Journal Search Engine
Search Advanced Search Adode Reader(link)
Download PDF Export Citaion korean bibliography PMC previewer
ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.17 No.4 pp.669-676

Modeling the Problem of Choosing an Optimal Strategy to Respond to Project Risks

Fahimeh Rezaee, Majid Sabzeparvar*, Hamed Tayebee
Department of Industrial Engineering, Karaj Branch, Islamic Azad University, Karaj, Iran
* Corresponding Author, E-mail:
May 29, 2018 July 25, 2018 September 17, 2018


The project risk management is a systematic process of identifying, analyzing and responding to project risks in order to maximize results of positive events and minimize consequences of bad and negative events that can affect main objectives of the project. In this process, the phase of risk response is a very important phase; because the effectiveness of responses directly determines increase or decrease of the project risk. Planning risk responses is the process of identifying different options and actions for reducing or eliminating threats and increasing or exploiting opportunities related to objectives of the project. Therefore, in this research, a systematic approach which is a combination of fuzzy multi-objective decision-making methods and zero-one integer programming model, is proposed to select the best solutions for responding to project risks. Also, since project risk management process has different stages, the stages before accountability phase include identifying and analyzing quality of the risks, and choosing critical risks is also done for accountability. Finally, in order to select the best solution for each of the critical risks, a zero-one multiobjective mathematical model is presented in a fuzzy environment and a case study is carried out on the Khangiran gas field (Shourijeh).



    The risk in projects is a non-deterministic, inevitable and future-related event or event that affects at least one of the project’s goals if it happens. Goals can be range, time, cost, and quality. Risk management is one of the 10 knowledge domains in body of Knowledge Management Project (PMBOK, 2012), that PMBOK considers risk management project including the following six phases: Risk Management Planning, Risk Identification, Quality Risk Analysis, Quantitative Risk Analysis, Risk Response Planning, Control And risk monitoring. The response to project risks is a striking issue in risk management that PMBOK has presented four risk response strategies:

    Avoidance, transfer, decrease and acceptance. Risk response planning is the process of continuously increasing opportunities by responding appropriately to risks and threats. Risk response planning should be proportional to the severity of risk, cost, real-time, project definition, and agreed upon by all project managers and stakeholders. It must also be determined that how risks should be allocated to individuals and groups in this program. Therefore, one of the key issues in risk management is identifying critical risks. On the other hand, when risk management is an effective project, the strategy for responding to critical risks is also effective, so choosing an appropriate risk response strategy and strategy is required (PMBOK, 2012). Therefore, considering the above and considering the shortcomings and weaknesses in previous studies, this research seeks to develop a model for choosing a risk response strategy and a fuzzy decisionmaking methodology with multiple goals. Finally, given the fact that organizations in turn have financial, time, etc. limits, a linear model is proposed to select the best response. In this model, we consider different risks that different responses can be selected for each risk. We also considered different limitations for the balance of selected responses. These constraints try to consider prerequisite and equi-requisite between risk responses and, on the other hand, prevent the selection of responses that are in conflict with each other. In the second part of this article, we will review the literature on previous works on risk response. In the third part, the problem model is presented for choosing the optimal solution to the risk response. In the next section, a case study is presented, and finally, conclusion is made in final part.


    In most of these models, responding to risks is one of the most important steps. Some models have simple steps and some have more details. With a general view, Lee et al. (2009) studied the project risk management process in two stages of assessment and risk response. Risk assessment consists of two parts including identification and analysis of risks. Several methods have been proposed to identify risks of projects that each of which can be used in its own circumstances (Lee et al., 2009).

    The risk response stage involves identifying, evaluating and selecting response actions. Risk response measures are classified in a variety of methods. Hilson provided an important category of preemptive and responsive responses. Preemptive / early response targets likelihood of occurrence of risk. The responsive response which is also called “healing / remedial / determinative / precautionary response” is also intended to reduce the effect of occurrence of risk. Preemptive responses have always been emphasized into responsive responses (Hillson, 2001). Hillson has introduced two levels of risk response measures. The first level is the general categorization of responses, which represents the response strategy, and the second level involves listing a set of specific actions under each strategy. To select the appropriate risk response strategy, some general frameworks have been developed (Fan et al., 2015). Hillson described the common approach in identifying and selecting risk response measures in a cascade diagram. In this method, first, the risk avoidance strategy is investigated and if it is not possible, the transfer strategy is studied and, if no response is chosen, the reduction strategy is studied and, finally, the risk acceptance will be investigated (Hillson, 2001). Fan et al. (2018) have proposed a planned method for generating project risk responses based on samplebased reasoning or CBR methodology. This method consists of five steps. The first step is to introduce the problem and the past related issues. The second step is to retrieve past existing cases by comparing risks that exist in past cases and cover our project. The third step is to measure the similarity between past and present cases and the fourth step, reviewing applied risk responses that are analyzed in the similar past cases, as well as analyzing the relationship between any extracted responses in current project risks. Finally, the fifth step is to create an appropriate response with evaluation and selection among the set of selected responses. Fan et al. (2018) also presented a conceptual framework that explains the relationship between risk responses and project characteristics (project size, flotation, and technical complexity). This conceptual model describes a quantitative relationship between all the variables in the project. Finally, an optimization analysis is proposed to select the response strategies for current risks, so that the cost is minimized. Lopez and Salemron (2012) have presented a study on identifying risks of software projects. The main disadvantages of this tool are the identification of risks and their ranking process, as well as reluctance of employees to enter information related to causes of risk. In another study by Fang and and Marle (2012), DSS was developed to model and manage project risks and link these risks to the project. The framework of this system includes five phases: (1) identifying the risk network, (2) evaluating the risk network, (3) analyzing the risk network, (4) planning the risk response, and (5) controlling and responding to risk. In this research, a riskresponse model is proposed with a decision support system design approach. The proposed model has close proximity to the project planning system, including project appraisal systems, project rankings, risk assessment, risk rating, response evaluation, and response rating. It also emphasizes the importance of equivalence of risk and response. In existing studies, generally, the methods for producing response to project risks strategies are divided into four approaches, which can be seen in Table 1.

    2.1. Problem Model

    In this research, using the optimization problem (OB) approach, that is the fourth approach, choosing project risk responses, we first discuss the proposed planning methodology for choosing the optimal solution with respect to structural, budget, time and quality constraints, and uncertain estimates of risk values. The overall strategy selection process begins by identifying the main objectives of the project in the risks affecting them, using the risk breakdown structure (RBS) (identification phase). Due to the lack of previous data, the vague nature of the risks and the amounts of risks which have uncertain nature, the fuzzy logic theory and linguistic terms are used. In the process of qualitative assessment, the following steps are taken:

    • Among the average results of time, cost, and quality factors, we select the factor which has the greatest impact on the project.

    • Calculation of the risk value is carried out according to equation (1).

    R = P × Max ( I )

    where P and I are respectively the probability of occurrence and the effect of any risk.

    Prioritization of risk factors is obtained based on the amount of risk in descending order (qualitative analysis phase); then, risk response strategies are defined and the way by which the strategy impacts on the probability of occurrence of risks, risk impact on goals in implementation of strategies and the approximate cost of implementing strategies are estimated. The structural constraints that we face when choosing risks are also identified (the initial phase of risk response planning). Given all available information and by applying the three-objective mathematical model which is presented below, one can choose the optimal solution in such a way that the structural constraints of risk selection and constraint of budget, time and quality of coping with risk are met (quantitative analysis phase + secondary phase of risk response planning). The presented mathematical model is an integer linear model, that desired answer can be reached simply and accurately using the conventional math optimization software.

    2.2. Presentation of a Three-Objective Math Model for Choosing Optimal Risk Response Strategy

    The mathematical model presented in this paper intends to select appropriate responses to project risks. The presented model is a three-objective zero-one linear model in a fuzzy environment.

    Set and Indices:

    Set risks: J   = { 1 , 2 , 3 , j , | J |

    Set strategy: I = { 1 , 2 , 3 , i , , | I |


    • mij: If strategy i can be used for risk j, it is 1, otherwise it is 0.

    • Oii': If strategy i is equi-requisite with the strategy i', it is 1 otherwise it is 0.

    • P ˜ i j : The probability of risk j, while strategy i is chosen to control it (TFN)

    • I ˜ i j C : The impact of risk j on cost while strategy i is selected for its control (TFN)

    • I ˜ i j T : The impact of risk j on time while strategy i is selected for its control (TFN)

    • I ˜ i j Q : The impact of risk j on quality while strategy i is selected for its control (TFN)

    • c ˜ i j : Increase of cost if strategy i is applied on risk j (TFN)

    • t ˜ i j : Increase of time if strategy i is applied on risk j (TFN)

    • q ˜ i j : Reduction of quality if strategy i is applied on risk j (TFN)

    Variables: sij: If strategy i is allocated to risk j, it is 1, otherwise it is 0.

    M i n   z 1 = i j P ˜ i j . I ˜ i j C . s i j

    M i n   z 2 = i j P ˜ i j . I ˜ i j T . s i j

    M i n   z 3 = i j P ˜ i j . I ˜ i j Q . s i j

    i j c ˜ i j . s i j C M

    i j t ˜ i j .    s i j T M

    i j q ˜ i j . s i j Q M

    i m i j . s i j 1 ;     j J

    s i j s i j . o i i + ( 1 o i i ) ; j J , i , i I

    s i j s i j . o i i ; j J , i , i I

    j s i j 1 ;   i I

    s i j { 0 , 1 } ; j J , i I

    The relation (2) shows first objective function of the problem, according to which the sum of effects of risks on the cost is minimized. Relation (3) shows the second objective function of the problem, based on which the sum of risks is minimized on time, and finally relation (4) represents the third objective function of the problem that minimizes impact of risks on quality. Relationship (5) states that increase in costs by allocating different strategies should not be exceeded permissible limit. Relation (6) states that allocation of strategy to risks should be such that the increase in time does not exceed permissible limit. Relation (7) also states that strategies can be allocated to risks that do not decrease the quality beyond the permissible limit. Relation (8) ensures that at least one strategy is allocated to each risk. In relations (9) and (10), equirequisite of two different strategies is controlled. Accordingly, if the two strategies i and i' re equi-requisite (oii =1 ), then these two strategies either both are used or not (sij = si′j ). Note that if both strategies i and i' are not equi-requisite (oii = 0 ), then relations (9) and (10) will be deactivated. Equation (11) ensures that each strategy is allocated utmost to one risk. Finally, in (12), the binary representation of the decision variable of the problem is shown.

    2.3. Approach to Solving the Mathematical Model

    To solve this model, we need to address two issues. First, how to resolve the uncertainty in the problem parameters, and secondly, how to simultaneously optimize each of the three proposed objective functions. As seen, model parameters are uncertain both in the objective function and in the limitations. In order for the above model to be solved with conventional optimization software, we need to use a method that gives us linear equivalent of used nonlinear functions. Similarly, in order to simultaneously optimize two target functions, since integer variables are present in the model, problem solving space is no longer convex. In this case, the use of a simple weighting method for both objectives and their unification is not permissible, since there may be unsupported Pareto answers in space of problem objectives, that this method cannot find such answers. For this purpose, a suitable method has to be used that has access to all Pareto responses and, at the same time, provides only strong Pareto responses. In the following, we will explain suggested appropriate techniques for dealing with this issue.

    2.3.1. Defuzzing Technique

    If the TFN (Triangular Fuzzy Number) is in an optimization model, there will be several approaches to defuzz it. One of these approaches is the replacement of a finite value instead of it that this is a function of left, center, and right values of the TFN. Equation 13 is replaced:(13)

    D e F u z z y ( P ˜ ) = P l + λ . P n + P u 3 + ( λ 1 )

    where λ ≥ 1 is a control parameter that shows the amount of attention to the central part of the triangle with the ratio of the left and right flanks. In order to defuzz the proposed model, instead of any TFN contained in the model, we replace the value resulted from above formula in terms of its TFN components, that the following defuzzed model is obtained.(14)(15)(16)(17)(18)(19)

    M i n   z 1 = i j P i j l + λ . P i j n + P i j u 3 + ( λ 1 ) . I i j l C + λ . I i j n C + I i j u C 3 + ( λ 1 ) . s i j

    M i n   z 2 = i j P i j l + λ . P i j n + P i j u 3 + ( λ 1 ) . I i j l T + λ . I i j n T + I i j u T 3 + ( λ 1 ) . s i j

    M i n   z 3 = i j P i j l + λ . P i j n + P i j u 3 + ( λ 1 ) . I i j l Q + λ . I i j n Q + I i j u Q 3 + ( λ 1 ) . s i j

    subject to

    i j c i j l + λ . c i j n + c i j u 3 + ( λ 1 ) . s i j C M

    i j t i j l + λ . t i j n + t i j u 3 + ( λ 1 ) . s i j T M

    i j q i j l + λ . q i j n + q i j u 3 + ( λ 1 ) . s i j Q M

    2.3.2. Multi-Objective Optimization Method Based on MinMax

    After defuzzing, we use the MinMax method to solve the above three-objective model. For this purpose, the optimal value of each target is calculated first, regardless of the other two objectives, which are shown with z 1 * , z 2 * , z 3 * respectively. z 1 z 1 * z 1 * , z 2 z 2 * z 2 * , z 3 z 3 * z 3 *   represent deviation of the first, second and third objective of its optimal value (Ben-David and Raz, 2001;Zhang and Fan, 2014; Sufi Fard, and Khazar Bafrouie, 2017) that in in the MinMax method maximum deviation must be minimized. So MinMax model of the problem is as follows:(20)(21)(22)(23)

    M i n   z = M a x { z 1 z 1 * z 1 * , z 2 z 2 * z 2 * , z 3 z 3 * z 3 * }

    subject to

    z 1 = i j P i j l + λ . P i j n + P i j u 3 + ( λ 1 ) . I i j l C + λ . I i j n C + I i j u C 3 + ( λ 1 ) . s i j

    z 2 = i j P i j l + λ . P i j n + P i j u 3 + ( λ 1 ) . I i j l T + λ . I i j n T + I i j u T 3 + ( λ 1 ) . s i j

    z 3 = i j P i j l + λ . P i j n + P i j u 3 + ( λ 1 ) . I i j l Q + λ . I i j n Q + I i j u Q 3 + ( λ 1 ) . s i j

    The model is linearized and converted into a single objective as follows:(24)(25)(26)(27)

    M i n   z s u b j e c t   t o

    z z 1 z 1 * z 1 *  

    z z 2 z 2 * z 2 *  

    z z 3 z 3 * z 3 *  

    The above model is the final model of the problem, which is as an integer linear programming problem. This model is coded in the GAMS software environment and is solvable by the CPLEX Solver. In the next section, we will use the method of choosing the proposed solution in the Khangiran Gas District (Shoorijeh).

    3. RESULTS

    The Khangiran area is located 25 km northwest of the Sarakhs border town and 135 km northeast of the city of Mashhad. This field has two reservoirs called Mozdooran and Shoorijeh. Shoorijeh reservoir was discovered in 1347 and its exploitation has started in 1979 for gas supply to Mashhad city after dehydration at a factory built in Khangiran. After the separation of gas liquids in highpressure separators, the resulting gas is delivered to the old dehydration of Gas Company. The gas of this reservoir is sweet, and the gas liquids and carbon dioxide gas in the lower part is somewhat higher than the upper part. Due to the changing nature of natural gas consumption in different seasons, part of this production capacity will remain unused when demand is reduced, so the way out of this crisis is to create a reasonable balance between natural gas consumption and production as well as correction of consumption peak.

    In this research, 68 risks were identified through the Project Breakdown Structure (RBS). In the qualitative analysis stage, with regard to experts’ opinions and determination of the critical factor of risks, 6 critical risks of project have been selected. The most important identified risks with high priority are respectively, as follows: 1. Change in design characteristics, 2. Failure to identify effective opponents before the run, 3. inappropriate allocation of resources and time, 4. financing risk, 5. economic sanctions, and 6. inappropriate suppliers. In order to evaluate the possibility of occurrence and the manner of influencing the risks on the objectives of the project, experts’ estimation is collected in the form of the following verbal variables. These verbal variables are represented according to the described mode in a triangular fuzzy [ - 32-31-30]. In the following tables, the maximum, the most probable and the smallest possible amount considered for these verbal variables are considered:

    The possibility of occurrence and impact of the risks considered on the project objectives in the form of verbal variables by experts’ opinions is considered according to Table 2. Table 3 presents possible strategies for encountering six critical risks considered. The magnitude of the probability of occurrence and the effect of the risk on each of the project objectives is given in Table 4.

    The structural constraints that we should consider in choosing solutions are that M22 strategy requires that M13 strategy be selected, and that the selection of SM23 strategy is required to select M11 strategy.

    3.1. Optimization Using a Fuzzy Three-Objective Model

    This model is coded in the GAMS software environment, which results of optimal values is obtained in Table 5.

    Due to lack of a common strategy, optimal values of Z* are equal to Zs, which means they preserve their optimality. These values are obtained by considering the amount of budget, time, and quality limitations that are visible in Table 6.

    As shown in Table 7, for some risks, more than one implementation strategy is proposed that illustrates flexibility of the model in choosing optimal solution.


    In this paper, an integer linear programming model is proposed to solve the problem of choosing the appropriate solution for project risk responses. This model tries to select appropriate responses for different risks. In this paper, using fuzzy multi-objective optimization techniques and considering prerequisite constraints as well as budget, time, and quality, one can play a key role in decision making by executives about implementing strategies. The MAXMIN method is used to solve the model, which is coded in GAMZ software. This model has been implemented in the Kangiran gas field (Shoorijeh) and has yielded satisfactory results. Finally, the Pareto’s findings were analyzed and the results show that this model as a powerful tool will allow project managers to anticipate these responses before implementation of the project in order to increase desired effects of these responses. In order to carry out further research, the following suggestions are recommended to other researchers: study of secondary risks and their impacts for choosing the optimal strategy, use of other uncertainty management techniques, and the use of other algorithms such as genetic algorithm, simulation methods and multi-objective decision making methods, and comparing the results with the current proposed method and also, simultaneous application of fuzzy network analysis and ideal planning in order to evaluate the risks and responses of the project.


    The authors appreciate executor of the East and Sarajeh Qom projects and engineering management of the Oil Company of Iran central regions to do this article.



    Methods to generate response to project risks strategies

    The possibility of the occurrence and manner of influencing the risks on project objectives

    Strategies defined for risks

    Probability and impact on target and compliance with organizational strategies

    Optimal values of objective functions

    Problem resource values

    Optimal strategies for risk response


    1. Ben-David, I. and Raz, T. (2001), An integrated approach to risk response development in project planning, Journal of the Operational Research Society, 52(1), 14-25.
    2. Fan, M. , Lin, N. P. , and Sheu, C. (2018), Choosing a project risk-handling strategy: An analytical model, International Journal of Production Economics, 112(2), 700-713.
    3. Fan, Z. P. , Li, Y. H. , and ZhangY. (2015), Generating project risk response strategies based on CBR: Acase study, Expert Systems with Applications, 42(6), 2870-2883.
    4. Fang, C. and Marle, F. (2012), A simulation-based risk network model for decision support in project riskmanagement, Decision Support Systems, 52(3), 635-644.
    5. Hillson, D. (2001), Effective strategies for exploiting opportunities, Proceedings of the Project Management Institute Annual Seminars and Symposium, Nashville Tenn USA.
    6. Jabbarzadeh, A. , Pishvaee, M. , and Papi, A. (2016), A multi-period fuzzy mathematical programming model for crude oil supply chain network design considering budget and equipment limitations, Journal of Industrial and Systems Engineering, 9, 88-107.
    7. Lee, E. , Park, Y. , and Shin, J. G. (2009), Large engineering project risk management using a bayesian belief network, Expert Systems with Applications, 36(3), 5880-5887.
    8. Lopez, C. and Salmeron, J. L. (2012), Risks response strategies for supporting practitioners decision-makingin software projects, Procedia Technology, 5, 437-444.
    9. PMBOK (Project Management Institute (PMI)) (2012), Project Management Body of Knowledge, Project Management Institute, USA.
    10. Sufi Fard, R. and Khazar Bafrouie, M. (2017), Modeling the selection problem of project risk responses portfolio, International Conference on New Research Findings in Industrial Engineering and Mechanical Engineering, Tehran, Nikan Higher Education Institute, Iran, Tehran, 43-54.
    11. Zhang, Y. and Fan, Z. P. (2014), An optimization method for selecting project risk response strategies, InternationalJournal of Project Management, 32(3), 412-422.