project risk management: a deterministic quantitative ... · project risk management: a...

www.elsevier.com/locate/ijproman

Available online at www.sciencedirect.com

ScienceDirect

International Journal of Project Management xx (2017) xxx–xxx

JPMA-01981; No of Pages 21

Project risk management: A deterministic quantitative techniquefor assessment and mitigation

Cinzia Muriana a,c,⁎, Giovanni Vizzini b,c

a Grants & Project Management Division, IRCCS-ISMETT (Istituto Mediterraneo per i Trapianti e Terapie ad Alta Specializzazione), Palermo, Italyb Department for the Treatment and Study of Abdominal Diseases and Abdominal Transplantation, IRCCS-ISMETT (Istituto Mediterraneo per i Trapianti e Terapie

ad Alta Specializzazione), Palermo, Italyc University of Pittsburgh Medical Center (UPMC) Italy, Palermo, Italy

Received 6 September 2016; received in revised form 31 December 2016; accepted 12 January 2017Available online xxxx

Abstract

The paper presents a deterministic technique for assessing and preventing project risks, by determining the risk of the Work Progress Status.Firstly, the performance of the input factors, namely the costs, quality, and time, are detected, that reflect the Iron Triangle of the ProjectManagement. As each phase ends, the actual values of the input factors are detected and compared with that planned, and corrective actions aretaken for considering the impact of the actual performances on the overall project. Thus, the current risk degree of the project is determined throughthe Weighted Sum Method. If it is higher than planned, preventive actions are taken, in order to mitigate the risk of the entire project. Practicalapplications of the technique relate to routine projects and those cases in which the schedule/costs/requirements are to be defined in the planningphase, and deviations are detected in the progress phase.© 2017 Elsevier Ltd, APM and IPMA. All rights reserved.

Keywords: Risk assessment; Risk prevention; Risk mitigation; Risk management; Project risk management; Work Progress Status; European work programs

1. Introduction

Project Management (PM) is defined as “the application ofknowledge, skills, tools, and techniques to project activities tomeet the project requirements” (PMBOK® Guide, 2013).Because a project is “an endeavor temporary undertaken tocreate a product, service, or result that is unique” (PMBOK®Guide, 2013), it is conceivable that PM techniques are appliedin complex and multidisciplinary contexts. For a background ofthe history of the PM, see the review of the literature, in theSub-section 2.1. One of the activities that are supported by PMtechniques is project monitoring, which allows us to know thecurrent progress of the project itself, and compare it withexpected performances. In this context, Earned Value Manage-ment (EVM) enables project managers to tackle project schedule

⁎ Corresponding author at: Corso Calatafimi, 429, 90129 Palermo, Italy.E-mail addresses: [email protected] (C. Muriana),

[email protected] (G. Vizzini).

http://dx.doi.org/10.1016/j.ijproman.2017.01.0100263-7863/00/© 2017 Elsevier Ltd, APM and IPMA. All rights reserved.

Please cite this article as: C. Muriana, G. Vizzini, 2017. Project risk management: AManag. http://dx.doi.org/10.1016/j.ijproman.2017.01.010

deviations by taking corrective actions (see Chen et al., 2016).EVM can be empowered by associating it with the riskmanagement (RM) techniques, which incorporate the stochasticbehavior of the project activities, and take into consideration theimpact of adverse and unforeseeable events on project perfor-mances in terms of work performed, costs and, thus, projectcompletion. Generally, a project is divided into control points,namely Work Progress Status (WPS, see Cantore, 2008), whichidentifies time instants of control, chosen to control the progressof work of a portion of the project of fixed duration. EVM andRM techniques can effectively help project managers todetermine the project performances and manage them underboth deterministic and uncertain conditions, relying on thepossibility of comparing the planned values of the WPS alreadyperformed with actual ones. For this reason, they are generallyemployed at the end of each WPS, when actual performances areavailable. Knowing the deviations from planned values allowsthe project managers to be aware of the tardiness/earliness of theproject from the cost/time perspective, and take corrective actions

deterministic quantitative technique for assessment and mitigation, Int. J. Proj.

mailto:[email protected]

mailto:[email protected]

http://dx.doi.org/10.1016/j.ijproman.2017.01.010





Journal logo

Imprint logo

2 C. Muriana, G. Vizzini / International Journal of Project Management xx (2017) xxx–xxx

(e.g., intensify the resource employment to reduce/eliminate thetardiness by varying the activity duration, and reduce costs). Inparticular, RM techniques allow us to determine and manage theoverall risk associated with a project. Information about the riskprofile of each WPS, and of the entire project could allow projectmanagers to carry out corrective/preventive actions towards theWPSs not still performed, in order to mitigate the risk of theoverall project and balance the risk among the different WPSs.Based on these premises, the work here proposed implements thetechniques advocated by the PMBOK, such as risk identification,quantitative risk analysis, risk monitoring, and risk responseplanning (see the PMBOK® Guide, PMI, 2013). This paper aimsto propose a new technique for project risk assessment that makesuse of traditional techniques, such as Critical PathMethod (CPM)and Multi Criteria Decision-Making Models (MCDM), forquantifying the current risk degree of projects, and puttinginto place preventive and/or corrective actions that aim atpreventing and/or balancing the risk, allowing project managersto implement risk response plans for avoiding, reducing, oraccepting project risks. The technique takes into considerationcosts, time, and quality criteria (representing the Iron Triangle ofthe PM, Atkinson, 1999), as sources of risk that affect theprogress of the project. It focuses on the organization of theproject intoWPSs for the purpose of checking the progress statusof the project itself. The paper presents a technique for thedetermination of the risk associated with both the WPSs of aproject and the overall project, based on the performance of theinput factors that reflect the Iron Triangle of the ProjectManagement. The technique consists in monitoring the progressphase of the project by registering the actual values of the inputfactors, and comparing them with the planned ones. Thetechnique makes use of the Weighted Sum Method (WSM) forsynthesizing the impact of the input factors on the overallperformance of the project, and determining the weights of theinput factors through the covariance matrix, which allows us totake into consideration the mutual influence of factors. Thetechnique is deterministic, and the duration of the activities, aswell as the costs associated with them, are known in the planningphase with certainty. Thus, the model relies on the classic versionof the CPM for the estimation of the project completion time. At aglance, this could be considered a serious limitation of thetechnique, as it does not allow us to incorporate the impact of thevariability of the input factors on the overall project performance,and it could be argued that the projects are usually affected byuncertainty. This is true only in part, as in fact there are cases inwhich it is necessary to schedule the project with deterministicparameters, such as in the case in which someone wants to submita project proposal to European work programs (e.g., Horizon2020), and the development plan that is to be realized requiresthat the costs, times, and project quality requirements bedetermined with certainty, as the grants are calculated propor-tionally to them. These are the specific fields that triggered thedevelopment of the technique here proposed. In such cases,possible deviations from the planned values are admitted to beobserved in the progress phase at the end of each WPS, whenactual values are detected and compared with the planned ones. Itis worth noting that even in the case of a more general type of


project, the deviations arising from the comparison of actualperformances with the planned ones can be considered in allrespects as the consequence of the realization of uncertain events,which means that the proposed model incorporates the variabilityof the input factors. In fact, as will be clearer in the sectiondevoted to the algorithm, when a deviation from the plannedvalue is detected for one or more of the input factors, the time/cost/quality schedule of the project is to be updated, andcorrective actions implemented. So, if a deviation of the durationof the activities is detected at a certain time with respect to theplanned values, the scheduling phase is to be repeated for theentire project, and the completion time consequently calculated.In the same way, if a deviation is encountered in the cost/qualityfactors, their impact is determined, and the cost/quality valuesupdated. In this sense, the only difference with a nativeprobabilistic model is that in our model a probability function isnot associated with the performances of the input factors, thusconcealing the possibility of considering the probability ofnon-critical paths of becoming critical (as in Program Evaluationand Review Technique [PERT]), as well as their impact on theexpected completion time of the project, or determining theexpected value of the total cost. Consequently, our deterministicmodel considers the deviations from planned values as thedemonstration of occurrence of the uncertain events, even if theyare disclosed at the end of the WPS. However, the technique isproactive, as it allows managers to incorporate the impact ofuncertainty of the performed WPSs on those not still undertaken.On the other hand, the introduction of the stochastic behavior ofthe input factors does not imply that heavy changes andcomplications will be required for the proposed technique to beapplied, and the steps can be performed in the same way, as theonly difference is to substitute the deterministic values with theprobabilistic ones. Finally, the hypothesis of a deterministicmodel is compliant with the practice of PM in all cases in whichthe field of application of the project is well known (routineprojects) and, thus, it is conceivable that the activity duration, thecosts, and the quality requirements can be determined in advancewith certainty and are not subject to variations. The theoreticalcontribution of the proposed technique is that the risk associatedwith each WPS is determined, as well as its contribution to theoverall project risk, and the impact of already performed WPSson those not still undertaken is taken into consideration. Thismeans that the mutual influence among the activities that are onthe critical path, and those that are not, is considered in terms oftheir impact on the overall project risk. This involves correctiveactions that are put into practice to consider the impact of theactual performances on the overall project, determine the riskdegree of the project, and employ information about the riskdegree as a feedback to take preventive actions towards the WPSsstill not performed. The practical contribution of this technique isthat it allows the project managers to balance the risk level of thedifferent WPSs, thus mitigating the risk associated with theperformance variations. The comparison with the project riskdegree in the absence of preventive actions shows the effectivenessof the proposed approach. The technique proposed can be easilyapplied to all kinds of projects, without losing its generalizability.The paper is organized as follows: Section 2 addresses a review of



3C. Muriana, G. Vizzini / International Journal of Project Management xx (2017) xxx–xxx

the literature; Section 3 deals with the goal of the study, andprovides a background of the technique; Section 4 explains theproposed technique; Section 5 illustrates a numerical example;Section 6 addresses the discussions; and Section 7 reports theconclusions of the paper and future developments in technique.

2. Review of the literature

In order to design the research strategy, the first step that wasperformed was that of specifying the research question. For thepurpose of the paper, we followed the structured proceduresuggested by Cooper et al. (2009). The research questionaddressed the possibility of providing a new technique for PMthat involves the project risk assessment, and allows us to put intopractice RM techniques for performing corrective/preventiveactions. The second step involved the identification of the termsdescriptive of the topics addressed. They were “project risk,”“risk management,” “risk assessment,” “risk prevention,” “riskmitigation,” “Earned Value Management” (and its acronym,EVM), “project assessment,” and its synonym, “project perfor-mance evaluation,” and “project management.” The topics wereselected by starting with a preliminary reading of the most knownmanual on PM, the PMBOK® Guide, PMI, 2013, and relying onour previous knowledge and experience in the field of PM. Third,the search engines were identified: the ScienceDirect databaseand Google. The ScienceDirect database hosts more than 3,500of the most valuable academic journals (all the journals have animpact factor) and 34,000 e-books.

The research was conducted considering the topics abovecited, as key words. First the simple research function was used,followed by the “advanced search” (fourth step of the procedure).This function allowed us to specify what binary operators (AND,OR, AND NOT) are to be used that match the differentcombinations of keywords. So, the sentence “project” AND“risk” were sought, or “risk” AND “prevention”, and so on,specifying in what fields of the paper/book they are to be found,such as: “all fields,” “abstract,” “title,” and “keyword.” Thesearch was extended to the journal/book in the following areas ofknowledge: “business, management and accounting,” “computerscience,” “decision science,” and “engineering.” The period ofthe research was not specified so that the database could searchfor all years; for ScienceDirect this meant searching in the rangeof years 1823–2016, even if such a vast range of time is notavailable for all journals/papers. This time period was sufficientto investigate the topic of the paper, as RM and PM started todevelop in the 20th century. Theoretically, such an approachcould lead to excessively broad results, which also include thosenot matching the topic of the paper. This drawback was avoidedthanks to the function of the ScienceDirect database that sorts theresults for relevance with respect to the key words inserted in thesearch fields. This allowed us to easily understand when to stopthe search, making evident papers whose topic did not match thatof our paper with respect to the title. Another source of researchwas the Google search engine, in which we employed both thesimple and advanced search functions. The keywords used werethe same as the search on the ScienceDirect database. The choiceof using Google was the possibility of doing free searches on the


Web, allowing us to find conference papers that could not havebeen included in the ScienceDirect database, and all other usefultechnical reports. Even in the advanced search of Google, it waspossible to set the option of showing the most pertinent contentsin relation to the key words inserted. With Google, it was alsopossible to extend the search to American English in addition toBritish English. Finally, the documents found were examined,and the chosen ones included in the following subsections. Thesearch was conducted between January, 2016 and June, 2016.The documentation allowed us to know that the subject was to bedivided into two main fields: EVM and the risk assessment. Evenif, based on the PMBOK® Guide, PMI, 2013, RM is a branchof EVM, the number of techniques and publications are suchthat it is to be considered a specific field, worthy of properconsideration. On the other hand, for the purpose of good order, afirst introduction of the history of PM is provided in Sub-section2.1; thus a review of EVM is proposed with latter advancementsin Sub-section 2.2. Finally, a review of RM is presented inSub-section 2.3, which relates the specific topic addressed by thepaper.

2.1. Project Management

Though examples of PM can be found as far back as theEgyptian era, the origin of modern PM can be dated between1900 and the 1950s (see Kwak, 2003). In particular, before the1950s the focus of PM techniques was prevalently onscheduling, i.e., the understanding of activities and sequencing,and the main advancements in this field are related to theintroduction of the Gantt Chart thanks to Henry Gantt in 1917.Some studies identify the origin of PM with Henry Fayol, whosynthesized the 14 principles of management (Fayol, 1917),and the five functions of a manager (Fayol, 1949). Thus, CPMand PERT were invented in the 1950s. Subsequently, MaterialRequirement Planning (MRP) and other scheduling tools wereintroduced. In 1962, the Work Breakdown Structure (WBS)was invented. In 1965, the International Project ManagementAssociation (IPMA) was created, the world's first projectmanagement association, which is a federation of about 50national- and international-oriented project management asso-ciations aimed at promoting the diffusion of PM, and allowingthe development of the profession.

In 1969, the Project Management Institute (PMI) was launchedto promote the profession of PM. Today, PMI is known for its mainpublication, “A Guide to the Project Management Body ofKnowledge (PMBOK),” considered one of the essential tools forPM. In 1975, the PROMPTII Method was created by SimpactSystems Limited. It consisted of guidelines for managing computerprojects, in response to the delays that characterized such projectsin those years. In 1979, PROMPTII was adopted by the U.K.government's Central Computing and TelecommunicationsAgency (CCTA) for all information systems projects. Moreover,the introduction of the PMBOK, in 1987, allowed projectmanagers to “provide a common lexicon within the profession fortalking about project management,” providing “a basic referencefor anyone in the profession of project management” (seePMBOK® Guide, 2013). Today, the PMBOK is a reference




manual for PM, as it proposes widely recognized PM techniquesthat allow project managers to effectively carry out both theplanning and the execution phases. In particular, it providesproject managers with techniques for the monitoring of theproject, through the employment of EVM. In fact, since 1987, thePMBOK has outlined the importance of EVM, which hasbecome a reference model for PM, thanks to the Undersecretaryof Defense for Acquisition, which identified EVM as a valuabletool for PM. In 1989, the PRINCE Method was developed byPROMPTII, which became the U.K. standard for all govern-ment information systems projects. It was revised in 1996 bythe CCTA, with the publication of PRINCE 2®, which wascharacterized by a greater applicability to any project type. In1997, the Critical Chain Project Management (CCPM) wasinvented, which allowed project managers to manage flexibleresources. In 1998, the PMBOK became a standard thanks torecognition by the American National Standards Institute(ANSI). In 2006, the "Total Cost Management Framework"was released by the Association for the Advancement of CostEngineering (AACE) International, with the aim of applyingthe skills and knowledge of cost engineering to PM. In 2008,the 4th Edition of the PMBOK Guide was published, enrichingthe previous version. In 2009, a revision of PRINCE 2® wasoffered by the Office of Government Commerce (OGC), andenhanced the previous version by introducing the basicprinciples that contribute to project success. In 2012, the ISO21500:2012 Standard for Project Management was released,and was specifically conceived for use by any kind oforganization, including public, private, or community groups,and for any project, regardless of complexity, size, andduration. In December 2012, the fifth edition of the PMBOKintroduced the tenth knowledge area, “Project StakeholderManagement,” and added four new planning processes withrespect to the previous version.

Moreover, with the advent of computers and the Internet, sincethe 1980s the endeavor of researchers in the field of PM has alsofocused on the possibility of embedding PM techniques intocomputer programs for personal computers (1970s–1980s), whichallow us to share project information through the use of bothDesktop and Web-based solutions.

2.2. Earned Value Management

PM is a critical activity, determining the success or failure ofa project. For this reason, several techniques have beenperfected over time in order to simplify the efforts related tosuch an activity, and increase its usefulness. As stated before,the first attempt to support project managers in the schedulingphase was made with the introduction of CPM in 1950 (seeModer, 1988 for a discussion of this), which is a deterministictechnique that allows us to determine the longest path in thenetwork (i.e., the “critical path”), which is taken as the earliesttime for project completion. The PERT was introduced someyears later (Malcolm et al., 1959), adding the hypothesis ofuncertainty regarding the activity duration. Finally, the MonteCarlo Simulation (MCS) was proposed for project schedulingin the early 1960s (see Van Slyke, 1963), rapidly becoming one


of the most used technique for projects affected by uncertaintyof the activities. The true attempt to structure the process of PMwas made with the introduction of EVM. EVM was introducedin 2000 in the PMBOK® guide (PMI, 2000), and is todaybroadly employed in the field of PM for measuring projectperformances (Vanhoucke and Vandevoorde, 2007), because itcombines measurements of the Iron Triangle of the PM. Asreported by Chen et al. (2016), “EVM produces variance andperformance indices for project costs and schedules, and thuspredicts project costs and schedules at completion, providingearly indications of expected project performance results.” Theusefulness of EVM in forecasting the project performances iswidely recognized (Narbaev and De Marco, 2014; PMBOK®Guide, 2013), and considerable research has been publishedthat attempts to extend this technique. EVM makes use of someperformance indicators, such as planned value (PV), earnedvalue (EV), and Budgeted and Actual Costs (BC and AC) fordiscerning the progress of the project, determining scheduleand cost deviations from the planned values through the use ofSchedule Variance (SV), Cost Variance (CV), SchedulePerformance Index (SPI), and the Cost Performance Index(CPI). Lipke in (2003), introduced the Earned Schedule (ES)concept to overcome limitations of the SV and SPI. Based onthese, recent literature has been prompted by the possibility ofenriching traditional indicators with more advanced ones, andapplying statistical and fuzzy techniques to the EV indicators inorder to improve the potential of EVM. Analysis of theliterature allowed us to identify the most relevant publishedpapers that address the issue of project control and monitoring.The approach generally proposed is that of identifying projectdeviations both in deterministic and probabilistic schedules,though the possibility of addressing actions devoted to reducingdeviations from the planned configuration through corrective/preventive actions has not been considered. The papersmentioned below show the approach usually employed. Lipkeet al. (2009), focused on the prediction of final duration for theschedule component of projects, and developed a forecastingmethod for the determination of the final cost and durationusing control charts, the limits of which dynamically varybased on actual project performances. They focused on thevariability that can affect time/cost factors, considering thatearliness/tardiness of time/cost factors necessarily will impact onthe overall final time/cost of the project. Differently from theperspective of the proposed technique, they limited their work tothe determination of the actual time/cost variation with respect tothe planned values, without considering the possibility of puttinginto practice corrective/preventive actions on the schedule.Moreover, they do not correlate the input factors among oneanother, and did not consider the impact of the input factorvariation in terms of project risk. Naeni and Salehipour (2011),presented a set of fuzzy earned value indices with specificapplications in projects affected by uncertain conditions.Warburton (2011), illustrated a methodology for enrichingEVM, deriving time-dependent expressions for the PV, EV,AC, CPI, and SPI. He tested the model with a software projectdataset, demonstrating that the project's final cost convergesfaster to the correct value, with less variability compared with




traditional Estimate at Completion (EAC) calculations. How-ever, he did not address the issue of the project-related risk dueto performance deviations from planned values, and limited hisdiscussion to the determination of the expected final cost.Colin and Vanhoucke (2014), proposed a project progressmonitoring methodology based on control charts, in whichcontrol limits for Shewhart control charts are represented byEV/ES indices, and are determined on the basis of MovingAverage (MA) techniques. Unlike the technique we presenthere, their work was limited to the detection of possible projectperformance deviations (outliers), without addressing theimplications in terms of corrective/preventive actions able toreduce performance variability. Similarly, Khamooshi andGolafshani (2014), proposed an Earned Duration Management(EDM) in which they developed a number of indices to measureprogress and performance of schedule and cost, as well as theefficacy and efficiency of the plan at any level of the project.Naeni et al. (2014), presented a fuzzy-based earned value model,determining the EV indices, and the time and the cost estimates atcompletion, under conditions of uncertainty. Narbaev and DeMarco (2014), proposed a new equation for the calculation ofthe Cost Estimate at Completion (CEAC), which predictsexpected cost for the remaining work with the Gompertzgrowth model, using nonlinear regression curve fitting. Theirequation integrated the ES concept, which indicates the expectedduration at completion, as a factor influencing cost performance.Khodakarami et al. (2007), employed the Bayesian Networks fordetermining the project completion under uncertainty of theactivities. Moreover, they considered the causal relationshipbetween the uncertainty sources and the project parameters, aswell as the mutual dependency among activities. Khodakaramiand Abdi (2014), proposed a very similar approach to that ofKhodakarami et al. (2007) paying attention to the uncertainty ofthe costs, and the mutual impact of costs variations on thetotal cost of the project. The main difference between theirapproach and the technique here employed is that we consider adeterministic network in which the uncertainty is taken intoconsideration from the point of view of the difference betweenplanned and actual values of the already scheduled WPSs, and interms of impact of the actual performances of already scheduledWPSs on those still not undertaken. Our approach is to payattention not only to the planning phase of the project, but also tothe state of progress, determining the deviations between theplanned and actual values, as well as their impact on the overallproject risk level. Moreover, Khodakarami et al. (2007) andKhodakarami and Abdi (2014), considered input factors one at atime (uncertainty of the duration of the activities and costs), asresponsible for the project performance, while our approach ismultifactorial, i.e., it considers the simultaneous impact ofmultiple factors on the project completion time and the overallperformance. Acebes et al. (2015), described an integratedmethodology for project control in the presence of uncertaintysources based on EVM and MCS, but corrective/preventiveactions are not provided to reduce the impact of the uncertaintyon the project performances. Colin et al., 2015, proposed amultivariate model for EVM/ES, which implements a PrincipalComponent Analysis (PCA) on a simulated schedule control


reference. They used this model to project the actual EVM/ESobservations onto the principal components identified throughPCA. They found that this approach leads to improvements andpractical advantages compared with traditional univariate EVM/ES models. Even in this case, information about projectperformances is not employed in corrective/preventive actionsable to reduce the deviations from the initial risk level of theproject. Dodson et al. (2015), who proposed a Quality EarnedValue (QEV) index, focused on the possibility of defining aquantitative Quality Index for enhancing the EVM technique,with the aim of measuring the project's ability to deliver thequality requirements. Willems and Vanhoucke (2015), carriedout an overview of the existing literature on project control andEVM, with the aim of highlighting the current trends andpotential areas for future research in this field. In particular,they found that main research topics are related to the stochasticnature of projects, the use of historical datasets or simulationexperiments for validating the methodologies proposed, theexpansion of integrated control models with focus on time andcost as well as other factors such as quality and sustainability, andmodels of development and validation of corrective actionprocedures. Chen et al. (2016), focused on the use of PV,considered an initial estimate of the earned value and actual costprior to project execution, for predicting EV and AC values.Their study proposed a modeling method for improving thepredictive power of PV before executing a project. They showedthat the method improves forecasting accuracy by an average of23.66% and 17.39% for EV and AC, respectively, providingproject managers with predictive information that is more reliableconcerning EV and AC performance, which allows them to takeproactive actions. Finally, Govan and Damnjanovic (2016),focused on the link between strategic planning theory, namely theResource-based View (RBV), and project risk management,considering that within an organization, different units involvedifferent risks, depending on their primary function. Theirapproach relied on the realization of a project causal networkthat allows for both data-intensive and conceptual evaluation ofthe project risks, focusing mainly on cost impacts. Govan andDamnjanovic (2016), considered only the impact of theresource-related risks on the project completion time, while ourpaper simultaneously considers the impact of multiple concurrentfactors, such as time, cost, and quality on the project completiontime and the overall performance.

2.3. Risk assessment

Project risk is defined as: “an uncertain event or conditionthat, if it occurs, has a positive or negative effect on one ormore project objectives such as scope, schedule, cost, orquality” (PMBOK® Guide, PMI, 2013). Among RM tech-niques, the most known are the PERT, the probability-impactrisk matrix, Pareto diagrams, stochastic simulation models suchas MCS, decision trees, Failure Models and Effect Analysis(FMEA), System Dynamics models, sensitivity analysis, andseveral other good practices (see PMBOK® Guide, 2013, andPRINCE 2®, 2009, for a better understanding of RMprocedures and techniques). As an example, PERT allows us




to determine the risk of overcoming the estimated completiontime as a consequence of uncertainty factors related to theactivities. In addition to these premises, a criticism usuallyrelated to this technique is that if the activities along the criticalpath are not also the riskiest, the risk of overcoming thecompletion time is erroneous, as activities that are not on thecritical path, but have a high probability of varying, can impactthe completion time more than those along the critical path.This implies that the PERT does not represent an effectivetechnique for measuring the risk associated with a project.Moreover, it does not allow us to know the impact of theearliness/tardiness of the performed WPSs on the WPS still notundertaken, and how the risk profile of the entire project varies,consequently. In the field of risk assessment and management,the recent literature is replete with examples of new meth-odologies that aim at supporting project managers in thedecision-making process under conditions of uncertainty. Theprincipal evidence in the literature is here presented, and thedifferences with the technique proposed by the authorunderlined. Nguyen et al. (2013), proposed a decision-makingtool to help the project manager choose the best risk treatmentstrategy. The methodology developed, called ProRisk, uses theconcepts of risk scenario, treatment scenario, and projectscenario to determine the consequences of possible riskscombined or not with preventive and/or corrective treatmentactions. However, unlike the technique proposed by the author,they did not consider the interdependencies among risks andthe impact of a risk of one or more activities on the project riskprofile. In other words, they did not optimize the projectschedule by considering the simultaneous effect of the riskassociated with one task on the other risks factors. Fang et al.(2013), proposed a quantitative framework of analysis forsupporting decision making in project risk response planning.They used a design structure matrix representation to capturerisk interactions and build a risk propagation model forpredicting the global mitigation effects of risk response actions.Unlike the technique proposed by the author, they did notexploit the potential of the methodology for exploring theimpact of the risks on the single activity, thus neglecting howthe network topology could change in relation to the riskpropagation, determining possible project delays. Acebes et al.(2013), proposed a methodology to integrate EVM with riskmanagement based on traditional EVM indicators and MCS,which allows project managers to detect negative and positivedeviations from planned values, corresponding to cumulativepositive or negative cost/schedule buffers. Such informationcan be usefully employed to take corrective actions or identifythe sources of improvement, and further optimize projectactivities. However, they limited their work to the determina-tion of the deviations from planned values, without focusing onpreventive/corrective actions that can be put into practice.Similarly, Gładysz et al. (2015), proposed a PERT-based mixedlinear programming model that supports time-related projectrisk management and which, in turn, helps discern betweenrisks that have to be accepted and risks that can be removed insome way, ensuring that client requirements with respect toproject completion time be satisfied at minimal cost. Acebes et


al. (2014), focused on a methodology for project control underuncertainty. In particular, they integrated EVM with project riskanalysis. The goal was to help project managers to knowwhether the project deviations from planned values are withinthe “expected” deviations derived from activity plannedvariability. They limited their work to the risk assessment,and did not explore possible solutions to balance the riskamong the activities for minimizing the risk of the entireproject, and the impact of worse performances on the entireproject. Pfeifer et al. (2015), focused on the quantification ofrisk associated with project performances, and the identificationof those tasks mainly responsible for project risk that lead todelays in the project completion. They considered stochasticactivities, developed an optimization model to maximizeproject delay, and proposed a genetic algorithm to identifythose tasks that are involved principally in project completiondelay. They found that, due to the uncertainty in the activitycompletion time, critical tasks are not necessarily thosebelonging to the critical path, and that the performances ofthe algorithm are affected by the network topology of theproject rather than the network size. However, they neglectedthe effect of project-delay maximization in the projectcompletion time, and how such an approach could lead tofurther loss of money due to penalties associated with delays of theactivities. On the contrary, the approach followed by the authorallows project managers to take into consideration possibleinteractions among input factors and, thus, to infer how a badperformance on the cost/time/requirement can impact the otherinput factors and the overall project risk profile. Rudnik andDeptuła (2015), illustrated a probabilistic fuzzy system for projectrisk assessment that represents an extension of the Mamdaniprobabilistic fuzzy system. In particular, the knowledge base ispresented as fuzzy IF–THEN rules together with probabilitymeasures of fuzzy events. Results of the system inferencecompared with the regression model andMamdani fuzzy inferencesystem show that the proposed model is more precise with respectto traditional ones. They did not propose risk response plans inorder to mitigate/prevent the impact of the risk on the projectcompletion. Similarly, Kumar and Yadav (2015), analyzed thecorrelation between risk factors and project outcome with regard tosoftware risk analysis. They proposed a probabilistic software riskestimation model using the Bayesian Belief Network (BBN) thatfocuses on the top software risk indicators for risk assessment insoftware development projects. Kosztyán (2015), proposed amatrix-based project planning method that took into considerationtask importance or probability of completions, thus determining theranks of the importance or probability of possible project scenariosand project structures. However, he hypothesized that the activitieshave flexible dependencies. This implies that, in the presence of ahigh probability of not being concluded, such activities can beexcluded from the schedule. This approach limited the work ofKosztyán (2015), only to projects in which flexible dependenciesand task exclusions can be allowed. Rodríguez et al. (2016),addressed information technology projects and proposed a riskassessment method based on a combination of Fuzzy AnalyticHierarchy Process (FAHP) and Fuzzy Inference System (FIS).Their model takes into consideration the different levels of




uncertainty, the relationships among groups of risk factors, andthe possibility of adding or removing options, ensuring that theconsistency of judgments with previous evaluations is main-tained. They did not address preventive/corrective plans for riskprevention/balancing. Zhao et al. (2016), proposed a fuzzy-basedrisk assessment model that calculates the likelihood of occur-rence, magnitude of impact, and risk criticality of a set of riskfactors, in order to determine the most critical ones with respect tothe project's success. However, unlike the model proposed by theauthor, they did not link the risk factors to specific activities of theproject network, and thus the impact of the risks on the networktopology is not determined. Finally, Mohammadipour andSadjadi (2016), proposed a multi-objective mixed integer linearprogramming for minimizing the “project total extra cost,”“project total risk enhancement,” and “project total qualityreduction,” in the case in which the initial project schedule issubject to a shortening due to client needs. The model proposedconsidered only the increase of the risk related to projectshortening, and neglected the case in which the project durationcan be prolonged due to the occurrence of risks related to specificactivities.

3. Goal of the study and background of the technique

From an analysis of the literature it appears clear that thefocus in the field of risk management is on identification andassessment of risk, but there are few examples of riskmonitoring and prevention in PM. In fact, only some of thepapers we found deal with quantitative methodologies for riskprevention and balancing, able to prevent project risks, andsupport management in the decision-making process. Summa-rizing, the main shortcomings found in the analysis of theliterature relate to the possibility of simultaneously consideringthe following elements:

• interdependency of the risks related to different activities ofthe project,

• change in the network topology as a consequence of theoccurrence of a risk condition related to one or moreactivities of the project,

• definition of a risk index related to the entire project and thesingle phases,

• definition of preventive/corrective actions that are able toimprove the risk profile of the project and the single phases,both in the progress phase and in the early planning phase,

• consideration of the relation among different input factors onwhich the risk profile of the project depends (based on thePM Triangle).

In particular, we could not identify papers that provideinformation on the overall risk of a project, or that identify themost or least risky phase of the project, both in the planning andprogress control stage. Moreover, models present in theliterature do not allow us to adapt the preventive and correctiveactions to the project performance detected in progress,considering the impact of already performed phases on thosestill not performed. If available, such an approach could allow


us to put in practice preventive actions capable of moderatingthe project risk, still in the planning stage, mitigating the riskamong the different project phases. In addition, the modelspresent in the literature usually deal with risks in relation to thecompletion time of the project (and, thus, uncertainty of thecompletion time of the activities), and cost factors, but do notaddress the quality factor. Conversely, taking into account aquality factor would allow us to entirely implement the IronTriangle of the PM, providing a wide view of projectperformances. Finally, the models present in the literature donot take into account the mutual dependence of the factors, withthe result that a poor performance in one of them could impactthe others. This paper proposes a new technique for riskmanagement, by focusing on the concept of WPS, whichovercomes the shortcomings highlighted above, and is capableof identifying the most critical WPS, and enabling preventiveand corrective actions in PM. Based on the definition of riskgiven in Sub-section 2.3, the focus of the this paper is on therisk assessment and prevention with regard to cost, schedule,and quality. The perspective here considered is that the risk canbe detected by assessing its impact on the input factors,highlighted by the deviation of the actual values from theplanned ones. In this respect, the proposed technique providesproject managers with a tool that allows them to diagnosevariations of the project performances with respect to theplanned phase, and the practical contribution of the techniqueto the decision-making process of the project managers consistsin providing them with the possibility of carrying outpreventive and corrective actions on WPSs still not performedin order reduce the deviation of risk level from that calculatedin the planned phase. As said in the Introduction, a project canbe organized in control points, namely WPSs, that identify timeinstants of control, which are chosen to control the progress ofwork of a portion of the project, of fixed duration. So, if aproject, based on the schedule, is 40 months long, it can bedivided, e.g., into 10 WPSs. In this case, each WPS will checkthe progress status of the project in relation to a time-window of4 months. This means that the progress status of the projectwork will be checked every 4 months. So, WPS1 is related tothe activities that are ongoing between months 1 and 4. Thedifferent activities of the project can belong to one or moreWPSs, thus an activity can be still in progress at the end ofthe time-window to which the i-th WPS is related. In thishypothetical case, the WPS1,2,3,…10 will be put in relation tothe end of months 4,8,12,…, 40, and the performances ofthe project registered correspondingly to such time instants.The technique aims at providing a tool for the prediction ofthe project risk degree, combining planned and actual infor-mation on the performances of the input factors, supportingmanagement in the decision-making process, and enabling bothpreventive and corrective actions towards the WPSs of theproject. The technique relates to risks involved in WorkProgress, cost, and quality of activities, and relies on the IronTriangle of the PM. The factors considered are: the ResidualMan Days (RMD) of the project, the Work Progress (WP), theActual Cost of Work Performed (ACWP), and the QualityIndex (QI). The technique employs both planned and actual




information to determine a synthetic risk index of each WPS,and to continually update the risk degree of the project. At theend of each WPS, when information about actual performancesof the WPSs already performed is known, the risk index of allthe WPSs is determined. For WPSs that have already ended,actual values of the factors responsible for the projectperformances are employed, while for those WPSs that arestill to be performed, only planned values are considered. Theseplanned values are updated at the end of each WPS byconsidering the impact of the actual performances of thealready performed WPSs. The risk index is calculated throughthe WSM, which allows us to determine the performance ofeach WPS in terms of risk, as well as the risk degree of theoverall project. The weights of the factors are determinedstarting with the covariance among factors, meaning that theweight will be higher or lower on the basis of the greater orlower dependence among the factors. In this sense, because thecovariance is a measure of the mutual impact between twovariables, it allows us to take into consideration the impact ofthe performance of one factor on the others, thus contributing tothe increase or decrease of the risk index related to thosefactors. The technique requires that, once the risk index isknown for each WPS, the risk level of the project is determinedby calculating the average risk degree. Thus, the best candidateWPS is identified in relation to the risk index of the WPSs. Thebest WPS will be that in relation to which preventive actionswill be carried out. As the actual performances can differ fromthe planned ones due to the resources available, the tardiness orearliness in the activity completion or the work performed, thecorrective and the preventive actions may require thescheduling of the project that could impact the WPSs not stillimplemented. So, as an example, if at a certain step the workperformed has been lower/greater than that planned due tofewer/more resources available, the activities involved in thisWPS will inevitably be completed later/earlier. Thus, in the firstphase of the technique the project is to be scheduled once againto determine the new project duration (corrective action basedon the actual performances) and the risk degree of the project.Then, the overall degree of risk is compared with that beforethe actual values were recorded. In the case in which theperformance is worse than before, preventive actions that aimat improving the risk profile of the project are needed,balancing the risk among the different WPSs. For this purpose,the second phase involves identifying the best candidate WPS,and preventive actions are implemented, shortening orextending the duration of the activities belonging to the bestcandidate WPS. As a result, the set of activities within eachWPS will change, and a new risk profile will be calculated foreach WPS of the project. This means that the technique takesinto account how the actual performances of ended WPSshave an impact on those still to be performed. Finally, acomparison with the risk project degree in the case of absenceof preventive actions will be made, showing the effectivenessof the proposed technique. The Value of Information (VoI),i.e., “the amount a decision maker would be willing to pay forinformation prior to making a decision” (Hubbard, 2016), iscalculated as the percent deviation of the scenario in the


absence of preventive actions with respect to that in thepresence of preventive actions, representing the suitability ofundertaking such actions. The technique is illustrated inSection 4.

4. Materials and methods

The algorithm has been formulated through the followingnotations:

Symbols and initialisms

i Number of WPSj Number of activities of the projectk Number of factorsWPS Work Progress StatusPDj Planned Duration of the j-th activityUj Unit of resources of the j-th activityDi Time-interval between the i-1-th WPS and the i-th

WPSNWPS Number of WPSsRMD Residual Man Days, i.e., the time remaining at the

completion of the project, at the i-th WPSWP Work Progress of the i-th WPSACWP Actual Cost of Work PerformedQIi Quality Index of the i-th WPSCW Cost of WorkDWH Daily Working Hours, i.e., the amount of hours

worked per dayNRMDi Normalized Residual Man Days of the i-th WPSNWPi Normalized Work Progress of the i-th WPSNACWPi Normalized Actual Cost of Work Performed of the

i-th WPSNQIi% Normalized percent of the Quality Index of the i-th

WPS

The technique makes use of an algorithm that consists of thefollowing steps:

START

1. DEFINE INPUT VARIABLES AND INITIALCONFIGURATION:

1.1 Define the planned duration (PDj) and the units ofresources (Uj) of the j-th activity, and determine itseffort as: ej=PDj∗Uj,

1.2 Determine the Total Effort (TE) of the project, as thesum of the effort of the activities, as: TE ¼ ∑n

j¼1 e j1.3 Set the duration (Di). Being the i-th WPS a time instant

of control of the project progress, Di identifies thetime-interval between the i − 1-th WPS and the i-thWPS and corresponds to a portion of the project, towhich the i-th WPS is referred. For the first WPS, Di isthe time-interval between the zero time and the end ofthe first WPS,




1.4 Schedule the project with CPM technique and determinethe time of completion (Tc) of the project, as well as theStart Time (STj) and End Time (ETj) of each activity thatcorrespond to the “as soon as possible” schedule,

1.5 Determine the Number of WPS (NWPS) as: NWPS ¼intþ

�TcDi

�1.6 Determine the start and end time instant of the i-thWPS,

based on Di, as: STi={ETi−1}, where ETi − 1 is the endtime of the i − 1-th WPS, and ETi={STi+Di}, whereSTi = 0 is the Start Time (ST) of the project, i.e., the zerotime,

1.7 Determine the effort of the i-th WPS, which is the effortof the activities belonging to the i-th WPS, as: Ei=Ei , 1 +Ei , 2+Ei , 3+Ei , 4, where Ei;1 ¼ ∑m

j¼1 e j;1 where m isthe set of activities that entirely fall into the i-th WPS,i.e., m∈α={ j : (STi≤STj)⋀ (ETi≥ETj)}, and ej,1 isthe effort of the j-th activity determined as in step 1.1;Ei;2 ¼ ∑n

j¼1 e j;2, where ej ,2 = (Dj− (ETj−ETi))Uj∗DWHand n∈α={ j : (STi≤STj)∧ (ETj≥ETi)}, for the activi-ties that start at the i-thWPS and end in following WPSi,and DWH are the Daily Working Hours; Ei;3 ¼ ∑p

j¼1e j;3 where ej ,3 = (Dj− (STi−STj))Uj∗DWH, and p∈α={ j : (STjbSTi)∧ (ETjbETi)}, for the activities that startat previous WPSi and end at the i-th; Ei;4 ¼ ∑q

j¼1 e j;4 ,where e j;4 ¼ ∑q

j¼1ðDj−ððET j−ETiÞ þ ðSTi−ST jÞÞÞU j �DWH , and q∈α={ j : (STj bSTi)∧ (ETj NETi)}, for theactivities that start at the previous WPS and end at thefollowing WPS.

2. SET PROJECT FACTORS:2.1 Residual Man Days (RMD), i.e., the time remaining at

the completion of the project, at the i-th WPS (days),2.2 Work Progress of the i-th WPS, (WPi),2.3 Actual Cost of Work Performed (ACWP) of the

activities falling into the i-th WPS (€),2.4 Quality Index of the i-th WPS (QIi), namely the sum of

Number of Quality Requirements (NQRj) of theactivities belonging to the i-th WPS. For the j-thactivity, NQRj corresponds to the number of deliver-ables of the activity itself, such as hardware, software,documents and other products. QIi is determined as:

QIi ¼∑ j∈WPSi

ðe j;1þe j;2þe j;3þe j;4Þ�NQR j

e j.

3. Define the Cost of Work (CW).4. Define the amount of Daily Working Hours (DWH).5. IN THE PLANNING PHASE:

5.1 Determine the RMD for the first WPS, as: RMD1 ¼ TE−EiDWH

and RMDi ¼ RMDi−1− EiDWH for i=2,….NWPS,

5.2 Determine the Work Progress of the i-th WPS, as:WPi ¼ Ei

TE5.3 Determine the ACWP for the i-th WPS, as: ACWPi=

CW∗TE∗WPi and determine the Total Cost of theproject (TC) as: TC ¼ ∑n

i¼1 ACWPi

5.4 Determine the progress of the QI, as: QIi% ¼ QIi∑iQI i

5.5 Normalize the scores of the factors with a normalizationtechnique and determine the normalized scores of thefactors of steps 2.1–2.4, namely NSi, i.e., NRMDi,NWPi, NACWPi, NQIi%,


5.6 Determine the covariance matrix among factors as:covar ðz; yÞ ¼ ∑ Eðz−EðzÞÞðy−EðyÞÞ

i ; z; y∈ k , and deter-mine the weight of the factors wk, starting from thecovariance matrix, with an approximate technique,

5.7 Determine the final score of i-th WPS with the WSM,which corresponds to the Risk Index of the i-th WPS(RIi), as: RI i ¼ ∑k

a¼1 NSi;k � wk. Generally speaking, thescore of the WSM indicates the performance of theWPS, meaning that the greater the score the better theperformance. In the context of this paper, this conditionmeans that the WPS with the greater score will alsobe that with the greater risk, as variations of theperformances in this WPS could have a strong impacton the other WPSs, and on the overall project. In fact,the WPS with the greatest score is the WPS in which theinput factors have a high score (i.e., the greater part ofthe work will be performed, the greater part of thequality requirements are to be realized, and the greaterpart of the cost is to be supported). Thus, tardiness/earliness in such WPS could lead to an increase in therisk level of the project,

5.8 Determine the minimum RIi and the maximum RIi,which represent the WPS with the minimum and themaximum risk index, respectively, and calculate theaverage measure and standard deviation of all the RIi, as:

μRIi ¼ ∑NWPSi¼1 RIiNWPS , SD ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi∑NWPS

i¼1 ðRIi−μRIiÞ2

NWPS

qto determine the

risk degree of the overall project.6. IN THE PROJECT PROGRESS PHASE: AT THE

END OF THE i-th WPS, SET x = i, WITH x =1,….,NWPS.This phase corresponds to the monitoring of the projectprogress, and consists in registering the actual values for theinput factors of the project, and determining their performancevariations with respect to the planning phase. In particular, themodel takes into account the possibility, at a certain iterationor WPSi, of having available fewer or more resources thanplanned. This implies that the work performed at the iterationx for the j-th activity will be lesser or greater than planned.Another hypothesis of the model that is very compliant withthe true operative requirements of PM is that the TotalEffort ej of an activity can be greater or less than planned,such that the duration of the activity will consequentlychange. The deviation of the ej in the project progress phasewith respect to the planned value corresponds to the factthat management has noticed a planning mistake thatinvolved corrective actions on the planned value of the ejduring the project execution. Finally, even the activityduration registered at the progress phase can differ from theplanned value, with the consequence that the projectcompletion can vary. Thus, the actual factors will bedetermined, and the new risk degree of the projectcalculated, consequently.6.1 WPSx = WPSNWPS? IF YES, THEN GOTO steps 6.2

to 6.11, THEN STOP the procedure. The project hasended. The μRIi represents the final risk degree of theproject. IF NO, GOTO the next step,




6.2 At the end of the WPSx, register the actual value of the unitof resources (Actual Units, (AUj,x)), and/or of the ActualDuration (ADj,x), and/or the Actual Work (AWj,x),

6.3 Based on Table 1, identify the case (Earliness/Tardiness/Intime). For this purpose, define β={ j∈WPSx :AUj ,x≠Uj ,x−1∨ADj ,x≠ADj ,x−1∨AWj ,x≠AWj ,x−1}. For all ac-tivities in β, set the independent variables and determinethe dependent variable. So, e.g., if the units at iteration xhave increased with respect to iteration x − 1, and theactual work is equal to that of iteration x − 1, it is necessaryto calculate the actual duration, based on the equation:ADj;x ¼ AWj;x−1

AUj;x�DWH where AWj ,x−1 is the planned valuecalculated as in step 1.7 for the first iteration. This meansthat once the actual units increase/decrease, such variationremains constant for the entire activity duration. Thus, theresource variation is permanent. The hypothesis is that theresource variation is highlighted at the start of the j-thactivity, and the possibility of having a different number ofresources in different units of time is not permitted. If theactivity duration at iteration x has increased with respect toiteration x − 1, and the actual work is equal to that ofiteration x − 1, it is necessary to calculate the unit ofresources, based on the equation:AUj;x ¼ AWj;x−1

ADj;x�DWH. If atiteration x, the actual work has changed with respect tothe value of iteration x − 1, and the activity duration isconstant, it is necessary to determine the unit ofresources, based on the equation AU j;x ¼ AWj;x

ADj;x−1�DWHwhere the ADj,x − 1 is the PDj for the first iteration.Finally, if at iteration x, the actual work has changedwith respect to the value of iteration x − 1, and the unitof resources is constant, it is necessary to determinethe duration of the activity, based on the equation

ADj;x ¼ AWj;x

AUj;x−1�DWH where the AUj,x − 1 is the Uj for the

first iteration. Of course, it is possible that twovariables can change simultaneously and, as a result,the third variable must be determined. So, if atiteration x, the actual work has changed with respectto the value of iteration x − 1, and the activity durationhas changed as well, it is necessary to determine theunit of resources, based on the equation AUj;x ¼

AW j;x

AD j;x�DWH. Finally, If at the iteration x, the actual work has

changed with respect to the value of iteration x − 1, andthe unit of resources has changed as well, it is necessary to

Table 1Relation among different variables.

Case number Variation of the factors with respect to the planned vax − 1

1 ej = Constant AUj,x = Constant2 ej = Constant AUj,x = Increase3 ej = Constant AUj,x = Decrease4 ej = Increase AUj,x = Constant5 ej = Increase AUj,x = Increase6 ej = Decrease AUj,x = Constant7 ej = Decrease AUj,x = Decrease


determine the actual duration of the activity, based on the

equation ADj;x ¼ AWj;x

AUj;x�DWH

6.4 Based on results of step 6.3, in order to put correctiveactions into practice, when needed, schedule the projectwith the CPM technique, determine the Tc and the NWPSxas in step 1.5 and determine the amount of effort Ei of theWPSi and the set of activities belonging to eachWPS, as insteps 1.6 and 1.7, for allWPSi, where the units are AUj,x fortheWPSx, Uj,x − 1 forWPS from x+1 to NWPS and for theWPS from 1 to i − 1, and the duration of the activities areADj,x for the WPSx, and ADj,x − 1 for WPS from x + 1 toNWPS and from 1 to i − 1,

6.5 Determine TEx at iteration x as in step 1.2,6.6 Determine the RMDi as:RMDi ¼ TE−AWi

DWH , for WPS1, andRMDi ¼ RMDi−1− AWi

DWH , for other WPSi, i = 2,….,NWPSx,

6.7 Set WPi ¼ EiTE as in step 5.2,

6.8 Determine the ACWPi, as in step 5.3,6.9 Determine the Actual Quality Index (AQIi) as in step 2.4

and the progress of AQI (AQI%) for all WPSi, as in step5.4,

6.10 GOTO steps 5.5–5.7,6.11 Determine the μRIi ,x and the SD as in step 5.8,6.12 Compare μRIi ,x with μRIi ,x−1

IF μRIi ,x≤μRIi ,x−1 THEN STOP. The performanceof iteration x is better than the previous iteration. SetAUj,x – 1 = AUj,x, ADj,x – 1 = ADj,x, AWj,x – 1 = AWj,x,retain the CPM schedule of such iteration and RMDi,WPI, ACWPi, and QIi%, pose x = x + 1, andGOTO step6.1,IF μRIi,xNμRIi,x−1 THEN GOTO to step 6.13 for thePREVENTIVE ACTIONS,

6.13 PREVENTIVE ACTIONS. Consider β as in step 6.3,and quantify the tardiness/earliness as: tardiness=earliness j;x ¼ ∑ j∈β jADj;x−ADj;x−1j , where ADj,x is theactual duration of the j-th activity at iteration x, and theADj,x − 1 is the actual duration of the j-th activity atiteration x − 1 (for the first step ADj,x – 1 = PDj). Thismeans that in the case in which the actual parametersdo not lead to tardiness or earliness of the activities,the preventive actions will not be undertaken. Thishappens, e.g., when the actual effort at iteration x isdifferent from the value of the iteration x − 1, due to

lue/the value of the iteration Variation of the activity duration

Dnew, j,x = Constant On timeDnew, j,x = Decrease EarlinessDnew, j,x = Increase TardinessDnew, j,x = Increase TardinessDnew,j,x = Constant On timeDnew, j,x = Decrease EarlinessDnew,j,x = Constant On time



Fig. 1. Graph of the project.


unit of resources variation, while the duration is keptconstant. In this case, there will be no changes in theactivity duration, and the project will be on time withrespect to iteration x − 1. The variation of the effortcannot lead to worse performance of the project, andno preventive actions will be considered,

6.14 Identify the set γ={WPSi, i= x+1, … ,NWPS :STWPSiNETWPSx∧ ∃ j∈WPSi :STj≥ETWPSx}, where WPSi arethe WPSs that have not been already realized at the endof the WPSx, which contain at least one activity thathas not been started at the end of the WPSx, based onthe CPM in the case of “as soon as possible” schedule.In the case of Tardiness, take BC=min {γ}, and in thecase of Earliness, take BC= max{γ}. The choice oftaking the minimum/maximum γ in the case of tardiness/earliness is due to the fact that the tardiness/earliness ofactivities of the WPSx will be distributed to the activitiesof the WPS with the lower/greater risk index. In this waythe risk can be balanced, moving it from the more/lessrisky WPS to the less/more risky WPS. IF BC = {Ø},

Fig. 2. CPM schedule


THEN pose x = x + 1 and GOTO step 6.1, IFBC ≠ {Ø}, THEN GOTO the next step,

6.15 Attribute the tardiness/earliness to the BC, anddetermine the new duration of the activities of the BCWPS, Dj,new,x, distributing the tardiness/earliness pro-portionally to ADj,x, keeping constant the work anddetermining the units as: AUj ,x=AWj ,x/Dnew , j ,x. Forcalculating Dj,new,x, initially determine the earliness ortardiness that is to be applied to the j-th activity, as:

Earliness or Tardiness j ¼ Total Earliness or Total tardiness�AD j;x

∑ j∈BCAD j;x.

Thus, the earliness/tardiness is to be summed with/subtracted from the Dj,x, determining new Dj. Dj ,neww ,x =

ADj ,x−1±Earliness or Tardinessj. Finally, calculate

Uj,new,x as: U j;new;x ¼ AWj;x

D j;new;x�DWH

6.16 GOTO steps 1.4–1.7,6.17 GOTO steps 6.6–6.9,6.18 GOTO steps 5.5–5.7, then GOTO step 6.11,6.19 Compare μRIi in the presence of preventive actions

(μRIi_PA) with μRIi before the preventive actions,

with critical path.



Table 2Effort of each WPSi.

WPSi ST ET Ei Set of activities belonging to the WPSi

1 0 4 160 m = {Ø}, n = {A,B}, p = {Ø}, q = {Ø}2 4 8 88 m = {Ø}, n = {Ø}, p = {B}, q = {A}3 8 12 48 m = {Ø}, n = {C}, p = {A}, q = {Ø}4 12 16 32 m = {Ø}, n = {Ø}, p = {Ø}, q = {C}5 16 20 32 m = {Ø}, n = {Ø}, p = {Ø}, q = {C}6 20 24 32 m = {Ø}, n = {Ø}, p = {Ø}, q = {C}7 24 28 128 m = {D,E}, n = {Ø}, p = {C}, q = {Ø}8 28 32 160 m = {Ø}, n = {Ø}, p = {Ø}, q = {D,E}9 32 36 144 m = {Ø}, n = {Ø}, p = {D}, q = {E}10 36 40 48 m = {Ø}, n = {F}, p = {E}, q = {Ø}11 40 44 32 m = {Ø}, n = {Ø}, p = {Ø}, q = {F}12 44 48 8 m = {Ø}, n = {Ø}, p = {F}, q = {Ø}


IF μRIi_PA≤μRIi, THEN STOP. The performance ofiteration x is improved. The risk degree of the projecthas been reduced, as the risk is balanced among theWPSi, GOTO step 6.20,IF μRIi_PANμRIi come back to the configuration in theabsence of preventive actions, as preventive actionshave worsened the project risk degree, retain the CPMschedule of the previous configuration and RMDi,WPi, ACWPi, and QIi%, pose x = x + 1, and GOTOstep 6.1, and pose x = x + 1,

6.20 Set ADj,x – 1 = Dj,new,x and AUj,x – 1 = Uj,new,x, retainthe CPM schedule of such iteration, and RMDi, WPI,ACWPi, and QIi%, pose x = x + 1, andGOTO step 6.1.

END

Table 1 is to be read based on the relation:

Effort j ¼ Duration j � Unit of resources j � DWH

As a result, in Table 1, the variation of two of the variablesmeans that the third varies correspondingly. So, e.g., in cases 2

Fig. 3. Gantt chart


and 3, respectively, if the actual resources increase/decrease, inorder to keep ej constant it is necessary to decrease/increase theactivity duration. But the same cases can be read saying that ifthe duration decreases/increases and you want to keep ejconstant, it is necessary to increase/decrease the unit ofresources. Thus, the variation of the effort with respect to theplanned value can be interpreted by admitting planning mistakesthat rendered the actual effort greater or lesser than plannedvalues, or variations of the resource or activity duration. Thevariation of the unit of resources can be due to the availability ofthe resources that can actually be constant/decreasing/increasingwith respect to the planned value. Finally, the variation of theactual duration can be due to planningmistakes or drawbacks thatcan prolong or reduce the activity duration itself. The variation ofthe activity duration can have an impact on the projectcompletion, involving the earliness or tardiness with respect tothe Tc. This depends on whether the activities responsible fortardiness/earliness are in the critical path or not. From Table 1, itcan be seen that the case in which the units of resources aregreater than planned corresponds to the case of overtime, whilethe case in which the units of resources are fewer than planned

of the project.



Table 3Quality Index of each WPSi.

WPSi QIi

1 6.82 3.23 2.0666674 2.1333335 2.1333336 2.1333337 2.2333338 2.2666679 1.86666710 1.29166711 1.512 0.375

Table 5Normalized scores of the factors.

WPSi NRMDi NWPi NACWPi NQIi

1 0.000 1.000 0.000 1.0002 0.117 0.526 0.474 0.4403 0.181 0.263 0.737 0.2634 0.223 0.158 0.842 0.2745 0.266 0.158 0.842 0.2746 0.309 0.158 0.842 0.2747 0.479 0.789 0.211 0.2898 0.691 1.000 0.000 0.2949 0.883 0.895 0.105 0.23210 0.947 0.263 0.737 0.14311 0.989 0.158 0.842 0.17512 1.000 0.000 1.000 0.000Max/min factor Min Max Min Max


corresponds to the case of lack of resource availability. This isconsonant with the common experience in the PM, where theactual effort/duration/unit of resources can differ from theplanned values. Moreover, the possibility of varying the activityduration is usually considered a valid solution, when penaltycosts for project completion delays are not expected, and projectextensions are admitted.

5. Numerical example: the project risk assessment method

In this section, a numerical example is presented to illustratein detail the algorithm described in Section 4.

5.1. Data set

The numerical example is related to a project, the graph ofwhich is reported in Fig. 1, where the activity durations Dj indays, the number of resources Uj, and the Number of QualityRequirements NQRj are also reported.

The DWH is equal to 8h/day, the Di for each WPSi is 4 days,the CW is 10€/h. Based on the graph in Fig. 1, the project wasscheduled with the CPM technique, and the results are reportedin Fig. 2, where the ej for each activity was determined as instep 1.1.

The Total Effort TE is 912h (step 1.2). Based on theschedule, the Tc is 45 days. The NWPS is 12 (step 1.5), the STand ET of each WPSi (step 1.6), and the effort of each WPSi as

Table 4Performance measures of the planning phase.

WPSi RMDi (days) WPi ACWPi (€) QIi

1 94 0.17544 1600 0.242862 83 0.09649 880 0.114293 77 0.05263 480 0.073814 73 0.03509 320 0.076195 69 0.03509 320 0.076196 65 0.03509 320 0.076197 49 0.14035 1280 0.079768 29 0.17544 1600 0.080959 11 0.15789 1440 0.0666710 5 0.05263 480 0.0461311 1 0.03509 320 0.0535712 0 0.00877 80 0.01339


well as the set of activities belonging to each WPS (step 1.7) arereported in Table 2.

The Gantt chart of the project that highlights the distributionof the activities among the different WPSi is reported in Fig. 3.

Thus, the QIi was determined for each WPSi (as in step 2.4)and results reported in Table 3.

5.2. Planning phase

For the purpose of this paper, the technique was applied witha Microsoft Excel spreadsheet, manually applying the CPMtechnique. Such an approach can be easily implemented and isnot excessively time-consuming, since the procedure is to beimplemented at fixed control points that correspond to the endof each WPSi, and considering that the numerical examplepresented is represented by a project composed of fewactivities. However, in the case of more complex projects, thealgorithm can be easily automated with common programminglanguages that implement the entire procedure. In fact, the mosttime-consuming step in the implementation of the algorithmthrough programming languages is the application of the CPMtechnique, but now, free and open source solutions thatimplement the CPM that can be easily imbedded in the codeare available (see Comella, 2014, for example).

The performance measures related to the planning phase asin steps 5.1–5.4 are summarized in Table 4.

The normalized values (step 5.5) of the performance measuresof Table 4 are reported in Table 5. For the purpose ofnormalization, the technique of the deviation from the Nadir has

been employed, and is:Normalized score ¼ Score of the factor k−NadirTarget−Nadir ,

where the score of the k factor is the score of the k-th factor at thei-th WPS; the Nadir value is the worst performance of the k-th

Table 6Covariance matrix.

NRMD NWP NACWP NQI

NRMD 1 −0.018524 0.018524 −0.05683NWP −0.018523703 1 −0.12812 0.049144NACWP 0.018523703 −0.128116 1 −0.04914NQI −0.056828426 0.0491444 −0.04914 1



Table 7Weights of the normalized factors.

Weight of the normalized factor

NRMD 0.259819NWP 0.248616NACWP 0.231746NQI 0.259819


factor, which corresponds to the greater score of the k-th factor forminimizing factors and to the lower score for maximizing factors;and Target is the best performance of the k-th factor, whichcorresponds to the lower score of the k-th factor for minimizingfactors and to the greater score for maximizing factors.

The covariance matrix (step 5.6) of the normalized scores isreported in Table 6.

The final ranking was thus obtained by applying the WSMas in step 5.7, where the weights of the factors wk aredetermined through the following approximate technique, as:

wk ¼ ∑cov ð f ;kÞ∑cov ð f ;rÞ ; ∀k; with f ; r ¼ 1…:k factors (see Table 7).

Finally, Table 8 reports the ranking of the WPSi. The tablealso reports the average and standard deviation of the ranking.

Table 8 shows that the WPS with lower risk index is theWPS3, while that with the greater risk index is the WPS11.

5.3. Project progress phase

The phase of the project progress is that in which at the endof each WPS the actual performances are to be registered.

At the end of the WPSi = 1, set iteration x = 1. At the endof the first WPS, the project has the following conditions,(Table 9).

Table 9 shows that more work than planned was performed,for activity B, during the first WPS. Despite this, the units ofresources have remained constant with respect to the plannedvalue. In order to determine the consequence of such condition,we can use Table 1. Table 1 is to be read as saying that, giventhat the actual effort has increased with respect to the plannedvalue, and because the unit of resources is constant, the

Table 8Final ranking.

WPSi RI

1 0.508442 0.385273 0.351584 0.363565 0.374626 0.385677 0.444598 0.504779 0.5365810 0.5192511 0.5369612 0.49156Small RIi 0.35158Large RIi 0.53696μRIi_PA 0.45024SD 0.05919


duration of activity B is to be determined based on the relationsdescribed in step 6.3. In the case under examination, thiscondition means that the duration of activity B is to berecalculated, and is greater than planned. Thus, it is necessaryto re-schedule the project with the CPM technique in order tocarry out corrective actions and determine new projectperformances. Results are reported in Fig. 4.

As can be seen in this figure, because B is a non-criticalactivity, the Tc has not changed. The NWPS remains 12 and theEi and QIi are reported in Table 10.

From Table 10 it is possible to determine the TE1 which isequal to 942h.

The performance measures related to the WPS1 as in steps6.6–6.9 are summarized in Table 11.

The normalized values (step 5.5) of the performancemeasures of Table 11 are reported in Table 12.


The final ranking was thus obtained by applying the WSMas in step 5.7 (see Table 14).

Finally, Table 15 reports the ranking of the WPSi. The tablealso reports the average and standard deviation of the rankingcalculated in step 6.11.

The μRIi shows that the risk degree of the project hasworsened with respect to the planning phase, as in fact the ARI1is greater than that of the planning phase. The SD hasdecreased, meaning that the risk is more balanced among theWPSi than in the planning phase. Table 15 also shows that theWPS with lowest risk index is the WPS3, while that with thegreater risk index is the WPS9. The preventive actions areneeded.

BC = {WPS3}. The WPS3 can be taken as BC as it containsan activity (C) that has not been started at the end of the WPS1(Table 10 and Fig. 4). Based on step 6.13 β = {B} andTardiness = │6.25 − 5│ = 2.25. The Tardiness is to be appliedto the activity of the WPS3 still not started at the end of theWPS1, i.e., C. Thus, DC,new,1 = 15 − 2.25 = 13.75 days andUB,1 = 1.09090 (step 6.15). Thus, following steps 1.4–1.7 theproject has been scheduled. The Tc = 43.75, the NWPS = 11.The Ei, the QIi and the set of activities belonging to each WPSrelated to the new schedule are reported in Table 16.

It is worth mentioning that the application of the preventiveactions has led to a decrease in Tc with respect to the previousconfiguration, thus allowing project managers to gain a savingof time. The performance measures as in steps 6.6–6.9 aresummarized in Table 17.

The normalized values (step 5.5) of the performancemeasures of Table 17 are reported in Table 18.


The weights of the factors are reported in Table 20.Finally, Table 21 reports the ranking of the WPSi (with

WSM, as in step 5.7). The table also reports the average andstandard deviation of the ranking calculated by following step6.11.

The μRIi is lower than that of the case in the absence ofpreventive actions, meaning that the risk has decreased. The SD



Table 9Performances at the end of the WPS1.

WPSi Set of activities belonging to the WPSi AUj,1 AWj,1 (h) ADj,1 (days)

1 m = {Ø}, n = {A,B}, p = {Ø}, q = {Ø} AUB,1 = 3 AWB,1 = 150 h ADB,1 = 150/(3 ∗ 8) = 6.25


has increased, meaning that the risk is less balanced among theWPSi than in the case in the absence of preventive actions. Thisconfiguration will be employed in the following control point.

At the end of the WPSi = 2, set iteration x = 2. At the end ofthis WPS, the project is in line with the planned values.Average RIi and SD are the same as the previous iteration. Nocorrective/preventive actions are needed. This configurationwill be employed in the following control point.

At the end of the WPSi = 3, set iteration x = 3. At the end ofthis WPS, the project has the following conditions, (Table 22).

Table 22 shows that during the third WPS more resourcesthan planned were available for activity C, resulting in morework performed for this activity in the WPS analyzed. Despitethis, the Total Effort of activity C remained constant withrespect to the planned value. In order to determine theconsequence of this condition, we can use Table 1. Table 1 isto be interpreting as saying that given the units of resourcesactually available at iteration x for the j-th activity and its TotalEffort, the duration of the activity is to be determined basedon the relations described in step 6.3. In the case underexamination, this condition means that the duration of activityC is to be recalculated, and is lower than planned. Thus, it isnecessary to reschedule the project with the CPM technique(step 6.4) in order to carry out corrective actions and determinenew project performances. The schedule with the CPM leads tothe schedule reported in Fig. 5.

As can be seen in this figure, because C is an activity of thecritical path, the Tc has decreased and is equal to 33.75 days.The NWPS is 9; following, in sequence, steps: 6.6–6.9,5.5–5.7 and 6.11, the ranking of the WPSi as well as the

Fig. 4. CPM of the


average and standard deviation are determined, and reported inTable 23.

The μRIi is greater than that of the previous iteration,meaning that the risk has increased in average. The SD hasincreased as well, meaning that the risk is less balanced amongthe WPSi than in the previous iteration. Thus, preventiveactions will be taken at this iteration to improve the risk degreeof the project. Table 23 shows that the WPS with the lowestrisk index is WPS2, already realized, while that with thegreatest risk index is WPS4.

BC = {WPS4}. WPS4 can be taken as BC as it contains twoactivities (D and E) that have not been started at the end of WPS3(Table 23 and Fig. 5). Based on step 6.13, β = {C} andEarliness = │13.75 − 3.75│ = 10, the Earliness is to be appliedto activities D and E of the WPS4 still not started at the end of theWPS3. For step 6.15, the earliness is distributed between D and E.EarlinessD = 4.54545, EarlinessE = 5.45455, thus, DD,new,3 =14.54545 days and UD,new,3 = 1.375, and DE,new,3 = 17.54545days and UE,new,3 = 2.0625 (step 6.15). As a result, followingsteps 1.4–1.7 the project was scheduled. The Tc = 39.20455, theNWPS = 10. It is worth mentioning that the application of thepreventive actions has led that the Tc has decreasedwith respect tothe configuration of the preventive actions carried out at the end ofWPS1, thus allowing project managers to gain a saving of time.Following, in sequence, steps: 6.6–6.9, 5.5–5.7 and 6.11 we havethe ranking reported in Table 24.

The μRIi_PA is lower than that of the case in the absence ofpreventive actions, meaning that the overall risk degree hasdecreased. The SD has increased, meaning that the risk is lessbalanced among the WPSi than in the case in the absence of

first iteration.



Table 10Effort and Quality Index of each WPSi at the end of the WPS1.

WPSi Ei QIi Set of activities belonging to the WPSi

1 160 5.8400 m = {Ø}, n = {A,B}, p = {Ø}, q = {Ø}2 118 4.1600 m = {Ø}, n = {Ø}, p = {B}, q = {A}3 48 2.066667 m = {Ø}, n = {C}, p = {A}, q = {Ø}4 32 2.133333 m = {Ø}, n = {Ø}, p = {Ø}, q = {C}5 32 2.133333 m = {Ø}, n = {Ø}, p = {Ø}, q = {C}6 32 2.133333 m = {Ø}, n = {Ø}, p = {Ø}, q = {C}7 128 2.233333 m = {Ø}, n = {D,E}, p = {C}, q = {Ø}8 160 2.266667 m = {Ø}, n = {Ø}, p = {Ø}, q = {D,E}9 144 1.866667 m = {Ø}, n = {Ø}, p = {D}, q = {E}10 48 1.291667 m = {Ø}, n = {F}, p = {E}, q = {Ø}11 32 1.5 m = {Ø}, n = {Ø}, p = {Ø}, q = {F}12 8 0.375 m = {Ø}, n = {Ø}, p = {F}, q = {Ø}


preventive actions. This configuration will be employed in thefollowing control point.

At the end of WPSi = 4–7, set iteration x = 4, x = 5, x = 6,x = 7, respectively. At the end of this WPS, the project is inline with the planned values. Average RIi and SD are the sameas iteration x = 3. No corrective/preventive actions are needed.This configuration will be employed in the following controlpoint.

At the end of WPSi = 8, set iteration x = 8. At the end of thisWPS, the project has the following conditions, (Table 25):

Table 25 shows that more work has been performed thanplanned for activity F, during the eighth WPS. As the durationof the activity is kept constant, this means that the units ofresources are to be determined (Table 1) based on the relationsdescribed in step 6.3. In the case under examination, thiscondition means that the units of resources of activity F are tobe recalculated, and are greater than planned. In this case it isnot necessary to reschedule the project, as the project durationhas not changed. Following, in sequence, steps: 6.6–6.9,5.5–5.7 and 6.11, the ranking of WPSi and the average andstandard deviation are reported in Table 26.

The μRIi is lower than that of the previous iteration,meaning that the overall risk degree has decreased in average.The SD has increased, meaning that the risk is less balancedamong the WPSi than in the previous iteration. Because this isthe last WPS, the resulting μRIi represents the final risk degreeat the end of the project.

Table 11Performance measures of the WPS1.

WPSi RMDi (days) WPi ACWPi (€) QIi

1 97.75 0.16985 1600 0.208572 83 0.12527 1180 0.148573 77 0.05096 480 0.073814 73 0.03397 320 0.076195 69 0.03397 320 0.076196 65 0.03397 320 0.076197 49 0.13588 1280 0.079768 29 0.16985 1600 0.080959 11 0.15287 1440 0.0666710 5 0.05096 480 0.0461311 1 0.03397 320 0.0535712 0 0.00849 80 0.01339


If preventive actions had not been performed at iterationsi = 1 and 1 = 3, the final risk degree of the project would havebeen of 0.51467, with an increase in the risk level of about 5%.Associating a cost the risk incurred, it is possible to quantify theVoI. This technique allowed us to achieve significantimprovement in the risk profile of the project. The techniqueproposed shows that the information about the risk level of theproject can be easily achieved by measuring some data that areusually registered by project managers for the purpose of theproject monitoring, and allows decision makers to avoid/mitigatethe risk in project management by suggesting a procedure for riskbalancing and prevention. It is worth underlining that, even if thealgorithm is thought mainly for applying preventive andcorrective actions to deterministic and fixed project plans incase of deviation from the planning phase, it can be also appliedto flexible project plans, like those related to SoftwareDevelopment Projects (SDP). The principal managerial benefitto be derived from this proposed technique is understanding thatthe deviations of a project from planned values need not alwaysbe seen as a source of worsening for the project. In fact, thecorrective/preventive actions proposed by the technique allow, incertain cases, for improvement of the project performances interms of a Tc, that decreases, letting the project managers savetime with respect to the planned values. Moreover, the possibilityof calculating the impact of the deviation of WPSs alreadyperformed on those still not started, through the RI, allows the



1 0.000 1.000 0.000 1.0002 0.151 0.724 0.276 0.6933 0.212 0.263 0.737 0.3104 0.253 0.158 0.842 0.3225 0.294 0.158 0.842 0.3226 0.335 0.158 0.842 0.3227 0.499 0.789 0.211 0.3408 0.703 1.000 0.000 0.3469 0.887 0.895 0.105 0.27310 0.949 0.263 0.737 0.16811 0.990 0.158 0.842 0.20612 1.000 0.000 1.000 0.000Max/min factor Min Max Min Max




NRMD NWP NACWP NQI


Table 15Final ranking and synthetic measures.

WPSi RI

1 0.508502 0.463183 0.371854 0.383845 0.394476 0.405097 0.463078 0.521349 0.5483510 0.5262311 0.5449612 0.49150Small RIi 0.3718463Large RIi 0.548355μRIi 0.46853SD 0.04655


project managers to provide timely corrections before suchWPSsare started, thus avoiding that negative deviations of workperformed in some activities can propagate along all other projectactivities. The practical applicability of the technique relates, e.g.,to the monitoring of the progress status of projects funded by theEuropean work programs, such as Horizon 2020, in which thefunds are released at the end of each WPS, on the basis of theidentification of the actual values of the times/costs/requirementsof the activities involved in each WPS. In these projects, thehypothesis of deterministic schedule/cost/requirement is manda-tory for accessing the funds and the possible deviations from theplanned values are considered at the end of each WPS as thedifference between actual values and planned ones. Moreover,deterministic approaches can be effectively implemented inroutine projects, in which experience and references of past dataare available to those realizing the Gantt schedule, allowing usto set the activity durations with certainty. Other conditionspushing towards deterministic approaches are the cases in whichthe project is to be manually monitored, e.g., where specificinformation is needed that is not available in PM software, (e.g.,the variation of the risk profile as a consequence of resource andquality requirements variability, which are features that are notcurrently implemented in any PM software), or in cases of largeprojects (see Vallabhaneni, 2013, for reference). Finally, allprojects that are composed of activities that are subject to tightdeadlines (e.g., activities that characterize administrative pro-cesses or production that are bound to incoming orders) aredeterministic in nature.

6. Discussion and findings

The paper presented a new technique that allowed us tosimultaneously take into account some aspects of the projectmonitoring that are usual neglected, such as:

Table 16Effort and Quality Index of each WPSi at the end of the WPS2.

WPSi Ei QIi Set of activities belonging to the WPSi

1 160 5.8400 m = {Ø}, n = {A,B}, p = {Ø}, q = {Ø}2 118 4.1600 m = {Ø}, n = {Ø}, p = {B}, q = {A}

• the definition of a risk index related to both the entire projectand the single phases,

• the definition of preventive/corrective actions that are able toimprove the risk profile of the project and the single phases,both in the progress phase and in the early planning phase,





• the relation among different input factors on which the riskprofile of the project depends (based on the PM Triangle).

The technique allows project managers to adapt the preventiveand corrective actions to the project performance detected inprogress, considering the impact of already performed phases onthose not still performed. This enables the possibility of puttinginto practice preventive actions capable of moderating the projectrisk, still in the planning stage, balancing the risk among thedifferent project phases. This paper focused on the concept ofWPS, and was capable of identifying the most critical WPSs, andenabling preventive and corrective actions in the PM. The paperaddressed the risk assessment and prevention with regard to cost,schedule and quality. The perspective here considered is that therisk can be detected by assessing its impact on the input factors,highlighted by the deviation of the actual values from the plannedones. In this respect, the proposed technique provides projectmanagers with a tool that allows them to diagnose variations ofthe project performances with respect to the planned phase. Thepractical contribution of the technique to the decision-makingprocess of the project managers consisted in providing them withthe possibility of carrying out preventive and corrective actionson WPSs still not performed in order reduce the deviation of risklevel from that calculated in the planned phase. The techniqueaimed at providing a tool for the prediction of the project risk

3 49.45455 2.163636 m = {Ø}, n = {C}, p = {A}, q = {Ø}4 34.90909 2.327273 m = {Ø}, n = {Ø}, p = {Ø}, q = {C}5 34.90909 2.327273 m = {Ø}, n = {Ø}, p = {Ø}, q = {C}6 42.72727 2.323485 m = {Ø}, n = {D,E}, p = {C}, q = {Ø}7 160 2.266667 m = {Ø}, n = {Ø}, p = {Ø}, q = {E,D}8 160 2.266667 m = {Ø}, n = {Ø}, p = {Ø}, q = {E,D}9 120 1.41875 m = {Ø}, n = {F}, p = {D,E}, q = {Ø}10 32 1.5 m = {Ø}, n = {Ø}, p = {Ø}, q = {F}11 30 1.40625 m = {Ø}, n = {Ø}, p = {F}, q = {Ø}



Table 17Performance measures of the WPS2.after preventive actions.

WPS RMDi (days) WPi ACWPi (€) QIi

1 97.75 0.1698514 1600 0.208571432 83 0.1252654 1180 0.148571433 76.81818 0.05250 494.54545 0.077274 72.45455 0.03706 349.09091 0.083125 68.09091 0.03706 349.09091 0.083126 62.75 0.045358 427.27273 0.08298167 42.75 0.1698514 1600 0.080952388 22.75 0.1698514 1600 0.080952389 7.75 0.1273885 1200 0.0506696410 3.75 0.0339703 320 0.0535714311 0 0.0318471 300 0.0502232112 97.75 0.1698514 1600 0.20857143


NRMD NWP NACWP NQI



degree, combining planned and actual information on theperformances of the input factors, supporting management inthe decision-making process, and enabling both preventive andcorrective actions towards the WPSs of the project. Because thecovariance is a measure of the mutual impact between twovariables, the proposed algorithm allowed us to take intoconsideration the impact of the performance of one factor onthe others, thus contributing to the increase or decrease of the riskindex related to those factors. Moreover, using the covariancemeasure to determine the scores of the weights has anotheradvantage, as in fact it renders unnecessary the use of thejudgment of experts, which would inevitably introduce uncertaintydue to subjectivity of their opinions (as happens when you use theDelphi method and brainstorming for determining the weights ofthe factors). In this context, using the WSM to determine the riskindex for each WPS allowed us to take into account the impact ofdifferent factors and their mutual dependence.

It is worth underlining that the proposed technique might seemcomplex because of the number of calculations and the iterativeprocedure to be put in place. This complexity is mainly due to theflexibility of the technique, which takes into considerationchanges in cost, quality and time factors, as well as changes inresources, activity duration and work and their mutual relation-ship in determining the resulting performances of the risk profile.Summarizing, the main sources of complexity of the procedureare:



1 0.000 1.000 0.000 1.0002 0.151 0.677 0.323 0.6213 0.214 0.150 0.850 0.1714 0.259 0.038 0.962 0.2085 0.303 0.038 0.962 0.2086 0.358 0.098 0.902 0.2077 0.563 1.000 0.000 0.1948 0.767 1.000 0.000 0.1949 0.921 0.692 0.308 0.00310 0.962 0.015 0.985 0.02111 1.000 0.000 1.000 0.000Max/min factor Min Max Min Max


• each WPS can hold activities that are not already ended atthe end time of the WPS, meaning that it is necessary to splitactivities among different WPSs in order to determine therisk level of each WPS. This means that the end time of eachWPS is to be iteratively compared with the end time of eachactivity of the project schedule, making the procedure long,

• once the most/least risky WPS is identified, the identifica-tion of the activity to which apply the tardiness/earlinesscould be difficult to do in iterative procedures,

• the activity duration, the resource allocation, and the workare strongly related to one another.

The first shortcoming can be overcome by making the lengthof each WPS mobile, such that each WPS will hold endedactivities, and the splitting among different WPSs is not needed.As regards the second shortcoming, it can be removed byapplying the tardiness/earliness iteratively to all the activities ofthe BC WPS, and bringing forth the solution that minimizes therisk level of the project. Finally, the third shortcoming can beavoided by making the three variables (duration, resources andwork) independent among themselves. This will imply that achange in the duration will eventually impact only the completiontime of the project, and is to be interpreted as an extension of theactivity, while keeping fixed the resource availability and thework. At the same way, a change in the resource availability is tobe interpreted as a necessity of more/less resources than planned;the work will remain the same, meaning that less/more work willbe assigned to the given resources. Finally, a change in the workperformed is to be seen as the necessity of assigning more/lesswork for given resources and activity duration. These newhypotheses can reduce the complexity of the proposed procedureand make the computer implementation lighter. They may relateto future developments of the proposed technique, and be ofinterest to future studies.

7. Conclusions

The paper addressed the topic of risk assessment andmanagement, proposing a new technique for risk preventionand balancing, capable of supporting management in thedecision-making process by implementing risk response plans







WPSi RI

1 0.512552 0.444033 0.328284 0.347075 0.358906 0.374657 0.448108 0.502309 0.4845710 0.4832811 0.48745Small RIi 0.32827Large RIi 0.50229μRIi_PA 0.43374SD 0.04687


WPSi RI

1 0.500722 0.456623 0.541214 0.576235 0.494576 0.539987 0.508218 0.536009 0.49928Small RIi 0.4566223Large RIi 0.5762285μRIi 0.51698SD 0.00979


for avoiding, reducing, or accepting project risks. The tech-nique consisted in determining the risk degree of a projectthrough the monitoring of the actual performances of a set ofinput factors, and the application of WSM for the quantificationof the risk degree. Thus, preventive and corrective actions havebeen proposed to take into account the impact of the actualperformances of the input factors on the overall project risk,and to balance the risk among the different WPSs, mitigatingthe overall risk degree of the project. The theoretical contri-bution of the paper is that of introducing the possibility offocusing on the risk level of each WPS instead of only that ofthe entire project, based on the factors that constitute the IronTriangle of the PM. Such an approach allows project managersto make schedule changes in specified WPSs, thus mitigating

Table 22Performances at the end of the WPS5.

WPSi Set of activities belonging to the WPSi AUj,3

3 m = {Ø}, n = {C},p = {A}, q = {Ø}

AUc,3 = 4

Fig. 5. CPM of the


the risk of the entire project as a consequence of preventiveand/or corrective actions. In this respect, the practical contri-bution of the technique relates to the possibility of providingproject managers with a tool for the diagnosis of the differentWPSs of a project, focusing on the variation of risk level due tothe deviations of the actual performances with respect to thoseplanned. The technique allows us to determine the impact of theperformances of already performed WPSs on those still notperformed, and the corresponding risk level, enabling projectmanagers to keep the overall risk level of the project undercontrol. The technique can be usefully applied to all kinds ofprojects that rely on the well-known EVM, which is based onfixed control points. The limitation of the model proposed isthat it dealt with deterministic project plans, thus it did notincorporate the uncertainty related to the activities However, itcan be usefully employed in cases in which it is necessary to

AWj,3 (h) ADj,3 (days)

AWPA,3 = 2 ∗ 8 h/days ∗ 2 = 32AWPC,3 = 2 ∗ 8 h/days ∗ 4 s = 64

ADc,3 = 120/(4 ∗ 8) = 3.75

fifth iteration.




WPSi RI

1 0.496492 0.454573 0.539544 0.543775 0.431176 0.465847 0.500528 0.483429 0.5315510 0.52553Small RIi 0.43117Large RIi 0.54377μRIi_PA 0.49724SD 0.01331


WPSi RI

1 0.497482 0.452633 0.534964 0.536505 0.421546 0.453507 0.485478 0.468219 0.5233910 0.52448Small RIi 0.42154Large RIi 0.53496μRIi 0.48981SD 0.01445


schedule the project with deterministic parameters, such as inthe case of routine projects, or that of development plans forproject proposals for European work programs (e.g., Horizon2020), the management of which was among the issues thatprompted us to develop the technique, in which the costs, timesand project requirements are to be determined with certainty, asthe grants are calculated proportionally to them. In such cases,possible deviations from the planned values are admitted to beobserved in the progress phase, when actual values are detectedand compared to the planned ones.

Based on these considerations, future developments of theproposed technique may rely on the application of stochastictechniques for the scheduling of the project (PERT method),able to take into account the uncertainty about the activityduration. In this case, the risk index of each WPS should becoupled with the probability of performing a WPS, thusdetermining the expected value of the risk related to a WPS.Moreover, the variation of the actual cost as a function of theactivity duration (as in the model of crashing) should beaddressed, as it can impact the project risk degree. Futurestudies may also relate modification of the procedure proposed,for making it simpler both through manual or computerizedimplementation. Finally, a comparison with other models couldhave further confirmed the effectiveness of the technique, butunfortunately no similar models are present in the literature thatcould have been employed as a reference. Despite this, thetechnique is robust, as the comparison with the risk degree inabsence of preventive actions shows. In fact, the risk degree ofthe overall project in the absence of such actions would havebeen 5% greater than that in the presence of the preventiveactions (VoI), meaning that preventive actions had a positiveimpact on balancing and mitigating the risk of the project.

Table 25Performances at the end of WPS8.

WPSi Set of activities belongingto WPSi

AWj,8 (h) ADj,8 (days) AUj,8

8 m = {Ø}, n = {F},p = {D,E}, q = {Ø}

AWF,8 = 128 ADF,8 = 8 AUF,8 = 2


Conflict of interest

The authors declare that there are no conflicts of interest.

References

Acebes, F., Pajares, J., Galán, J.M., López-Paredes, A., 2013. Beyond earnedvalue management: a graphical framework for integrated cost, schedule andrisk monitoring. Procedia Soc. Behav. Sci. 74, 181–189.

Acebes, F., Pajares, J., Galán, J.M., López-Paredes, A., 2014. A new approachfor project control under uncertainty. Going back to the basics. Int. J. Proj.Manag. 32 (3), 423–434.

Acebes, F., Pereda, F.M., Poza, D., Pajares, J., Galán, J.M., 2015. Stochasticearned value analysis using Monte Carlo simulation and statistical learningtechniques. Int. J. Proj. Manag. 33, 1597–1609.

Atkinson, R., 1999. Project management: cost, time and quality, two bestguesses and a phenomenon, its time to accept other success criteria. Int.J. Proj. Manag. 17 (6), 337–342.

Cantore, A., 2008. L’inglese per l’impresa. Ready-Made Sentences for BusinessCorrespondence. Fourteenth ed. Franco Angeli, s.r.l., Milano Italy.

Chen, H.L., Chen, W.T., Lin, Y.L., 2016. Earned value project management:improving the predictive power of planned value. Int. J. Proj. Manag. 34,22–29.

Colin, J., Vanhoucke, M., 2014. Setting tolerance limits for statistical projectcontrol using earned value management. Omega 49, 107–122.

Colin, J., Martens, A., Vanhoucke, M., Wauters, M., 2015. A multivariateapproach for top-down project control using earned value management.Decis. Support. Syst. 79, 65–76.

Comella, R., 2014. Free and open source project management tools. TechnicalReport. SANS Institute InfoSec Reading Room [Available at: https://www.sans.org/reading-room/whitepapers/projectmanagement/free-open-source-project-management-tools-34495, Accessed: 22/04/2016].

Cooper, H., Hedges, L.H., Valentine, J.C., 2009. The Handbook of ResearchSynthesis and Meta-Analysis. second ed. Russel Sage Fundation, New York.

Dodson, M., Defavari, G., de Carvalho, V., 2015. Quality: the third element ofearned value management. Procedia Comput. Sci. 64, 932–939.

Fang, C., Marle, F., Xie, M., Zio, E., 2013. An integrated framework for theoptimization of project risk response plan under resource constraints withgenetic algorithm. IEEE Trans. Eng. Manag. 60 (3), 627–639.

Fayol, H. 1917. Administration industrielle et générale; prévoyance, organisa-tion, commandement, coordination, controle. Paris, H. Dunod et E. Pinat.

Fayol, H., 1949. General and Industrial Management. Translated by C. Storrs.Sir Isaac Pitman & Sons, London.

Gładysz, B., Skorupka, D., Kuchta, D., Duchaczek, A., 2015. Project risk timemanagement – a proposed model and a case study in the constructionindustry. Procedia Comput. Sci. 64, 24–31.


http://refhub.elsevier.com/S0263-7863(17)30061-3/rf0005






















https://www.sans.org/reading-room/whitepapers/projectmanagement/free-open-source-project-management-tools-34495

















Govan, P., Damnjanovic, I., 2016. The resource-based view on project riskmanagement. J. Constr. Eng. Risk Manag. 32 (7), 1233–1245.

Hubbard, D.W., 2016. How to Measure Anything: Finding the Value of“Intangibles” in Business. third ed. Study Guide, by CRAM101 TextbookReview.

Khamooshi, H., Golafshani, H., 2014. EDM: Earned Duration Management, anew approach to schedule performance management and measurement. Int.J. Proj. Manag. 32, 1019–1041.

Khodakarami, V., Abdi, A., 2014. Project cost risk analysis: a Bayesiannetworks approach for modeling dependencies between cost items. Int.J. Proj. Manag. 32 (7), 1233–1245.

Khodakarami, V., Fenton, N., Neil, M., 2007. Project scheduling: improvedapproach to incorporate uncertainty using Bayesian networks. Proj. Manag.J. 38 (2), 39.

Kosztyán, Z.T., 2015. Exact algorithm for matrix-based project planningproblems. Expert Syst. Appl. 42, 4460–4473.

Kumar, C., Yadav, D.K., 2015. A probabilistic software risk assessment andestimation model for software projects. Procedia Comput. Sci. 54, 353–361.

Kwak, Y.H., 2003. Brief history of project management. Chapter 2. In:Carayannis, Kwak, Anbari (Eds.), The Story of Managing Projects: anInterdisciplinary Approach. Quorum Books, Westport, Connecticut.

Lipke, W., 2003. Schedule is different. Meas News 31–34.Lipke, W., Zwikael, O., Henderson, K., Anbari, F., 2009. Prediction of project

outcome: the application of statistical methods to earned value managementand earned schedule performance indexes. Int. J. Proj. Manag. 27, 400–407.

Malcolm, D.G., Roseboom, J.H., Clark, C.E., Fazer, W., 1959. Application of atechnique for research and development program evaluation. Oper. Res. 7(5), 646–669.

Moder, J., 1988. Network Techniques in Project Management. ProjectManagement Handbook. second ed. Van Nostrand Reinhold, New York,pp. 324–373.

Mohammadipour, F., Sadjadi, S.J., 2016. Project cost–quality–risk tradeoffanalysis in a time-constrained problem. Comput. Ind. Eng. 95, 111–121.

Naeni, L.M., Salehipour, A., 2011. Evaluating fuzzy earned value indices andestimates by applying alpha cuts. Expert Syst. Appl. 38, 8193–8198.

Naeni, L.M., Shadrokh, S., Salehipour, A., 2014. A fuzzy approach for theearned value management. Int. J. Proj. Manag. 32, 709–716.


Narbaev, T., De Marco, A.D., 2014. An earned schedule-based regressionmodel to improve cost estimate at completion. Int. J. Proj. Manag. 32 (6),1007–1018.

Nguyen, T.H., Marmier, F., Gourc, D., 2013. A decision-making tool tomaximize chances of meeting project commitments. Int. J. Prod. Econ. 142,214–224.

Office of Government Commerce, 2009. Managing Successful Projects withPRINCE2.

Pfeifer, J., Barker, K., Ramirez-Marquez, J., Morshedlou, N., 2015. Quantifyingthe risk of project delays with a genetic algorithm. Int. J. Prod. Econ. 170,34–44.

PMI, 2000. Project Management Body of Knowledge (PMBOK). second ed.Project Management Institute, Newtown Square, PA.

PMI, 2013. A Guide to the Project Management Body of Knowledge:(PMBOK® Guide). fifth ed. PMI, Project Management Institute, NewtownSquare, PA.

Rodríguez, A., Ortega, F., Concepción, R., 2016. A method for the evaluationof risk in IT projects. Expert Syst. Appl. 45, 273–285.

Rudnik, K., Deptuła, A.M., 2015. System with probabilistic fuzzy knowledgebase and parametric inference operators in risk assessment of innovativeprojects. Expert Syst. Appl. 42, 6365–6379.

Vallabhaneni, S.R., 2013. Wiley CIA exam review 2013. Internal AuditKnowledge Elements, Chapter 5. John Wiley &Sons, Inc., Hoboken, NewJersey.

Van Slyke, R.M., 1963. Monte Carlo methods and the PERT problem. Oper.Res. 11 (5), 839–860.

Vanhoucke, M., Vandevoorde, S., 2007. A simulation and evaluation of earnedvalue metrics to forecast the project duration. J. Oper. Res. Soc. 58 (10),1361–1374.

Warburton, R.D.H., 2011. A time-dependent earned value model for softwareprojects. Int. J. Proj. Manag. 29, 1082–1090.

Willems, L.L., Vanhoucke, M., 2015. Classification of articles and journalson project control and earned value management. Int. J. Proj. Manag. 33,1610–1634.

Zhao, X., Hwang, B.G., Gao, Y., 2016. A fuzzy synthetic evaluation approachfor risk assessment: a case of Singapore's green projects. J. Clean. Prod.115, 203–213.













































































project risk management: a deterministic quantitative ... · project risk management: a...

Documents