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Modeling and risk analysis of virtual project team through project life cycle with fuzzy approach
Computers & Industrial Engineering 72 (2014) 98–105
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Modeling and risk analysis of virtual project team through project life cycle with fuzzy approach Mona Ghaffari a,⇑, Farrokh Sheikhahmadi b, Gholamreza Safakish c a
Department of Engineering, Alzahra University, Tehran 1993893973, Iran Department of Business Administration, College of Social Science, Semnan University, Semnan, Iran c CEO, Datis Management Consultants, Apt804, No. 55, Sarafraz St., Dr. Beheshti, Tehran 1587698474, Iran b
a r t i c l e
i n f o
Article history: Received 23 August 2013 Received in revised form 22 February 2014 Accepted 25 February 2014 Available online 15 March 2014 Keywords: Virtual project team Risk analysis Risk management Project life cycle Fuzzy set
a b s t r a c t The ongoing revolutions in e-business and progresses of IT and communication, has resulted in the increasing number of companies with formal virtual project teams. In such situation, Uncertainty analysis gains more importance, being conducted within risk management framework. In this paper, based on the six phases of risk management procedure in PMBOK methodology, a risk management process in virtual projects is introduced. In qualitative analysis phase (of PMBOK methodology), the most effective factors of project management in virtual project teams are prioritized. In quantitative analysis phase, for the very first time, ‘‘Fuzzy Linear Programming Model’’ is employed to assess project risks based on project life cycle. Also given time and budget constraints, a method for developing appropriate strategies of reacting to each risk factor is introduced. We use GAMS (General Algebraic Modeling System) to select these strategies. Finally, we test our model in a numerical example, as evidence. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction According to Luse, McElroy, Townsend, and DeMarie (2013), virtual teams (VTs) are characterized as a group of people with unique skills who work interdependently but are separated geographically and they need technological mediums to communicate. Thus, virtual teams allow members to accomplish specific tasks while transcending traditional restrictions of time and proximity. Consequently, VTs differ from classic teams which people are physically concentrated in one place. In VTs, members are physically separated from one another and they rely on technological devices for communication and information exchange. Project-based industries such as Architecture, Engineering and Construction are becoming more globalized as firms seeking to access specialized knowledge from all parts of the world. Gartner group (www.gartner.com) predicts that, by 2004, more than 60% of the professional workforces in the Global 2000 Companies will most probably work in virtual teams. By 2003, half of the existing VTs failed to meet either strategic or operational objectives due to inability to manage geographically distributed workforce (Iorio & Taylor, 2013). The concept of Dynamic Risk Management in virtual projects, which can be implemented according to project life cycle, is a new concept. In the model proposed in this paper, in order to apply ⇑ Corresponding author. Tel.: +98 9355130560. E-mail address: [email protected] (M. Ghaffari). http://dx.doi.org/10.1016/j.cie.2014.02.011 0360-8352/Ó 2014 Elsevier Ltd. All rights reserved.
dynamic risk management, project manager must repeatedly evaluate risk factors at the end of each phase or before big changes, and if necessary, s/he must apply suitable strategies for the next phases. In the literature of risk management and project life cycle, risk reaction strategies are barely discussed. For example, Xie, Zhang, and Lai (2006) introduced different periods of project life cycle in software projects then they determined risk factors and finally, according to project life cycle theory, they calculated total amount of project risk. In addition, Liu, Zhang, Zhang, and Zhou (2007) proposed a fuzzy risk analysis model in order to calculate total amount of project risk, they assigned risk factors to different periods of project life cycle. We have managed to identify strategies for effective management of these critical issues in VTs at a fine-grained level that prior studies using survey measures of generalized conflict management types have not achieved. Consequently, in order to fulfill this shortcoming, according to PMBOK methodology and considering risk factors and risk assessment systems in virtual project life cycle, we decided to articulate all the phases of risk management of virtual projects in one new model. Pervious mathematic programming models in virtual projects’ risk management are categorized in three classes: (1) without constraints, (2) with time constraint, and (3) with budget constraints, where time and budget constraints are definite values. In our model, since we cannot provide an appropriate risk reaction strategy based on merely budget
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constraint without considering time limitation, time and budget constraints are applied simultaneously. Furthermore, according to the virtual projects’ concepts we must use fuzzy values for budget and time of risk reaction strategies. There are many similarities between virtual project teams and classic project teams. In other words, a virtual project team and a classic project team are directed toward similar results. Moreover, basic project management methodology for both is the same, meaning that, whether the project team is gathered together in one building or is not centralized in a specific workplace, the fundamental procedures are the same (Trautsch, 2003). However, in contrast with classic project management methods, a virtual project requires more efficiency of cooperation between members of the project team. Ayok, Konrad, and Boyle (2012) stated that one major difference in the conflict in Face-To-Face Teams (FTFTs) and virtual teams (VTs) is technology and the lack of opportunity for faceto-face cues and interacting are major sources of conflict in VTs. Classic project management standards are based on the fact that the project can be managed by a predefined plan (Zigurs, 2003). However, in virtual project teams, plans must be updated and decision making must be shared with team members, and a more important distinction, in comparison with classic project teams, is that nothing should be hypothesized. Therefore, Management challenges increase in virtual projects. Therefore, Aldeaa, Popescua, Draghicia, and Draghicib (2012) underlined that VTs have the same problems as traditional teams, but they face new challenges. At the same time, VTs have the potential to achieve further benefits in processes and provide high quality solutions by assembling people with different types of knowledge and expertise. Members of virtual projects do not see each other face to face and for this reason; the cooperation in these teams may abate (Vaslet, 2008). Timing and scheduling in virtual projects, due to several complexities such as separate work places and different cultural backgrounds, are other obstacles that impede the process of defining and articulating project management goals. Managing a virtual team is about managing the whole communication strategies and performing project management technics.
Ending period: disengaging project team members and terminating processes of virtual project take place in this period. We use this classification in this paper in defining periods of virtual project life cycle.
2. Virtual project life cycles
3.1. Risk identification in virtual projects
Project life cycle entails a set of steps, which are critical for achieving project goals. Liu et al. (2007) defined four periods for virtual projects’ life cycle (Fig. 1). Steps of this life cycle are: recognition period, construction period, operation period, and ending period. These periods are discussed briefly as follows. Recognition period: this is the beginning of the project. The main objectives in this period are recognition, evaluation, and selection of opportunities in the business market. Construction period: this period includes determining and selecting work force, designing project structure and designing information and communication systems. Operation period: in this period, resources and expenses are monitored, project processes are conducted and management risks are analyzed.
The most important risk factors, which affect virtual projects, are identified in papers and researches during 2000–2012. Factors that are discussed in just one or two researches are not considered in this paper and we merely deal with those factors, which are discussed and repeated in more than five researches, as virtual project risk factors. We focus on risks stemmed from management shortcomings and in order to avoid intricate issues, we do not handle certain hazards of projects. The factors below are ordered by the emphasis they have received in the literature and researches so far:
Fig. 1. Periods of virtual project life cycle of Liu et al.
2.1. Managing fuzzy models For modeling uncertainty in project management, using fuzzy sets is a better solution. Considering the fact that most of the data about risk recognition are gathered from experts’ notions, it would be more beneficial to model these data within fuzzy context (Söderlund, 2004). Marhavilas, Koulouriotis, and Gemeni (2011) show most of popular risk analysis methods just rely on probability theories and operational research methods introduced in 1950s. Those methods cannot utilize implicit and imprecise information, which are gathered from experts and professionals’ viewpoints in unauthorized ways. From the other hand, due to low repeatability in most events pertaining to virtual projects, this is not reliable to merely use probability methods. Fuzzy models can be classified in four general classes; without time and budget constraints, only with time constraint, only with budget constraint and with both time and budget constraints. Each of which can be analyzed in a number of conditions: certain time and fuzzy budget, fuzzy time and certain budget, and fuzzy time and fuzzy budget. 3. Modeling risk management in virtual project Considering pros and superiorities of PMBOK methodology in providing a risk management framework, we discuss implementation process of virtual project risk management according to this methodology. Risk management process in PMBOK methodology is discussed in six phase: Planning Risk Management, Identifying Risks, Performing Qualitative Risk Analysis, Performing Quantitative Risk Analysis, Planning Risk Responses, Monitoring and Controlling Risks (PMBOKÒ Guide, 2008).
1. Insufficient communication: This factor discusses the shortcomings of communication in project team, which cause adjournments in conducting activities and less quality in doing project activities. In fact managing the communication between members of the team is as important as the relation between the organization and other establishments such as suppliers and customers. 2. Mistrust: lack of mutual trust among virtual team members. 3. Lack of commitment: lack of commitment of team members because of bad monitoring or low job security. 4. Lack of cooperation and coordination among team members: the objective is transforming personal knowledge to organizational knowledge. This objective requires designing an environment where all the people feel comfortable (and are motivated) to share their knowledge.
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5. Inappropriate leadership and control: because of physical absence of people in work place, their performance must be well directed and supervised efficiently. 6. Insufficient incentive and motivational system: due to lack of physical presence in a specific work place in a virtual project, and the possibility of termination of the cooperation between people after completion of the virtual projects, there should be a strong and effective motivational system to provide high motivation levels. 7. Insufficient knowledge and expertise: before the commencement of activities in project teams, it should be ensured that members have the sufficient knowledge and expertise in their specific field and how they communicate with other team members. 8. Lack of information security: due to the use of electronic communication technologies and the availability of such technologies for team members, the information of virtual project teams can be abused, in some cases, attacked, and wrecked. 9. Inappropriate design of project and organization: inappropriate delegation to employees may lead to interruptions in conducting tasks and/or project redesign. 10. Different cultures: this causes conflicts during work processes and even can lead to project set back in the middle. 11. Inappropriate tasks timing: since integration of such projects is much less than classic projects, inappropriate timing and planning of project tasks can cause numerous misfortunes. 12. Failure to provide resources: the provision of virtual projects resources is decentralized and resource management in such projects must be performed with more discretion and prudence so that managers will be able to easily monitor resources more precisely and facilitate provision. 13. Payment issues: those virtual projects which team members leave the team just after project termination face more payment problems with team members. 14. Political state: this is one of unpredictable factors, which should be noted in risk management. 15. Financial condition of target market: lack of correct appraisal of opportunities in target market because of unsatisfactory information and analyzing wrong data about market situation 16. Social state: this is one of unpredictable factors, which should be noticed in risk management.
We attributed risk factors derived from previous researches to each period of the project (one risk factor may be assigned to more than one period). In order to attribute risk factors to periods of project life cycle, in addition to probing papers, we gathered experts’ views in questionnaires. According to researches and the results of questionnaires, identified risks are ordered in risk breakdown structure on the basis of project life cycle of virtual projects. The risk breakdown structure of virtual project according to four periods of project life cycle is shown in Table 1. 3.2. Qualitative analysis of virtual project risks As previously indicated, experts’ views about the possibilities of occurrences of risk factors and the severity of their effects on project goals, were gathered in questionnaires. In order to prioritize risk factors we used Risk Decision Analysis Matrix. The Risk Decision Analysis Matrix is a systematic approach for risk approximation by which risk factors are measured and categorized based on probability and result. Importance of each risk factor is calculated by the following equation:
Risk ¼ probability result
ð1Þ
In order to calculate risk value for each risk factor (in linguistic forms), we used fuzzy variable table in PMBOK methodology containing five choice (very unlikely, unlikely, even, likely, very likely) for probability and (very low, low, medium, high, catastrophic) for Severity. Table 2 shows fuzzy risk values. As it is shown in the table, risk is a function of probability and severity of event. In this technic, probability of event, severity and risk for each factor are presented in linguistic figures. In the succeeding step those data are converted into fuzzy data and for this purpose, triangular fuzzy method is employed. The fuzzy values pertaining to the linguistic variables including probability and severity and risk statements are shown in Table 3. The Centre of Area (COA) method is employed to defuzzificate triangular fuzzy figures into non-fuzzy performance values. Supe ¼ ðal ; am ; au Þ is a triangular fuzzy number, then the outcome pose A of the equation below is a certain amount (Eq. (2)):
A¼
ðau al Þ þ ðam al Þ þ al 3
ð2Þ
Thus, the domain of fuzzy measures of risk, pertaining to each project objectives (time, budget and quality) is as below (Table 4):
Table 1 The risk breakdown structure of virtual projects according to four periods of project life cycle. Recognition period Virtual project team – Financial condition of target market – Inappropriate design of project and organization – Social state – Mistrust – Political state
Construction period
Operating period
Ending period
– Insufficient knowledge and expertise – Inappropriate leadership and control
– Failure to provide resources – Insufficient communication
– Political state – Payment issues
– Failure to provide resources
– Lack of information security
– Inappropriate design of project and organization – Different cultures
– Inappropriate leadership and control
– Financial condition of target market – Social state
– Lack of commitment – – – –
Financial condition of target market Political state Inappropriate tasks timing Social state
– Insufficient incentive and motivational system – Lack of cooperation and coordination Different cultures – Insufficient knowledge and expertise – Lack of commitment – Mistrust – Financial condition of target market – Inappropriate tasks timing – Social state – Political state
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M. Ghaffari et al. / Computers & Industrial Engineering 72 (2014) 98–105 Table 2 Matrix of risk decision analysis. Severity probability
Very low
Low
Medium
High
Catastrophic
Very Unlikely Unlikely Even Likely Very likely
Low Low Low Medium Significant
Low Low Medium Significant Significant
Medium Medium Significant Significant High
Significant Significant High High High
Significant High High High High
Table 3 Fuzzy and linguistic values of probability, severity and risk (Ebrat and Ghodsi, 2011). Linguistic value
Fuzzy value
Linguistic variables (probability of risk occurrence) Very unlikely Unlikely Even Likely Very likely
(0, 0.125, 0.25) (0.05, 0.275, 0.5) (0.25, 0.5, 0.75) (0.5, 0.725, 0.95) (0.75, 0.875, 1)
Linguistic variables (severity of risk occurrence) Very Little Little Medium High Catastrophic
(0, 1.25, 2.5) (0.5, 2.75, 5) (2.5, 5, 7.5) (5, 7.25, 9.5) (7.5, 8.75, 10)
Linguistic variables (risk value) Low Medium Significant High
(0, 0.165, 0.33) (0.05, 0.355, 0.66) (0.33, 0.64, 0.95) (0.66, 0.83, 1)
3.2.1. Prioritization of identified risk factors A three-step method was used in order to prioritize identified risk factors. 1. The numerical risk scales of each factor are calculated according to PMBOK methodology and pertaining to each project objectives (time, budget and quality). 2. For each risk factor, risk is multiplied in the weight of each objective and all such products are summed to generate average risk value of each factor. 3. Risk factors are arranged by ascending order of risk values. This paper offers a general model for risk analysis therefore the risk will be classified according to standard classifications. According to Liu et al. (2007), if the risk amount is bigger or equal to 70%, the risk is high, lower or equal to 30%, the risk is low and between these two amounts the risk is even. These figures may differ depending on the nature of the projects. According to this classification in qualitative analysis, the priority of risk factors in virtual projects can be categorized into three classes. Insufficient communication, failure to provide resources, insufficient knowledge and expertise, inappropriate leadership and control, lack of commitment, lack of cooperation and coordination, inappropriate design of project and organization, and inappropriate task timing factors are classified in the first class as the most risky factors. Insufficient motivational system, inappropriate
Table 4 Fuzzy scales of risk value. Cost – Time – Quality Low
Medium
Significant
High
(0, 0.165, 0.33) e ¼ 0:165 Fð AÞ
(0.05, 0.355, 0.66) e ¼ 0:355 Fð AÞ
(0.33, 0.64, 0.95) e ¼ 0:64 Fð AÞ
e ¼ 0:83 Fð AÞ
(0.66, 0.83, 1)
financial condition of target market, lack of information security, mistrust and political status are classified in the second class as the middle risky factors. Different cultural backgrounds, payment issues and social class are listed in the third class, which represents the least risky factors. In the next step, factors with higher priority in comparison other factors, are assigned higher importance in risk quantification process. 3.3. Accepting the risk or reaction? It is obvious that employing reaction strategies to risk entails certain amounts of time and budget. Therefore, the risk management team, on the basis of the information attained previously described in this paper, must decide between these choices: To ignore the risk or to react to the risk. This decision should not be made just based on total risk amount of project. Since there is a possibility that the risk amount of a period would be more than the acceptable limits, but because of other factors such as lower risk amounts of next periods, managers decide to accept the risk and overlook using reaction strategies. So in order to make sure that the right decision is made, the risk should be calculated for each period separately. For this purpose, we assigned weights to all periods and finally by multiplying these weights in the risk of the pertinent period, a partial risk named decision risk is produced. The weights of different periods of project life cycle are shown in Table 5. Hence, weights of different periods are obtained respectively from Eqs. (3)–(6):
@ t ¼ 1; w þ w=2 þ w=3 þ w=4 ¼ 1
ð3Þ
@ t ¼ 2; w þ w=2 þ w=3 ¼ 1
ð4Þ
@ t ¼ 3; w þ w=2 ¼ 1
ð5Þ
@ t ¼ 4; w ¼ 1
ð6Þ
If decision risk is lower than 30%, the risk is acceptable, there is no need to react to risk in that period, and we should wait for risk reanalysis process. If decision risk is between 30% and 70% then reaction to risk is an obligatory, which we discuss in next steps. Decision risk more than 70% specifies fatal condition and accordingly the whole characteristics must be immediately analyzed and this may lead to early termination of the project. 3.4. Quantitative risk analysis of virtual projects The objective of implementing this phase is to select appropriate risk reaction strategies to each risk factor, so that, given budget and time constraints, the total amount of project risk will be minimized. Strategies for reacting to risk factors, budget and time, and reaction process in each period of the project life cycle should be determined according to total budget and time of the whole project. To focus merely on risk reaction strategies in period t, regardless of those of the succeeding periods, most probably results in only minimizing risks of period t and also impedes formation of better risk reaction strategies in the next periods to reduce total
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Table 5 Weights of project life cycle periods.
Under Under Under Under
review review review review
@ @ @ @
period period period period
1 2 3 4
Weight of period 1
Weight of period 2
Weight of period 3
Weight of period 4
0.48
0.24 0.55
0.16 0.27 0.34
0.12 0.18 0.66 1
amount of project risk. To solve such problem in implementation phase of quantitative analysis model and therefore to reduce total risk of the project, we define a minimizing objective function for period t, containing risk factors of period t and succeeding periods. When period t is over, in the next period, strategies and parameters of the model are revised and it is examined if the optimum answer in the new period is changed. 3.4.1. Fuzzy mathematic programming model for quantitative analyzing of virtual project risks As we said, if any period needs a risk reaction strategy, quantitative analysis model in each period is performed. 3.4.1.1. Model hypotheses. 1. The number of risk factors is fixed and must be determined before. 2. Probability and severity of risk effects are definite and uncertain (fuzzy). 3. The amount of risk for each factor is available on the basis of PMBOK methodology and its defuzzificated value is used in the model. 4. The cost of risk reaction strategies and the time added to the project for implementing these strategies are certain and fuzzy (uncertain). 5. The model has several objective functions which by assigning weight to each of them as their importance degree, one main objective function is formed (three main characteristics comprising time, quality and cost, are weighted respectively 0.3, 0.4 and 0.3 and are used to calculate total risk of the project). It should be noted that weights of the main characteristics of project, depending on nature of the project and its specifications, might be assigned by different values. Suitable weights are the choice of project manager. In order to provide the quantitative analysis model of virtual project risks, some symbols are presented as follows (see Table 6). Quantitative analysis modeling of virtual project risks in period a is as follows:
Min ðaggregate risk of projectÞ
ð7Þ
s.t. ji nt X i X X ij xij 6 B e C
ð8Þ
t¼a i¼1 j¼0 ji nt X i X X t ij xij 6 T
ð9Þ
t¼a j¼1 j¼0 ji X xij ¼ 1; i ¼ 1; 2; . . . ; nt ; t ¼ a; . . . ; 1
ð10Þ
Table 6 Symbols and initiations of quantitative analysis model of virtual project risks. Description
Indexes
Number of risk factors, i = 1, . . ., nt Number of strategies for risk factor i, Ji = 0, . . ., ji Number of periods of project life cycle, t = 1, . . ., l Set of project objectives, S = {time, cost, quality}
I Ji T S
Description
Decision variables xij
Binary variables: if strategy j is chosen for risk factor i then xij = 1, else xij = 0 Description Number of risk factors for period t Number of periods Number of project objectives Number of strategies for risk factor i Defuzzificated value of risk factor i affected by strategy j according to objective s Value of risk factor i according to objective s Integrated risk of project in period t according to objective s Integrated risk of project according to objective s Total integrated risk of project Weight of risk factor i in period t according to objective s Weight of period t in determining total project risk Weight of objective s in determination of total project risk The amount of budget alloted to risk control as a fuzzy number Cost of strategy j for risk factor i as a fuzzy number The amount of time dedicated to risk control as a fuzzy number Time of strategy j for risk factor i as a fuzzy number
xij ¼
1 if j strategy is selected for i risk 0 if j strategy is not selected for i risk
ð11Þ
Ris IRst IRs IRp dist dt ds e ¼ ðbp ; bm ; bo Þ B e ij ¼ ðcp ; cm ; co Þ C ij ij ij e ¼ ðT p ; T m ; T o Þ T ~tij ¼ tp ; tm ; t o ij ij ij
Objective function (Eq. (7)) minimizes total amount of virtual project risk on the basis of selected risk reaction strategies. The first constraint (Eq. (8)) demonstrates the specific amount of budget allocated to risk reaction process in order to keep expenditures within predefined boundaries. Second constraint (Eq. (9)) illustrates time limitation for risk reaction process, in order to keep track of time (of implementing each strategy). Third constraint (Eq. (10)) ensures that there is a specific risk reaction strategy for each risk factor (selecting j = 0 strategy, means that some risk is incurred and there is no reaction plan regarding that risk). The last constraint (Eq. (11)) specifies feasible amounts of factors. Here is the procedure of calculating total amount of project risk (which is supposed to be minimized): 1. According to Huang, Qiang, ching, and Kuen (2011), using following formula, risk amount of factor i, based on subobjective s is:
Ris ¼
j¼ji X Rijs xij
ð12Þ
j¼0
j¼0
X ij ¼ 0 or i ¼ 1; . . . ; nt and j ¼ 0; . . . ; ji and t ¼ a; . . . ; l
Parameters nt L N ji Rijs
2. The cumulative risk of project in period t, according to objective s, is calculated as follows:
IRst ¼
nt X dist Ris i¼1
ð13Þ
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3. Total cumulative risk of the project, on the basis of each objective, is:
IRs ¼
l X dt IRst
ð14Þ
t¼a
4. In order to calculate total amount of project risk, we use parametric summation of fuzzy numbers. The coefficient for each variable in objective function is determined so that the target function will be transformed into certain linear programming (Ebrat & Ghodsi, 2011; Hyeongon & Mooyoung, 2010; Liu et al. 2007): N X IRp ¼ ds IRs
ð15Þ
s¼1
The result is a linear programming problem with fuzzy right hand sides and fuzzy coefficients of constraints. Considering the solution of such problems, quantitative analysis model of virtual projects in period a is as follows:
Min ðtotal project riskÞ
ð16Þ
s.t. ji nt X l X X p cpij xij 6 b
ð17Þ
t¼a i¼1 j¼0
ji nt X l X X p m ðcpij cm ij Þxij 6 ðb b Þ
ð18Þ
t¼a i¼1 j¼0
ji nt X l X X p o ðcpij þ coij Þxij 6 ðb þ b Þ
ð19Þ
t¼a i¼1 j¼0
ji nt X l X X t pij xij 6 T p
ð20Þ
t¼a i¼1 j¼0
ji nt X l X X p m ðt pij tm ij Þxij 6 ðT T Þ
ð21Þ
t¼a I¼1 j¼0
ji nt X l X X ðt pij þ toij Þxij 6 ðT p þ T o Þ
Before implementing quantitative analysis model, the total amount of project risk (extracted from expert judgement questionaires) is assumed as 0.5375 which is more than 0.3 and requires appropriate reaction. By running our model in GAMS, the amounts of risk for each periods of project life cycle are calculated according to selected strategies (Table 7) and the total amount of project risk is 0.2144. As Table 7 shows, by implementing risk strategies, the total project risk is reduced significantly, in addition budget and time constraints are satisfied. 4.2. Numeric example for second period of project life cycle It is necessary to revise the model in the beginning of each period. As a result of implementing risk reaction strategies in previous period, there is a possibility that risk of the current period is also reduced, and therefore there is no necessity for implementing risk reaction strategies in the upcoming period. On the other hand, by resolving model and changing parameters at the beginning of this period, strategies that were selected in previous periods may not produce the overall optimum solution any more. Thus, the quantitative analysis phase of the model should be reimplemented in different periods of project life cycle. After implementing strategies of first period, at the beginning of second period the total amount of project risk is recalculated. The total risk of the project at this time is 0.486. The amount of total project risk has declined at the beginning of second period; however it is still more than 0.3. Therefore the mathematic model and reactions to risk at the beginning of this period must be reimplemented. After implementing the model in GAMS, for the second period, the amount of risk in each period of project life cycle, according to selected risk reaction strategies, is calculated and shown in Table 8. The total amount of project risk is 0.1812. As it was expected, the selected strategies for some of risk factors in this period is different from those of previous periods. For instance, for the risk factor, ‘‘insufficient knowledge and expertise’’, in the first period, the strategy, ‘‘teaching required expertise and knowledge to team members’’, was selected, but in this period the strategy, ‘‘changing the composition of professionals in suitable places with specific expertise requirement’’, is chosen. This change is the result of the fact that, by elapsing the first period and implementing selected strategies for risk factors in the first period, the
ð22Þ
t¼a i¼1 j¼0
ji X xij ¼ 1 i ¼ 1; 2; . . . ; nt t ¼ a; . . . ; l
ð23Þ
j¼0
xij ¼ 0—1 i ¼ 1; . . . ; n j ¼ 0; . . . ; ji t ¼ a; . . . ; l xij ¼
ð24Þ
1 strategy j for risk factor i is choosen; 0
otherwise;
Table 7 The amount of project risk in each period of project life cycle, after implementing the model in first period. Period of life cycle
Risk amount
t=1 t=2 t=3 t=4
0.22021 0.19942 0.19292 0.24955
for solving the model for each situation a program has been written by Gams software, which is ready to be run in all periods. 4. Numerical example of virtual project risk management model 4.1. Numerical example for first period of project life cycle Implementing the model at the beginning of the first period of project life cycle, determines risk reaction strategies of first, second, third and fourth periods.
Table 8 The amount of project risk in each period of project life cycle, after implementing the model in second period. Period of life cycle
Risk amount
t=2 t=3 t=4
0.1745 0.18023 0.20295
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amount of risk, the budget and time of implementing strategies has changed for factors of second period. Thus updating such parameters, produces new optimum answer for the model. Examining these two strategies for the risk factor, ‘‘insufficient knowledge and expertise’’, indicates that the strategy, ‘‘changing the composition of professionals in suitable places with specific expertise requirement’’, consumes less time and budget in comparison with the other strategy ‘‘teaching required expertise and knowledge to team members’’. Also, the amount of risk of second period after implementing the model, is 0.1745 which is reduced in comparison with the previous amount of 0.1994. This decrease in risk indicates that the selected strategies of this period produce better optimum answers than those of previous periods. Furthermore, the total amount of project risk is 0.1812, which is less than the total risk amount in the previous period (0.2144). In order to analyze the model in detail, again we carry out the quantitative analysis model of project risk for fourth period. 4.3. Numeric example in fourth period of project life cycle After revising and updating model parameters in this period and implementation in GAMS, given selected strategies, the total amount of the project is 0.203.a. Eventually, the total amount of risk in fourth period shows that the amount of risk, by practicing reaction strategies, changes from 0.5275 to 0.2030. The total time and budget consumption for practicing reaction strategies of risk factors, can be easily calculated through summation of the whole time and budget consumed in each period of the project. 5. Discussion and conclusion In this research, by the aid of fuzzy logic, we tried to provide a risk analysis model for managing virtual projects in order to fulfill the lack of specific procedure in risk management of virtual projects. Since PMBOK methodology is the most popular methodology for project management, the risk management methodology employed for this research and including the components of risk analysis process, is PMBOK methodology. We also discussed the integrated use of fuzzy risk analysis model along with PMBOK standards to generate more accurate analyses. This includes implementing risk analysis and management at the beginning of each period as an iterative process. In recognition phase of risk factors, the risk breakdown structure was designed. Then risks stemmed from reasearch consequences were assigned to different periods of project life cycle, in order to be able to calculate its effects on each period (one risk factor may have been allotted to several periods). After recognition, in risk qualitative analysis phase, the factor of communication was intruduced as the most effective one in risk management of virtual projects. The other important factors, in the order of importance were lack of resource provision, insufficient knowledge and expertise, inappropriate leadership and control, lack of commitment, lack of cooperation and coordination, inappropriate design of project and organization, inappropriate task timing, insufficient motivational system, financial situation of the market, lack of information security, lack of mutual trust, political status, different cultures, payment issues and social status. Those factors with higher priority in comparison with other factors, were assingned more importance degrees in quantification process of risk. When decision risk was calculated at the beginning of each period (total risk of the project), if the amount of risk were lower than 0.3, the risk was acceptable and there was no necessity to implement risk reaction strategies. The risk between 0.3 and 0.7 indicated that there was an obligation to perform next steps and determination and
implementation of risk reaction strategies. When the risk was higher than 0.7, the situation was described as critical conditions and it shows that all the conditions should be reexamined and it may even lead to early termination. In quantitative analysis phase, risk reaction strategies were determined and the linear fuzzy mathematic programming model with time and budget constraints was introduced. We used fuzzy values for coefficients of constraints and the right side amounts for more actualization of the model. The model should be repeated throughout project life cycle periods. At the beginning of period t, the objective function of the model minimized the risk of project considering risk factors of period t and succeeding periods. After solving the model, risk reaction strategies for all factors were determined. Then the selected strategies for the ongoing period were implemented. At the beginning of next period, the decision risk (total amount of project risk) was calculated and if the risk was higher than 0.3, the model was reimplemented and risk reaction strategies were redetermined and practiced. These selected strategies in this period might have been different from the optimum strategies in the previous period and that was because, by implementing strategies selected in the previous period, and updating parameters and strategies of the model in the current period, the results may differ. In order to test implementation process of the proposed model, we used this model in numerical examples at the commencement of first, second and fourth periods of the project. At the beginning of first period the total amount of project risk was 0.5375 and as it was more than 0.3, risk reaction strategies were offered. The results showed that implementing risk analysis model in the example reduces the overall risk amount from 0.5375 to 0.2030 and meanwhile time and budget constraints were satisfied. Here are some suggestions for future works on the basis of this paper: 1. Analysis of proposed models as case studies in several firms with virtual projects. 2. Results comparison of proposed models in numeric examples without considering risk management in periods of project life cycles. 3. Solving the proposed model by using data derived from other researches and comparing results. 4. Estimating the trend of overall project risk according to time and budget of reaction strategy which can help managers to assess the time and budget needed to conduct a project before its start point.
References Aldeaa, Cosmina Carmen, Popescua, Anca-Diana, Draghicia, Anca, & Draghicib, George (2012). ICT tools functionalities analysis for the decision making process of their implementation in virtual engineering teams. Procedia Technology, 5, 649–658. Ayok, Oluremi B., Konrad, Alison M., & Boyle, Maree V. (2012). Online work: Managing conflict and emotions for performance in virtual teams. European Management Journal, 30(2), 156–174. Ebrat, M., & Ghodsi, R. (2011). Risk assessment of construction projects using network based adaptive fuzzy system. International Journal of Academic Research, 3(1), 411–417. Huang, M., Qiang, Lu. F., ching, W. Ki., & Kuen, Siu. T. (2011). A distributed decision making model for risk management of virtual enterprise. Expert systems with Applications Journal, 38(10), 13208–13215. Hyeongon, Wi., & Mooyoung, Jung. (2010). Modeling and analysis of project performance factors in an extended project-oriented virtual organization (EProVO). Expert Systems with Applications Journal, 37, 1143–1151. Iorio, Josh, & Taylor, John E. (2013). Boundary object efficacy: The mediating role of boundary objects on task conflict in global virtual project networks. International Journal of Project Management..
M. Ghaffari et al. / Computers & Industrial Engineering 72 (2014) 98–105 Liu, G., Zhang, J., Zhang, W., & Zhou, X. (2007). Risk assessment of virtual enterprise based on the Fuzzy Comprehensive Evaluation Method. IFIP – The International Federation for Information Processing, 251, 58–66. Luse, Andy, McElroy, James C., Townsend, Anthony M., & DeMarie, Samuel (2013). Personality and cognitive style as predictors of preference for working in virtual teams. Computers in Human Behavior Journal, 29(4), 1825–1832. Marhavilas, P. K., Koulouriotis, D., & Gemeni, V. (2011). Risk analysis and assessment methodologies in the work sites: On a review, classification and comparative study of the scientific literature of the period 2000–2009. Journal of Loss Prevention in the Process Industries, 24(5), 477–523. Project Management Institute, 2008. A guide to the project management body of knowledge (PMBOKÒ Guide) (4th ed.).
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Söderlund, J. (2004). Building theories of project management: Past research, questions for the future. International Journal of Project Management, 22(3), 183–191. Trautsch, B. R., 2003. MANAGING VIRTUAL PROJECT TEAMS. A research project submitted to the faculty of San Francisco State University in partial fulfillment of the requirements for the degree. Vaslet, S., 2008. Think globally: Managing a virtual team. In the Nova Scotia Business Journal, November edition. Xie, G., Zhang, J., & Lai, K. K. (2006). Risk avoidance in bidding for software projects based on life cycle management theory. International Journal of Project Management, 24(6), 516–521. Zigurs, I. (2003). Leadership in virtual teams: Oxymoron or opportunity? Organizational Dynamics Journal, 31, 339–351.
Contents lists available at ScienceDirect
Computers & Industrial Engineering journal homepage: www.elsevier.com/locate/caie
Modeling and risk analysis of virtual project team through project life cycle with fuzzy approach Mona Ghaffari a,⇑, Farrokh Sheikhahmadi b, Gholamreza Safakish c a
Department of Engineering, Alzahra University, Tehran 1993893973, Iran Department of Business Administration, College of Social Science, Semnan University, Semnan, Iran c CEO, Datis Management Consultants, Apt804, No. 55, Sarafraz St., Dr. Beheshti, Tehran 1587698474, Iran b
a r t i c l e
i n f o
Article history: Received 23 August 2013 Received in revised form 22 February 2014 Accepted 25 February 2014 Available online 15 March 2014 Keywords: Virtual project team Risk analysis Risk management Project life cycle Fuzzy set
a b s t r a c t The ongoing revolutions in e-business and progresses of IT and communication, has resulted in the increasing number of companies with formal virtual project teams. In such situation, Uncertainty analysis gains more importance, being conducted within risk management framework. In this paper, based on the six phases of risk management procedure in PMBOK methodology, a risk management process in virtual projects is introduced. In qualitative analysis phase (of PMBOK methodology), the most effective factors of project management in virtual project teams are prioritized. In quantitative analysis phase, for the very first time, ‘‘Fuzzy Linear Programming Model’’ is employed to assess project risks based on project life cycle. Also given time and budget constraints, a method for developing appropriate strategies of reacting to each risk factor is introduced. We use GAMS (General Algebraic Modeling System) to select these strategies. Finally, we test our model in a numerical example, as evidence. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction According to Luse, McElroy, Townsend, and DeMarie (2013), virtual teams (VTs) are characterized as a group of people with unique skills who work interdependently but are separated geographically and they need technological mediums to communicate. Thus, virtual teams allow members to accomplish specific tasks while transcending traditional restrictions of time and proximity. Consequently, VTs differ from classic teams which people are physically concentrated in one place. In VTs, members are physically separated from one another and they rely on technological devices for communication and information exchange. Project-based industries such as Architecture, Engineering and Construction are becoming more globalized as firms seeking to access specialized knowledge from all parts of the world. Gartner group (www.gartner.com) predicts that, by 2004, more than 60% of the professional workforces in the Global 2000 Companies will most probably work in virtual teams. By 2003, half of the existing VTs failed to meet either strategic or operational objectives due to inability to manage geographically distributed workforce (Iorio & Taylor, 2013). The concept of Dynamic Risk Management in virtual projects, which can be implemented according to project life cycle, is a new concept. In the model proposed in this paper, in order to apply ⇑ Corresponding author. Tel.: +98 9355130560. E-mail address: [email protected] (M. Ghaffari). http://dx.doi.org/10.1016/j.cie.2014.02.011 0360-8352/Ó 2014 Elsevier Ltd. All rights reserved.
dynamic risk management, project manager must repeatedly evaluate risk factors at the end of each phase or before big changes, and if necessary, s/he must apply suitable strategies for the next phases. In the literature of risk management and project life cycle, risk reaction strategies are barely discussed. For example, Xie, Zhang, and Lai (2006) introduced different periods of project life cycle in software projects then they determined risk factors and finally, according to project life cycle theory, they calculated total amount of project risk. In addition, Liu, Zhang, Zhang, and Zhou (2007) proposed a fuzzy risk analysis model in order to calculate total amount of project risk, they assigned risk factors to different periods of project life cycle. We have managed to identify strategies for effective management of these critical issues in VTs at a fine-grained level that prior studies using survey measures of generalized conflict management types have not achieved. Consequently, in order to fulfill this shortcoming, according to PMBOK methodology and considering risk factors and risk assessment systems in virtual project life cycle, we decided to articulate all the phases of risk management of virtual projects in one new model. Pervious mathematic programming models in virtual projects’ risk management are categorized in three classes: (1) without constraints, (2) with time constraint, and (3) with budget constraints, where time and budget constraints are definite values. In our model, since we cannot provide an appropriate risk reaction strategy based on merely budget
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constraint without considering time limitation, time and budget constraints are applied simultaneously. Furthermore, according to the virtual projects’ concepts we must use fuzzy values for budget and time of risk reaction strategies. There are many similarities between virtual project teams and classic project teams. In other words, a virtual project team and a classic project team are directed toward similar results. Moreover, basic project management methodology for both is the same, meaning that, whether the project team is gathered together in one building or is not centralized in a specific workplace, the fundamental procedures are the same (Trautsch, 2003). However, in contrast with classic project management methods, a virtual project requires more efficiency of cooperation between members of the project team. Ayok, Konrad, and Boyle (2012) stated that one major difference in the conflict in Face-To-Face Teams (FTFTs) and virtual teams (VTs) is technology and the lack of opportunity for faceto-face cues and interacting are major sources of conflict in VTs. Classic project management standards are based on the fact that the project can be managed by a predefined plan (Zigurs, 2003). However, in virtual project teams, plans must be updated and decision making must be shared with team members, and a more important distinction, in comparison with classic project teams, is that nothing should be hypothesized. Therefore, Management challenges increase in virtual projects. Therefore, Aldeaa, Popescua, Draghicia, and Draghicib (2012) underlined that VTs have the same problems as traditional teams, but they face new challenges. At the same time, VTs have the potential to achieve further benefits in processes and provide high quality solutions by assembling people with different types of knowledge and expertise. Members of virtual projects do not see each other face to face and for this reason; the cooperation in these teams may abate (Vaslet, 2008). Timing and scheduling in virtual projects, due to several complexities such as separate work places and different cultural backgrounds, are other obstacles that impede the process of defining and articulating project management goals. Managing a virtual team is about managing the whole communication strategies and performing project management technics.
Ending period: disengaging project team members and terminating processes of virtual project take place in this period. We use this classification in this paper in defining periods of virtual project life cycle.
2. Virtual project life cycles
3.1. Risk identification in virtual projects
Project life cycle entails a set of steps, which are critical for achieving project goals. Liu et al. (2007) defined four periods for virtual projects’ life cycle (Fig. 1). Steps of this life cycle are: recognition period, construction period, operation period, and ending period. These periods are discussed briefly as follows. Recognition period: this is the beginning of the project. The main objectives in this period are recognition, evaluation, and selection of opportunities in the business market. Construction period: this period includes determining and selecting work force, designing project structure and designing information and communication systems. Operation period: in this period, resources and expenses are monitored, project processes are conducted and management risks are analyzed.
The most important risk factors, which affect virtual projects, are identified in papers and researches during 2000–2012. Factors that are discussed in just one or two researches are not considered in this paper and we merely deal with those factors, which are discussed and repeated in more than five researches, as virtual project risk factors. We focus on risks stemmed from management shortcomings and in order to avoid intricate issues, we do not handle certain hazards of projects. The factors below are ordered by the emphasis they have received in the literature and researches so far:
Fig. 1. Periods of virtual project life cycle of Liu et al.
2.1. Managing fuzzy models For modeling uncertainty in project management, using fuzzy sets is a better solution. Considering the fact that most of the data about risk recognition are gathered from experts’ notions, it would be more beneficial to model these data within fuzzy context (Söderlund, 2004). Marhavilas, Koulouriotis, and Gemeni (2011) show most of popular risk analysis methods just rely on probability theories and operational research methods introduced in 1950s. Those methods cannot utilize implicit and imprecise information, which are gathered from experts and professionals’ viewpoints in unauthorized ways. From the other hand, due to low repeatability in most events pertaining to virtual projects, this is not reliable to merely use probability methods. Fuzzy models can be classified in four general classes; without time and budget constraints, only with time constraint, only with budget constraint and with both time and budget constraints. Each of which can be analyzed in a number of conditions: certain time and fuzzy budget, fuzzy time and certain budget, and fuzzy time and fuzzy budget. 3. Modeling risk management in virtual project Considering pros and superiorities of PMBOK methodology in providing a risk management framework, we discuss implementation process of virtual project risk management according to this methodology. Risk management process in PMBOK methodology is discussed in six phase: Planning Risk Management, Identifying Risks, Performing Qualitative Risk Analysis, Performing Quantitative Risk Analysis, Planning Risk Responses, Monitoring and Controlling Risks (PMBOKÒ Guide, 2008).
1. Insufficient communication: This factor discusses the shortcomings of communication in project team, which cause adjournments in conducting activities and less quality in doing project activities. In fact managing the communication between members of the team is as important as the relation between the organization and other establishments such as suppliers and customers. 2. Mistrust: lack of mutual trust among virtual team members. 3. Lack of commitment: lack of commitment of team members because of bad monitoring or low job security. 4. Lack of cooperation and coordination among team members: the objective is transforming personal knowledge to organizational knowledge. This objective requires designing an environment where all the people feel comfortable (and are motivated) to share their knowledge.
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5. Inappropriate leadership and control: because of physical absence of people in work place, their performance must be well directed and supervised efficiently. 6. Insufficient incentive and motivational system: due to lack of physical presence in a specific work place in a virtual project, and the possibility of termination of the cooperation between people after completion of the virtual projects, there should be a strong and effective motivational system to provide high motivation levels. 7. Insufficient knowledge and expertise: before the commencement of activities in project teams, it should be ensured that members have the sufficient knowledge and expertise in their specific field and how they communicate with other team members. 8. Lack of information security: due to the use of electronic communication technologies and the availability of such technologies for team members, the information of virtual project teams can be abused, in some cases, attacked, and wrecked. 9. Inappropriate design of project and organization: inappropriate delegation to employees may lead to interruptions in conducting tasks and/or project redesign. 10. Different cultures: this causes conflicts during work processes and even can lead to project set back in the middle. 11. Inappropriate tasks timing: since integration of such projects is much less than classic projects, inappropriate timing and planning of project tasks can cause numerous misfortunes. 12. Failure to provide resources: the provision of virtual projects resources is decentralized and resource management in such projects must be performed with more discretion and prudence so that managers will be able to easily monitor resources more precisely and facilitate provision. 13. Payment issues: those virtual projects which team members leave the team just after project termination face more payment problems with team members. 14. Political state: this is one of unpredictable factors, which should be noted in risk management. 15. Financial condition of target market: lack of correct appraisal of opportunities in target market because of unsatisfactory information and analyzing wrong data about market situation 16. Social state: this is one of unpredictable factors, which should be noticed in risk management.
We attributed risk factors derived from previous researches to each period of the project (one risk factor may be assigned to more than one period). In order to attribute risk factors to periods of project life cycle, in addition to probing papers, we gathered experts’ views in questionnaires. According to researches and the results of questionnaires, identified risks are ordered in risk breakdown structure on the basis of project life cycle of virtual projects. The risk breakdown structure of virtual project according to four periods of project life cycle is shown in Table 1. 3.2. Qualitative analysis of virtual project risks As previously indicated, experts’ views about the possibilities of occurrences of risk factors and the severity of their effects on project goals, were gathered in questionnaires. In order to prioritize risk factors we used Risk Decision Analysis Matrix. The Risk Decision Analysis Matrix is a systematic approach for risk approximation by which risk factors are measured and categorized based on probability and result. Importance of each risk factor is calculated by the following equation:
Risk ¼ probability result
ð1Þ
In order to calculate risk value for each risk factor (in linguistic forms), we used fuzzy variable table in PMBOK methodology containing five choice (very unlikely, unlikely, even, likely, very likely) for probability and (very low, low, medium, high, catastrophic) for Severity. Table 2 shows fuzzy risk values. As it is shown in the table, risk is a function of probability and severity of event. In this technic, probability of event, severity and risk for each factor are presented in linguistic figures. In the succeeding step those data are converted into fuzzy data and for this purpose, triangular fuzzy method is employed. The fuzzy values pertaining to the linguistic variables including probability and severity and risk statements are shown in Table 3. The Centre of Area (COA) method is employed to defuzzificate triangular fuzzy figures into non-fuzzy performance values. Supe ¼ ðal ; am ; au Þ is a triangular fuzzy number, then the outcome pose A of the equation below is a certain amount (Eq. (2)):
A¼
ðau al Þ þ ðam al Þ þ al 3
ð2Þ
Thus, the domain of fuzzy measures of risk, pertaining to each project objectives (time, budget and quality) is as below (Table 4):
Table 1 The risk breakdown structure of virtual projects according to four periods of project life cycle. Recognition period Virtual project team – Financial condition of target market – Inappropriate design of project and organization – Social state – Mistrust – Political state
Construction period
Operating period
Ending period
– Insufficient knowledge and expertise – Inappropriate leadership and control
– Failure to provide resources – Insufficient communication
– Political state – Payment issues
– Failure to provide resources
– Lack of information security
– Inappropriate design of project and organization – Different cultures
– Inappropriate leadership and control
– Financial condition of target market – Social state
– Lack of commitment – – – –
Financial condition of target market Political state Inappropriate tasks timing Social state
– Insufficient incentive and motivational system – Lack of cooperation and coordination Different cultures – Insufficient knowledge and expertise – Lack of commitment – Mistrust – Financial condition of target market – Inappropriate tasks timing – Social state – Political state
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M. Ghaffari et al. / Computers & Industrial Engineering 72 (2014) 98–105 Table 2 Matrix of risk decision analysis. Severity probability
Very low
Low
Medium
High
Catastrophic
Very Unlikely Unlikely Even Likely Very likely
Low Low Low Medium Significant
Low Low Medium Significant Significant
Medium Medium Significant Significant High
Significant Significant High High High
Significant High High High High
Table 3 Fuzzy and linguistic values of probability, severity and risk (Ebrat and Ghodsi, 2011). Linguistic value
Fuzzy value
Linguistic variables (probability of risk occurrence) Very unlikely Unlikely Even Likely Very likely
(0, 0.125, 0.25) (0.05, 0.275, 0.5) (0.25, 0.5, 0.75) (0.5, 0.725, 0.95) (0.75, 0.875, 1)
Linguistic variables (severity of risk occurrence) Very Little Little Medium High Catastrophic
(0, 1.25, 2.5) (0.5, 2.75, 5) (2.5, 5, 7.5) (5, 7.25, 9.5) (7.5, 8.75, 10)
Linguistic variables (risk value) Low Medium Significant High
(0, 0.165, 0.33) (0.05, 0.355, 0.66) (0.33, 0.64, 0.95) (0.66, 0.83, 1)
3.2.1. Prioritization of identified risk factors A three-step method was used in order to prioritize identified risk factors. 1. The numerical risk scales of each factor are calculated according to PMBOK methodology and pertaining to each project objectives (time, budget and quality). 2. For each risk factor, risk is multiplied in the weight of each objective and all such products are summed to generate average risk value of each factor. 3. Risk factors are arranged by ascending order of risk values. This paper offers a general model for risk analysis therefore the risk will be classified according to standard classifications. According to Liu et al. (2007), if the risk amount is bigger or equal to 70%, the risk is high, lower or equal to 30%, the risk is low and between these two amounts the risk is even. These figures may differ depending on the nature of the projects. According to this classification in qualitative analysis, the priority of risk factors in virtual projects can be categorized into three classes. Insufficient communication, failure to provide resources, insufficient knowledge and expertise, inappropriate leadership and control, lack of commitment, lack of cooperation and coordination, inappropriate design of project and organization, and inappropriate task timing factors are classified in the first class as the most risky factors. Insufficient motivational system, inappropriate
Table 4 Fuzzy scales of risk value. Cost – Time – Quality Low
Medium
Significant
High
(0, 0.165, 0.33) e ¼ 0:165 Fð AÞ
(0.05, 0.355, 0.66) e ¼ 0:355 Fð AÞ
(0.33, 0.64, 0.95) e ¼ 0:64 Fð AÞ
e ¼ 0:83 Fð AÞ
(0.66, 0.83, 1)
financial condition of target market, lack of information security, mistrust and political status are classified in the second class as the middle risky factors. Different cultural backgrounds, payment issues and social class are listed in the third class, which represents the least risky factors. In the next step, factors with higher priority in comparison other factors, are assigned higher importance in risk quantification process. 3.3. Accepting the risk or reaction? It is obvious that employing reaction strategies to risk entails certain amounts of time and budget. Therefore, the risk management team, on the basis of the information attained previously described in this paper, must decide between these choices: To ignore the risk or to react to the risk. This decision should not be made just based on total risk amount of project. Since there is a possibility that the risk amount of a period would be more than the acceptable limits, but because of other factors such as lower risk amounts of next periods, managers decide to accept the risk and overlook using reaction strategies. So in order to make sure that the right decision is made, the risk should be calculated for each period separately. For this purpose, we assigned weights to all periods and finally by multiplying these weights in the risk of the pertinent period, a partial risk named decision risk is produced. The weights of different periods of project life cycle are shown in Table 5. Hence, weights of different periods are obtained respectively from Eqs. (3)–(6):
@ t ¼ 1; w þ w=2 þ w=3 þ w=4 ¼ 1
ð3Þ
@ t ¼ 2; w þ w=2 þ w=3 ¼ 1
ð4Þ
@ t ¼ 3; w þ w=2 ¼ 1
ð5Þ
@ t ¼ 4; w ¼ 1
ð6Þ
If decision risk is lower than 30%, the risk is acceptable, there is no need to react to risk in that period, and we should wait for risk reanalysis process. If decision risk is between 30% and 70% then reaction to risk is an obligatory, which we discuss in next steps. Decision risk more than 70% specifies fatal condition and accordingly the whole characteristics must be immediately analyzed and this may lead to early termination of the project. 3.4. Quantitative risk analysis of virtual projects The objective of implementing this phase is to select appropriate risk reaction strategies to each risk factor, so that, given budget and time constraints, the total amount of project risk will be minimized. Strategies for reacting to risk factors, budget and time, and reaction process in each period of the project life cycle should be determined according to total budget and time of the whole project. To focus merely on risk reaction strategies in period t, regardless of those of the succeeding periods, most probably results in only minimizing risks of period t and also impedes formation of better risk reaction strategies in the next periods to reduce total
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Table 5 Weights of project life cycle periods.
Under Under Under Under
review review review review
@ @ @ @
period period period period
1 2 3 4
Weight of period 1
Weight of period 2
Weight of period 3
Weight of period 4
0.48
0.24 0.55
0.16 0.27 0.34
0.12 0.18 0.66 1
amount of project risk. To solve such problem in implementation phase of quantitative analysis model and therefore to reduce total risk of the project, we define a minimizing objective function for period t, containing risk factors of period t and succeeding periods. When period t is over, in the next period, strategies and parameters of the model are revised and it is examined if the optimum answer in the new period is changed. 3.4.1. Fuzzy mathematic programming model for quantitative analyzing of virtual project risks As we said, if any period needs a risk reaction strategy, quantitative analysis model in each period is performed. 3.4.1.1. Model hypotheses. 1. The number of risk factors is fixed and must be determined before. 2. Probability and severity of risk effects are definite and uncertain (fuzzy). 3. The amount of risk for each factor is available on the basis of PMBOK methodology and its defuzzificated value is used in the model. 4. The cost of risk reaction strategies and the time added to the project for implementing these strategies are certain and fuzzy (uncertain). 5. The model has several objective functions which by assigning weight to each of them as their importance degree, one main objective function is formed (three main characteristics comprising time, quality and cost, are weighted respectively 0.3, 0.4 and 0.3 and are used to calculate total risk of the project). It should be noted that weights of the main characteristics of project, depending on nature of the project and its specifications, might be assigned by different values. Suitable weights are the choice of project manager. In order to provide the quantitative analysis model of virtual project risks, some symbols are presented as follows (see Table 6). Quantitative analysis modeling of virtual project risks in period a is as follows:
Min ðaggregate risk of projectÞ
ð7Þ
s.t. ji nt X i X X ij xij 6 B e C
ð8Þ
t¼a i¼1 j¼0 ji nt X i X X t ij xij 6 T
ð9Þ
t¼a j¼1 j¼0 ji X xij ¼ 1; i ¼ 1; 2; . . . ; nt ; t ¼ a; . . . ; 1
ð10Þ
Table 6 Symbols and initiations of quantitative analysis model of virtual project risks. Description
Indexes
Number of risk factors, i = 1, . . ., nt Number of strategies for risk factor i, Ji = 0, . . ., ji Number of periods of project life cycle, t = 1, . . ., l Set of project objectives, S = {time, cost, quality}
I Ji T S
Description
Decision variables xij
Binary variables: if strategy j is chosen for risk factor i then xij = 1, else xij = 0 Description Number of risk factors for period t Number of periods Number of project objectives Number of strategies for risk factor i Defuzzificated value of risk factor i affected by strategy j according to objective s Value of risk factor i according to objective s Integrated risk of project in period t according to objective s Integrated risk of project according to objective s Total integrated risk of project Weight of risk factor i in period t according to objective s Weight of period t in determining total project risk Weight of objective s in determination of total project risk The amount of budget alloted to risk control as a fuzzy number Cost of strategy j for risk factor i as a fuzzy number The amount of time dedicated to risk control as a fuzzy number Time of strategy j for risk factor i as a fuzzy number
xij ¼
1 if j strategy is selected for i risk 0 if j strategy is not selected for i risk
ð11Þ
Ris IRst IRs IRp dist dt ds e ¼ ðbp ; bm ; bo Þ B e ij ¼ ðcp ; cm ; co Þ C ij ij ij e ¼ ðT p ; T m ; T o Þ T ~tij ¼ tp ; tm ; t o ij ij ij
Objective function (Eq. (7)) minimizes total amount of virtual project risk on the basis of selected risk reaction strategies. The first constraint (Eq. (8)) demonstrates the specific amount of budget allocated to risk reaction process in order to keep expenditures within predefined boundaries. Second constraint (Eq. (9)) illustrates time limitation for risk reaction process, in order to keep track of time (of implementing each strategy). Third constraint (Eq. (10)) ensures that there is a specific risk reaction strategy for each risk factor (selecting j = 0 strategy, means that some risk is incurred and there is no reaction plan regarding that risk). The last constraint (Eq. (11)) specifies feasible amounts of factors. Here is the procedure of calculating total amount of project risk (which is supposed to be minimized): 1. According to Huang, Qiang, ching, and Kuen (2011), using following formula, risk amount of factor i, based on subobjective s is:
Ris ¼
j¼ji X Rijs xij
ð12Þ
j¼0
j¼0
X ij ¼ 0 or i ¼ 1; . . . ; nt and j ¼ 0; . . . ; ji and t ¼ a; . . . ; l
Parameters nt L N ji Rijs
2. The cumulative risk of project in period t, according to objective s, is calculated as follows:
IRst ¼
nt X dist Ris i¼1
ð13Þ
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3. Total cumulative risk of the project, on the basis of each objective, is:
IRs ¼
l X dt IRst
ð14Þ
t¼a
4. In order to calculate total amount of project risk, we use parametric summation of fuzzy numbers. The coefficient for each variable in objective function is determined so that the target function will be transformed into certain linear programming (Ebrat & Ghodsi, 2011; Hyeongon & Mooyoung, 2010; Liu et al. 2007): N X IRp ¼ ds IRs
ð15Þ
s¼1
The result is a linear programming problem with fuzzy right hand sides and fuzzy coefficients of constraints. Considering the solution of such problems, quantitative analysis model of virtual projects in period a is as follows:
Min ðtotal project riskÞ
ð16Þ
s.t. ji nt X l X X p cpij xij 6 b
ð17Þ
t¼a i¼1 j¼0
ji nt X l X X p m ðcpij cm ij Þxij 6 ðb b Þ
ð18Þ
t¼a i¼1 j¼0
ji nt X l X X p o ðcpij þ coij Þxij 6 ðb þ b Þ
ð19Þ
t¼a i¼1 j¼0
ji nt X l X X t pij xij 6 T p
ð20Þ
t¼a i¼1 j¼0
ji nt X l X X p m ðt pij tm ij Þxij 6 ðT T Þ
ð21Þ
t¼a I¼1 j¼0
ji nt X l X X ðt pij þ toij Þxij 6 ðT p þ T o Þ
Before implementing quantitative analysis model, the total amount of project risk (extracted from expert judgement questionaires) is assumed as 0.5375 which is more than 0.3 and requires appropriate reaction. By running our model in GAMS, the amounts of risk for each periods of project life cycle are calculated according to selected strategies (Table 7) and the total amount of project risk is 0.2144. As Table 7 shows, by implementing risk strategies, the total project risk is reduced significantly, in addition budget and time constraints are satisfied. 4.2. Numeric example for second period of project life cycle It is necessary to revise the model in the beginning of each period. As a result of implementing risk reaction strategies in previous period, there is a possibility that risk of the current period is also reduced, and therefore there is no necessity for implementing risk reaction strategies in the upcoming period. On the other hand, by resolving model and changing parameters at the beginning of this period, strategies that were selected in previous periods may not produce the overall optimum solution any more. Thus, the quantitative analysis phase of the model should be reimplemented in different periods of project life cycle. After implementing strategies of first period, at the beginning of second period the total amount of project risk is recalculated. The total risk of the project at this time is 0.486. The amount of total project risk has declined at the beginning of second period; however it is still more than 0.3. Therefore the mathematic model and reactions to risk at the beginning of this period must be reimplemented. After implementing the model in GAMS, for the second period, the amount of risk in each period of project life cycle, according to selected risk reaction strategies, is calculated and shown in Table 8. The total amount of project risk is 0.1812. As it was expected, the selected strategies for some of risk factors in this period is different from those of previous periods. For instance, for the risk factor, ‘‘insufficient knowledge and expertise’’, in the first period, the strategy, ‘‘teaching required expertise and knowledge to team members’’, was selected, but in this period the strategy, ‘‘changing the composition of professionals in suitable places with specific expertise requirement’’, is chosen. This change is the result of the fact that, by elapsing the first period and implementing selected strategies for risk factors in the first period, the
ð22Þ
t¼a i¼1 j¼0
ji X xij ¼ 1 i ¼ 1; 2; . . . ; nt t ¼ a; . . . ; l
ð23Þ
j¼0
xij ¼ 0—1 i ¼ 1; . . . ; n j ¼ 0; . . . ; ji t ¼ a; . . . ; l xij ¼
ð24Þ
1 strategy j for risk factor i is choosen; 0
otherwise;
Table 7 The amount of project risk in each period of project life cycle, after implementing the model in first period. Period of life cycle
Risk amount
t=1 t=2 t=3 t=4
0.22021 0.19942 0.19292 0.24955
for solving the model for each situation a program has been written by Gams software, which is ready to be run in all periods. 4. Numerical example of virtual project risk management model 4.1. Numerical example for first period of project life cycle Implementing the model at the beginning of the first period of project life cycle, determines risk reaction strategies of first, second, third and fourth periods.
Table 8 The amount of project risk in each period of project life cycle, after implementing the model in second period. Period of life cycle
Risk amount
t=2 t=3 t=4
0.1745 0.18023 0.20295
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amount of risk, the budget and time of implementing strategies has changed for factors of second period. Thus updating such parameters, produces new optimum answer for the model. Examining these two strategies for the risk factor, ‘‘insufficient knowledge and expertise’’, indicates that the strategy, ‘‘changing the composition of professionals in suitable places with specific expertise requirement’’, consumes less time and budget in comparison with the other strategy ‘‘teaching required expertise and knowledge to team members’’. Also, the amount of risk of second period after implementing the model, is 0.1745 which is reduced in comparison with the previous amount of 0.1994. This decrease in risk indicates that the selected strategies of this period produce better optimum answers than those of previous periods. Furthermore, the total amount of project risk is 0.1812, which is less than the total risk amount in the previous period (0.2144). In order to analyze the model in detail, again we carry out the quantitative analysis model of project risk for fourth period. 4.3. Numeric example in fourth period of project life cycle After revising and updating model parameters in this period and implementation in GAMS, given selected strategies, the total amount of the project is 0.203.a. Eventually, the total amount of risk in fourth period shows that the amount of risk, by practicing reaction strategies, changes from 0.5275 to 0.2030. The total time and budget consumption for practicing reaction strategies of risk factors, can be easily calculated through summation of the whole time and budget consumed in each period of the project. 5. Discussion and conclusion In this research, by the aid of fuzzy logic, we tried to provide a risk analysis model for managing virtual projects in order to fulfill the lack of specific procedure in risk management of virtual projects. Since PMBOK methodology is the most popular methodology for project management, the risk management methodology employed for this research and including the components of risk analysis process, is PMBOK methodology. We also discussed the integrated use of fuzzy risk analysis model along with PMBOK standards to generate more accurate analyses. This includes implementing risk analysis and management at the beginning of each period as an iterative process. In recognition phase of risk factors, the risk breakdown structure was designed. Then risks stemmed from reasearch consequences were assigned to different periods of project life cycle, in order to be able to calculate its effects on each period (one risk factor may have been allotted to several periods). After recognition, in risk qualitative analysis phase, the factor of communication was intruduced as the most effective one in risk management of virtual projects. The other important factors, in the order of importance were lack of resource provision, insufficient knowledge and expertise, inappropriate leadership and control, lack of commitment, lack of cooperation and coordination, inappropriate design of project and organization, inappropriate task timing, insufficient motivational system, financial situation of the market, lack of information security, lack of mutual trust, political status, different cultures, payment issues and social status. Those factors with higher priority in comparison with other factors, were assingned more importance degrees in quantification process of risk. When decision risk was calculated at the beginning of each period (total risk of the project), if the amount of risk were lower than 0.3, the risk was acceptable and there was no necessity to implement risk reaction strategies. The risk between 0.3 and 0.7 indicated that there was an obligation to perform next steps and determination and
implementation of risk reaction strategies. When the risk was higher than 0.7, the situation was described as critical conditions and it shows that all the conditions should be reexamined and it may even lead to early termination. In quantitative analysis phase, risk reaction strategies were determined and the linear fuzzy mathematic programming model with time and budget constraints was introduced. We used fuzzy values for coefficients of constraints and the right side amounts for more actualization of the model. The model should be repeated throughout project life cycle periods. At the beginning of period t, the objective function of the model minimized the risk of project considering risk factors of period t and succeeding periods. After solving the model, risk reaction strategies for all factors were determined. Then the selected strategies for the ongoing period were implemented. At the beginning of next period, the decision risk (total amount of project risk) was calculated and if the risk was higher than 0.3, the model was reimplemented and risk reaction strategies were redetermined and practiced. These selected strategies in this period might have been different from the optimum strategies in the previous period and that was because, by implementing strategies selected in the previous period, and updating parameters and strategies of the model in the current period, the results may differ. In order to test implementation process of the proposed model, we used this model in numerical examples at the commencement of first, second and fourth periods of the project. At the beginning of first period the total amount of project risk was 0.5375 and as it was more than 0.3, risk reaction strategies were offered. The results showed that implementing risk analysis model in the example reduces the overall risk amount from 0.5375 to 0.2030 and meanwhile time and budget constraints were satisfied. Here are some suggestions for future works on the basis of this paper: 1. Analysis of proposed models as case studies in several firms with virtual projects. 2. Results comparison of proposed models in numeric examples without considering risk management in periods of project life cycles. 3. Solving the proposed model by using data derived from other researches and comparing results. 4. Estimating the trend of overall project risk according to time and budget of reaction strategy which can help managers to assess the time and budget needed to conduct a project before its start point.
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