Pergamon International Journal of Project Management, Vol. 15, No. 6, pp. 377-387, 1997 © 1997 ElsevierScienceLtd and IPMA. All rights reserved Printed in Great Britain 0263-7863/97 $17.00+0.00 PII: S0263-7863(96)00088-9 Measuring uncertainty and criticality in network planning by PERT-path technique Giovanni Mummolo Department of lndustrial Design and Production, Polytechnic of Bari, Viale dapigia 182, 70126 Bari, Italy The use of uncertainty and criticality measures in network planning of engineering projects by PERT networks is limited in practice because of their unreliability or complexity. The measures appear as inappropriate to support the definition of contractual obligations when based on uncertain information. The author proposes new uncertainty and criticality measures based on the identification and analysis by PERT-path technique of possible completion sequences of project activities. The measures prove to be effective in project planning and contracting. An algorithm and a stochastic analytical model suitable for the quantification of the measures concerned are proposed. A numerical example is developed. © 1997 Elsevier Science Ltd and IPMA Keywords:projectplanning, networktechniques,uncertainty measures Introduction Failure risks of an engineering project mainly depend upon difficulties inherent to the project, human skills, unpredict- able and uncontrollable events and upon uncertainty of information on which decisions are based. A relevant aspect of the last form of risk is the ability of contractual parties to manage at best information available in technical documents supporting contract definition. Project planning is of particular importance in this respect as it contributes to define contractual technical documents. The drawing up and agreement on planning marked by high uncertainty often leads both contractual parties to commit obligations without full awareness. If the plant is very complex and its implementation subject to great uncertainty, owner and contractor often agree to share failure risks. The goodness of risk appraisal depends on planning estimates reliability and on planning technique adopted. Several ways of conceiving project planning exist and there are as many ways of formalising it. Project modelling results only in a formal and incomplete representation of planner's ideas and of risks he perceives. Yet, once planning has been shared between owner and contractor, project modelling can lead to contract obliga- tions. In this phase uncertainty and criticality measures contribute to estimate project risks. The measures are widely investigated in the literature concerned. They are, however, sometimes unreliable, sometimes difficult to determine, and anyway unsuited at contract stage to estimating project risks. In this scenario new uncertainty and criticality measures in project planning and contracting are needed. After reviewing main results in the literature concerning uncertainty and criticality in network planning of projects, this paper addresses the theoretical framework to define and calculate new measures for project planning and contracting. Uncertainty and criticality measures in network planning Criticality and uncertainty measures concerning the evolu- tion of a project are of varying complexity and reliability according to the network technique adopted in project planning. One of the most widely used techniques is the Critical Path Method (CPM).I CPM assumes that activity times are not subject to uncertainty and bases the identification of project criticality on the slack time allowed for each activity completion. The attention of planners is mostly devoted to zero total slack time activities, that it to those activities belonging to the so called "critical path". Differently from CPM, PERT assumes that activity time varies randomly according to probability density functions (pdfs) which usually are of Beta type. Under the assumption of statistical independence among activity times, the pdf of project completion date is determined. This pdf is assumed to be normal, with expected value and variance equal to the sum, respectively, of expected values and variances of activity times belonging to the critical 377