**at a cost, in the formof extra computing effort. However, as we see below, under the assumption of

independence of arc durations, the total effort is still well below the effort required

for the calculation of en. §2.2 The Second Approach The second approach is

based on the following (rather obvious) observation: if all arrows in a directed

acyclic network, such as in PERT, are reversed, the average duration of the

project en ...

Page 273

The results are shown in Table 4.5, together with the values

Martin's approach. The results are remarkably good. However, they leave some

doubts on the precision of Martin's results, since the lower bounds for values of y

= 2\ and y>2"i are higher than Martin's estimates! This is because a small

deviation (even at the tenth decimal place) in a polynomial coefficient of Martin's

formula may give very different results. The above approximation of the PDF was

The results are shown in Table 4.5, together with the values

**obtained**usingMartin's approach. The results are remarkably good. However, they leave some

doubts on the precision of Martin's results, since the lower bounds for values of y

= 2\ and y>2"i are higher than Martin's estimates! This is because a small

deviation (even at the tenth decimal place) in a polynomial coefficient of Martin's

formula may give very different results. The above approximation of the PDF was

**obtained**in ...### What people are saying - Write a review

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### Contents

Structure and Terminology 1 | 18 |

3 COST CONSIDERATIONS | 31 |

DIGRAPHS AND LINE DIGRAPHS | 39 |

Copyright | |

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### Common terms and phrases

activity durations activity networks adjacency matrix algorithm allocation analysis analytical application approach approximation arc durations assume assumption Beta beta distribution Chapter completion computing Consider constraints construction cost function critical path critical path method defined denote determine discussion distribution dual equal equations evaluate example exclusive-or expected duration expected value feasible Figure flow GERT given hence heuristic labeled Laplace transform line digraph linear lower bound Mason's rule minimize modified Monte Carlo N/A N/A network of Fig Normally distributed obtained optimal optimum parameters PERT estimate PERT model possible precedence primal probability problem procedure project duration project network random random variables reader realization of node reduce representation result sample schedule Section Semi-Markov Processes SF lag shown in Fig slack solution specified subnetwork subset Table tasks terminal node Theorem tion transmittance variables variance vector yields z-transform