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Estimating project and activity duration: a risk management approach using network analysis NASHWAN DAWOOD Division of Civil Engineering and Building School of Science and Technology, The University of Teesside, Middlesborough TSI 3BA, UK Received 21 December 1995; accepted 14 August 1997 Variations in the durations of activities are commonplace in the construction industry. This is due to the fact that the construction industry is influenced greatly by variations in weather, productivity of labour and plant, and quality of materials. Stochastic network analysis has been used by previous researchers to model variations in activities and produce more effective and reliable project duration estimates. A number of tech- niques have been developed in previous literature to solve the uncertain nature of networks, these are: PERT (program evaluation and review techniques), PNET (probabilistic network evaluation technique), NRB, (narrow reliability bounds methods) and MCS (Monte Carlo simulation). Although these techniques have proved to be useful in modelling variations in activities, dependence of activity duration is not considered. This can have a severe impact on realistically modelling projects. In this context, the objective of the present research is to develop a methodology that can accurately model activity dependence and realistically predict project duration using a risk management approach. A simulation model has been developed to encapsulate the methodology and run experimental work. In order to achieve this, the following tasks are tackled: iden- tify risk factors that cause activity variations using literature reviews and conducting interviews with contrac- tors; model risk factors and their influence on activity variations through conducting case studies and identifying any dependence between them; develop a computer based simulation model that uses a modi- fied Monte Carlo technique to model activity duration and dependence of risk factors; and run experimental work to validate and verify the model. Keywords: Network analysis, Monte Carlo simulation, PERT, stochastic analysis Background bounds), and MCS (Monte Carlo simulation). Diaz and Hadipriono (1993) found that PERT is the simplest Uncertainty in network analysis has been used by pre- method and yields the most optimistic results, while vious researchers in an attempt to model activity dura- MCS produces the most conservative results. They used tion variations more accurately and produce more several types of network and the evaluation is based on effective and reliable project duration estimates. survival function and computer time. Ranasinghe Variations of activity duration do occur due to the expo- (1994) has introduced an equation to model the uncer- sure of construction projects to numerous uncontrol- tainty in activity duration, and developed a quantifica- lable risk factors. Several probabilistic methods have tion for uncertainty in project duration been developed to solve the problem of uncertainty The research in the area of uncertainty in network in network analysis. Amongst these methods are analysis which has been developed over the last decade (Illumoka, 1987; Chapman, 1990): PERT (program has refined the techniques used; however, a number evaluation and review technique), PNET (probabilistic of problems still exist. Uncertainty in analysis is applied network evaluation technique), NRA (narrow reliability with survival of the project in mind, rather than
applying it to projects with the survival of the company that there are a number of risk factors that might as the basis of the decision. Obviously, before the cause variation in activity duration, and their uncertainties of projects can be combined a good influence can differ from one activity to another. In understanding of the uncertainties in each project is general, the following are considered to be the risk needed. Furthermore, the techniques used still need factors. enhancing to produce more accurate models of the interactions between uncertainties and activities varia- Type of soil and site condition tions. In this context it is hypothesized in this research Weather conditions that unless some form of dependence between activity Material and equipment failure variations exist, accurate modelling of uncertainty in Incomplete design scope networks is unattainable. The objective of this research Defective design is to explore a methodology, based on a risk manage- Design changes Fluctuation in labour productivity ment approach, that models variations in the duration Artificial obstruction of activities and their dependence on risk factors. It is hypothesized that such a methodology can improve Subcontractors default project duration estimates and provide practitioners Landslide with a tool for testing several mitigating strategies to Each of the above factors can be modelled using a counter detrimental events and their influence on representative distribution and have a minimum value project duration (0) and a maximum value (1). As in MCS, random The following tasks have been performed to achieve numbers for each risk factor are generated from a the objective. (1) Identify risk factors that cause activity particular representative distribution. The type of variations using a literature review and conducting distribution can vary from one activity to another or interviews with contractors. (it) Model risk factors and can be kept fixed for the project once it has been gener- activities' duration variations and identify dependence ated. It is proposed that certain risk factors will have between them. (ii) Develop a simulation model to the same influence on the project regardless of time, encapsulate and test the new methodology. (iv) Run for example, type of soil and site condition, labour experimental work on case studies to validate the productivity, etc. On the other hand, other risk factors methodology. might be changed with time and might have different values from one activity to another, for example, weather conditions, equipment failure, incomplete Methodology design, design defect, In thi: case, random numbers will be generated for each activity or for a In this section the proposed methodology of model particular time in the project calendar. Several distri- ling variations in the duration of activities and their butions are used to model risk factors, as shown in dependence on risk factors is discussed. It is assumed Table 1 (Bekr, 1990). Application Equipment failure Table 1 The distributions, their possible use and the parameters required Name Use Parameters Event Where there is a risk an event Outcome and probability can occur Rectangle Where there is an equal chance The lower and upper extremes of outcome between two values Triangle Where the outcome is between The lower and upper and the two extremes and the tendency is most likely outcome towards one outcome Design changes and incomplete design scope Weather condition, labour productivity, materials delay, soil conditions Weather, subcontractors default Trapezium Where there is a range between which the outcomes are equally likely, and the probability of an outcome beyond that range decreases the further away from it, towards the extreme outcome The lower and upper extremes and the lower and upper likely outcomes
Stochastic network analysis 43 The influence of each risk factor on variations of In order to illustrate the above equation, Table 3 activity duration should be established. As an example, shows an example of four runs for activity A. As can Table 2 shows a matrix that gives the influence of the be seen, in Run 1 all risk factors have materialized to risk factors on variations of activity duration. As can the very extreme and the duration of the activity is 20, be seen, each risk factor has a certain contribution on which is the maximum. In Run 2 none of the risk activity variations (risk factor 1 has 20% influence on factors has materialized and the duration of the activity duration variations in activity A). The total influence is the minimum, 10. Run 3 shows a duration of 12.5 of all factors should be 100% on any given activity. In days resulted from 50% materialization of each risk reality the influence of factors will be assessed judge- factor. Finally, Run 4 shows the results of having two mentally through knowledge elicitation. This will be risk factors, 1 and 2, with 100% materialization. In discussed later in the paper. order to validate the methodology, a simulation model Once distribution has been allocated using a combi- has been developed using the Turbo-Pascal platform. nation of historical data and knowledge of distribution The model encapsulates risk factors, their distribution theories) to risk factors and the influence matrix is and influences on each activity and the logic of a given developed, the remaining task is the calculation of project. The following section introduces a hypothet- activity duration. In order to achieve this, the following ical case study to illustrate the proposed methodology equation is developed Duration of activity A = Min Time + Case study [MaxTime - Min Time) [(RF, * Random) + The case study is a small civil engineering project as (RF, * Random.) + shown in Table 4. The risk factors that affected each (RF, * Random) + activity in the project and their influence are given in (RF, * Random) Table 5. The distributions representing the possible outcome of each risk factor are also given in Table 5. where Min Time is the minimum duration that can be A suitable distribution has been allocated to each risk assigned to an activity, MaxTime is the maximum factor using site information and judgement. The duration that can be assigned to an activity, RF, is the quantification of the risk factors has been achieved influence of risk factor n on a particular activity (from through selecting a probability distribution which activity/risk factor matrix), and Random, is a random shows the possible outcomes of the variables and the number that should be generated using a representa- relative likelihood of each possible outcome. Figures tive distribution of risk factor n. 1, 2 and 3 show the distributions of weather, soil and Table 2 Activity/risk factors matrix Activity Sum RISK FACTOR 3 4 1 2 5 6 A B с D E 20% 0 20% 100% 50% 20% 0 20% 0 50% 40% 0 40% 0 0 50% 0 0 0 0 40% 0 0 20% 10% 20% 0 0 100% 100% 100% 100% 100% 0
Table 4 Logic of the project Activity Activity No. Start 1 Min. duration Max, duration Preceded by Nil 0 0 Followed by Pile&Cap E Pile&Cap C Pile&Cap W SubStr E SubStr C SubStr w WN 2 3 4 Start Start Start 18 13 و في نه 29 22 12 Pile&Cap E Pile&Cap C Pile&Cap W SubStr E SubStr C SubStr w Insitu Span 5 6 7 8 Insitu Span Insitu Span PC Span Surface Surface 18 13 15 25 29 22 25 35 PC Span Pile&Cap E Pile&Cap C Pile&Cap W SubStr E SubSur C SubStr C SubStr W Insitu Span PC Span Surface Finishes 9 2 8 Surface 10 Finishes 2 2 7 Finishes End 11 12 End Nil 10 0 18 0 Act Act 5 Act 6 Act 7 Act 8 Act 9 Act 10 Act 11 0.30 0.30 0.30 0.30 0.40 0.10 0.50 0.50 0.40 0.10 0.10 0.10 0.00 0.00 0.00 0.00 Table 5 Risk factors influencing the project's activities Risk Distribution Mean STD Act Act factors 2 3 Weather Triang 0.59 0.21 0.30 0.30 (0,0.8,1) Soil Triang 0.63 0.22 0.40 0.40 (0,0.9,1) Productivity Triang 0.28 0.2 0.15 0.15 (0,1) Equipment Event 0.21 0.15 0.15 (0,0.6,1) Delay of Triang 0.53 0.21 0.00 0.00 materials (0,0.6,1) Sum 1 1 0.15 0.30 0.30 0.30 0.30 0.30 0.20 0.20 0.53 0.15 0.10 0.10 0.10 0.10 0.20 0.15 0.15 0.00 0.20 0.20 0.20 0.20 0.40 0.15 0.15 1 1 1 1 1 1 1 1 0.10 Probability 0.08 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.06 0.04 0.02 1 0.00 0.01 0.00 Random Number Random Number
0.1 1.00 008- 0.80 0.06 0.04 0.60 0.02 0.40 0 0.20 Random Number 0.00 Figure 3 Distribution of reliability of equipment Possible project duration Figure 5 Cumulative distribution for project duration 0.12 Probability 0.10 Risk factors 0.08 0.06 Weather Productivity 0.04 h. 0.02 Delay of materials Equipment Soil 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.00 57 61 65 69 73 77 81 85 89 93 Possible project duration Figure 4 Distribution for the project duration number of runs 1000, min. value 57 days, max. value 94 days, average 78.7 days, SD 7.5, and skewness - 0.115 Correlation coefficient Figure 6 Correlation of the risk factor with project duration reliability of equipment, respectively. The influence of each risk factor on the activity duration is assigned. Obviously, the influence of the risk factors should affect the outcome of the project, and a range of exper- imental work can be designed to investigate the risk factors. It should be mentioned that the objective of this paper is to present the methodology and its oper- ation. Construction managers should be able to use it as a test bench to pinpoint the effect of risk factors on their projects. The distributions that represent the risk factors might differ from project to project and therefore the methodology is designed to accept a wide range of distributions to suit particular applica- tions. significantly to the total. The results of the runs are compared with Monte Carlo simulation using the Beta distribution to model activity variations. Figure 4 shows the results generated from 1000 iterations of the model; the minimum duration (optimistic) of the project is 57 days and the maximum duration (pessimistie) is 94 days. The mean value of the project duration is 78.7 days with 7.5 standard deviation and -0.115 skewness (.e. the mean is shifted towards the pessimistic value). The cumulative density function in Figure 5 indicates that around 80% of the results are between 74 and 94 days. In order to identify the influ- ence of the risk factors on the duration of the project, a correlation analysis between the risk factors and project duration is conducted. Figure 6 shows that weather and productivity have a high correlation (0.68 and 0.62, respectively) and this is regarded as a strong influence on the project duration compared with other factors. This type of analysis should help project management on focusing on the risk factors that influ- ence the project duration substantially. Analysis of the results Having described and quantified the uncertainty of the risk factors, the next stage is to determine the combined effect of uncertainties on the project dura- tion and to identify the factors which contribute
0.12 0.14 0.12 Probability 0.10 0.10 0.08 0,08 0.036 0.06 0.04 0.04 0,02 0.02 0.001 0.00 Possible project duration Figure 7 Beta distribution for the project Possible project duration Figure 9 Distribution for the project duration 0.14 Probability 1.00 CDF 0.80 0.12 0.10 0.08 0.06 0.04 0.02 0.00 0.60 + 0.40 0.20 0.00 Possible project duration Figure 8 Cumulative distribution for the project: number of runs 1000, min. value 61 days, max. value 94 days, average 78 days, SD 6.9, and skewness - 0.21 Possible project duration Figure 10 Cumulative distribution for the project duration: number of runs 1000, min. value 54.4 days, max. value 94.661 days, average 72.9 days, SD 7.7, and skewness 0.17 In order to compare the results generated from the proposed methodology with the traditional PERT approach, the model was allowed to run the same case study using the Beta distribution. The maximum and minimum values for each activity that were used in the Beta distribution are shown in Table 4. Figures 7 and 8 show the results generated from 1000 iterations of the case study, and the results are similar to the proposed methodology, however, the PERT solution has provided a slightly lower standard deviation (6.9) and a higher skewness of (-0.21). The PERT approach has produced an overall expectation of the project duration without any indication regarding the causes of such wide outcomes in the project duration, pessimistic part of the project duration. The method- ology developed is well suited to targeting the detri- mental effect of the risk factors and consequently reducing the impact of such factors. In the case study, it was concluded that the weather and productivity risk factors have a strong impact on the project duration, and the intention is to reduce the effect of these factors. In order to achieve this, it was suggested that the project used in the case study be constructed over the summer; this way, the effect of the weather can be minimized. 1000 iterations were run using the same information presented in Table 4 and changing the mean of the weather distribution to (0.2). Figures 9 and 10 show that the possible project duration has been shifted towards the optimistic part. It can be seen that the mean value is 54 days with skewness of 0.17. More experimental work is under way with the object- ive of minimizing the detrimental effect of the risk Risk response Having identified the possible outcomes of the project duration, the management needs to identify the possi- bility of reducing the variations and minimizing the
factor. From Figures 9 and 10 it can be concluded that the detrimental effect of the risk factors can be minimized and a more optimistic duration can be produced. However, the question to be asked is: at what cost can this be achieved? Management should be able to evaluate the cost/benefit of each option. This subject is under investigation. Figures 11-14 show the results of a set of experi- ments designed to demonstrate the effect of varying certain risk factors while keeping the rest fixed. The objective is to examine the sensitivity of the projects towards certain risk factors. Figure 11 shows the distri- bution of the project duration while varying only the weather factor and fixing the rest of the factors. Compared with Figure 4 (varying all risk factors), the results suggest that the spread of data in Figure 11 is smaller (SD 5.2, min. 64, max. 88), however, the project is still risky, quite sensitive to the influence of weather and needs management attention to counter the uncertainty in the project. Figure 12 shows the distribution of the project duration while varying only the soil risk factors, and the spread of data is reduced further (SD 5.8, min. 75, max. 80) and the uncer- tainty is minimized. Figure 13 shows the distribution of the project duration while varying only the weather and soil factors, and in Figure 14 all the risk factors except productivity are varied. The figures show that the spread of data is wider than in Figures 11 and 12, and the project is highly uncertain and sensitive to weather and soil factors when they are combined. 0.12 0.10+ 0.08 0.06 0.12 0.10 0.08 0.06 0.04 0.02 0.00 0.04 0.02 0.00 Possible project duration Figure 11 Distribution for the project duration, varying just the weather factor number of runs 1000, min, value 64 days, max. value 88 days, average 78 days, and SD 5.2 Possible project duration Figure 13 Distribution for the project duration, varying just the weather and soil risk factors: number of runs 1000, min. value 63 days, max. value 69 days, average 78 days, and SD 5.8 0.12 0.10 0.10+ 0.08 0.08 0.06 0.06 0.04 0.04 0.02 0.02 0.00 0.00 Possible project duration Possible project duration Figure 14 Distribution for the project duration, varying all the risk factors except productivity: number of runs 1000, min. value 60 days, max. value 92 days, average 78 days, and SD 6.1 Figure 12 Distribution for project duration, varying just the soil risk factor: number of runs 1000, min, value 75 days, max. value 80 days, average 78 days, and SD 5.8
factors is highly judgmental and there is room for mis- takes; and the methodology is dependent on historical data and most construction companies do not have accurate records of construction sites. References Conclusions The objective of this research is to explore a method- ology that models variations in the duration of activities and their dependence on risk factors. It is hypothesized that such a methodology can improve project duration estimates and provide practitioners with a tool for testing several mitigating strategies to counter detrimental events and their influence on pro- ject duration A case study has been used to illustrate the method- ology and a simulation model has been developed and used to encapsulate this methodology. It is concluded that the results generated using the methodology are very beneficial to forecasting project duration accurately aand estimating the impact of risk factors on project duration. It should be mentioned that the practical application of this method has a number of limitations, eg.: allocation of the influence of the risk factors on wariations of activity duration needs considerable expe- rience and judgement; identifying and modelling risk Bekr, GAR. (1990) Client's control of construction, Ph.D. thesis, University of Nottingham. Chapman, C.B. (1990) A risk engineering approach to project risk management, International Journal of Project Management, 8(1). Diaz, C.F. and Hadipriono, F.C. (1993) Non-deterministic networking methods, ASCE Journal of Construction Engineering and Management, 119(1), 40-57, Illumoka, A.A. (1987) A tolerance analysis approach to network scheduling for engineering project management, International Journal of Production Research, 25(4), 531-47. Ranasinghe, M. (1994) Qualification and management of uncertainty in activity duration networks, Construction Management and Economics, 12(1), 15-29