## The Critical Path Method: Application of the PERT Method and Its Variants to Production Study ProgramsGraphs and sequencing; Establishing a program of research of production; Generalizing the PERT method; Optimizing the economic function of costs. |

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### Contents

ONE Graphs and Sequencing | 1 |

Strict relation in a connected graph without circuit | 6 |

Decomposition into levels of a connected graph without circuit | 7 |

Finding a sequence | 19 |

TWO Establishing a Program of Research or Production | 23 |

Date of realization of the set of activities Critical path | 33 |

Floating time Job margins | 35 |

Finding the critical path Algorithms used | 40 |

Some precision on the terminology used | 81 |

Enumerating possible terminal events | 83 |

Probability of terminal events | 84 |

The entropy function | 86 |

The PERT method generalized | 87 |

FOUR Optimizing the Economic Function of Costs | 89 |

Lowering the total cost of a program | 90 |

Accelerating a program at the least cost | 94 |

Two mapping examples | 48 |

Jobs of uncertain duration | 62 |

Obtaining a schedule | 73 |

Use of an electronic computer | 75 |

THREE Generalizing the PERT Method | 79 |

Beta distribution | 141 |

Subdivision of jobs and realization of a schedule | 153 |

APPENDIX rv Application of the method of potentials | 160 |

165 | |

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### Common terms and phrases

accelerate assume central limit theorem column conjunctive paths connected graph construction corresponding critical jobs critical path method curve OA date limit date of realization dates of events decision event delay disjunctive display process distribution duration of job dynamic programming equation estimate event date event Et expected value final event floating forebear formula free margin Fulkerson algorithm function graph of figure graph without circuit job Ptj Kaufmann matrix mean date mean value moving to phase noncritical jobs operations operations research optimal program optimal solutions paragraph parametric linear program permits PERT method possible terminal events probability of realization problem program graph program linear graph realization date reduced normal law relative entropy representation represented schedule sequence set of activities set of arcs shown subactivities tasks and constraints tion total cost total execution period total margin transitive closure variance

### Popular passages

Page 166 - Nouvelle Methode Permettant d'Explorer un Ensemble de Possibilites et de Determiner un Optimum (A New Method of Exploring a Set of Possibilities and Determining an Optimum).

Page 166 - Expected critical path lengths in PERT networks", Operations Res., 10, No.

Page 166 - Cheminement et connexite dans les graphes. Application aux problemes d'ordonnancement", METRA, Ser.