The risk of delay of a project in terms of the morphology of its network

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Abstract

The risk of the duration of a project exceeding a certain limit has been studied since the early papers proposing the PERT method but no results are available relating the statistical distribution of the total duration with the morphological features of the network. In this paper, a set of indicators is proposed to describe the morphology of the project network and an experimental research is carried out to relate the distribution of the total duration with such indicators. A random generator of project networks is used as well as a model to produce graphical representations of the network. Major results are presented showing how sensitive are the parameters of the distribution of the total duration to the morphology of the network, allowing the project manager to estimate the risk of delay in terms of the proposed indicators. Thus, these results can be used as a decision aid to select alternative designs for the project network taking into account the correspondent risk of delay.

Introduction

The control of the duration of a project and the estimation of the risk of exceeding a given limit (risk of delay) have been a central objective of the development of most methods of Project Management since the early papers proposing the PERT (Clark, 1962, Battersby, 1967).

The development of Project Management is directly dependent on significant advances achieved in the area of modelling to produce efficient scientific representations of projects. These representations can be called models and are always based on the well-known concept of project network describing the activities, their features and precedence restrictions of each project through a directed non-cyclic connected graph.

Nowadays, any software of Project Management includes the study of the project network but little or no attention has been given to:

  • the analysis and classification of the shape or morphology of each project network;

  • the automatic production of easily readable graphic representations of the network to have a visual image of the network's morphology;

  • the relationship between the morphology and the uncertainty concerning the total duration of the project.

This last issue is particularly relevant to help the project manager identifying the level of difficulty to keep the project on time in terms of its project network.

The objective of this paper is the development of a system of indicators to describe the morphology of a project network and to study the statistical distribution of the total duration in terms of such indicators. The risk of delay above any given limit can be easily determined using the estimated distribution. Also, an automatic procedure to produce pictures of the network is discussed and successfully tested.

Section snippets

The concept of project network

The concept of project network may be considered as the most basic model in Project Management and it can be defined by:

  • (a) a set of activities, Ω={Ai:i=1,…,N} where Ai denotes each activity i and N is the number of activities;

  • (b) a set of activities directly precedent of i, with i=1,…,N, and denoted by J(i). Obviously, there are one or more activities, i′, with an empty J(i′). The set of activities which just can be started after completing j is denoted by I(j);

  • (c) a set of features describing

The morphology of a project network

The proposed concept of “morphological type” of a project network is herein defined in terms of three major perspectives:

  • (A) the graphical shape of the network's representation using the AoN rule and representing each precedence by an arrow with the same length and each activity by a circle of the same size. (See previous examples in Fig. 1.)

  • (B) the number of non-redundant direct precedence links, D. Usually, a network with a higher number of these links is more complex to be managed.

  • (C) the

A software to draw project networks

The study of the morphologic type of each project network implies the automatic production of a graphical representation of each network.

The software developed – NETVIEW – using Visual C++ attempts to simulate the human intuition searching for the most convenient automatic drawing of the network.

This software is based on the following procedures:

  • the activities are represented by nodes and they are located in terms of their progressive level being equally spaced in each level along a central

The simulation of the project network

For each set of values of the indicators I1,…,I6, a certain number, S, of networks is generated.

The realization of each network implies the generation of the duration of each activity.

Then, the statistical distribution of the duration of each activity i, with i=1,…,N has to be defined. For comparative purposes, the following assumptions are adopted:

  • the distribution follows either the normal (Case A) or the lognormal law (Case B);

  • the distribution is specified by the mean, μi, and by the

The study of the total duration in terms of the morphologic indicators

The application of this methodology was done using the following data:

S=100;Z=100,

CV=0.5;a=1000 and Δ=10,

I1=10→100,

I2=0.1→1.0.

I3 corresponding to have a width for the first or last hierarchical level equal to half of the value for the central level and a linear variation between them.

I4=0→0.4,

I5=0→0.3,

I6=0→0.3.

The upper bounds of I4,I5,I6 have been chosen lower than 1 because the networks generated with these indicators above the selected bounds have precedence links much longer than it is

Conclusions

The developed software to represent project networks is quite successful to draw complex networks.

The morphology of the network is synthesized by six indicators and the study of the relationship between the total duration, DT, and the morphology allows the following conclusions assuming that the total deterministic duration with Di=μi is constant for the studied project network:

  • An increase of the number of activities or of the serial nature of the network reduces the uncertainty of DT.

  • An

Acknowledgements

This research was supported by Fundação de Ciência e Tecnologia – Project Praxis XXI – no. 3/3.1/CEG/267795.

References (4)

  • Battersby, A., 1967. Network Analysis for Planning and Scheduling. Macmillan, New...
  • C.E. Clark

    The PERT model for the distribution of an activity time

    Operations Research

    (1962)
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