The aim of this paper is to develop an interactive two-phase method that can help the Project Manager (PM) with solving the fuzzy multi-objective decision problems. Therefore, in this paper, we first revisit the related papers and focus on how to develop an interactive two-phase method. Next, we establish to consider the imprecise nature of the data by fulfilling the possibilistic programming model, and we also assume that each objective work has a fuzzy goal. Finally, for reaching our objective, the detailed numerical example is presented to illustrate the feasibility of applying the proposed approach to PM decision problems at the end of this paper. Results show that our model can be applied as an effective tool. Furthermore, we believe that this approach can be applied to solve other multi-objective decision making problems.
In recent years, the project managers have faced the competitive environment such as the product’s life cycle is becoming short and customers want more-customized services. It means when the project managers face the complicated situations, it is difficult for them to use resources and take decisions in a perfect way. With today’s projects, much of the uncertainty surrounding information management simply can’t be eliminated. In this case, we apply the fuzziness to improve the chances of success in project management. In addition, the degree of fuzziness not only deals with the lack of information but also supports the project managers that can make the wrong decisions in lower possibility. In another word, the experiences of the project managers on the project appropriate application reduces errors due to poor decisions may lead to opportunities for project failure.
Recently, both practitioners and academicians have been more interested in considering the issues of the relationship between project management decisions and possible problems. Numerous mathematical programming techniques and heuristics for considering the fuzzy theory have been developed for solving PM problems, each with its own advantages and disadvantages. Okuhara, Shibata, and Ishii (2007) utilized the genetic algorithm to the adaptive assignment of worker and workload control in PM decision problems. After that, Lin (2008) utilized statistical confidence-interval estimates and level (1 − α) fuzzy numbers to solve project time–cost tradeoff problems. Arikan and Güngör (2001) utilized fuzzy goal programming (FGP) approach to solve PM decision problems with two objectives—minimizing both completion time and crashing cost. After that, Wang and Fu’s work (1998) applied fuzzy mathematical programming to solve PM decision problems. The aim of these models was to minimize complete project cost and whole crashing cost simultaneously. In addition, Wang, Liang, Li and other scholars have developed and researched an interactive multiple fuzzy goal programming (MFGP) model to solve PM decision problems in a fuzzy environment. It aimed to minimize total costs, whole completion time, and complete crashing costs simultaneously ( Li et al., 2008, Liu et al., 2009, Lv et al., 2010, Suo et al., 2012, Wang and Fu, 1998 and Wang and Liang, 2004).
According to some related studies, the decision-making process is closer to the possibilistic than probability. Besides, Zadeh (1978) presented the theory of possibility, which was related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction. It acts as an elastic constraint on the values that can be assigned to a variable. Since the expression of a possibility distribution could be viewed as a fuzzy set, possibility distribution might be manipulated by the combination rules of fuzzy sets and more particular about fuzzy restrictions. Buckley (1988) formulated a mathematical programming problem in which all parameters might be fuzzy variables by their possible distribution, and moreover, illustrated this problem using the possibilistic linear programming (PLP) approach. After that, Liang (2009) formulated a possibilistic programming (PLP) model to solve fuzzy multi-objective PM problems with imprecise objectives and constraints. Some related works such as Inuiguchi and Sakawa, 1996 and Hussein, 1998 and Tanaka and Guo (2000) applied possibilistic programming linear method to address the decision-maker problems. In addition, some researchers extended the related research scope such as Kwong, Chen, Chan, and Wong (2008) proposed a hybrid fuzzy least-squares regression (HFLSR) approach to modeling manufacturing processes which features the capability of dealing with the two types of uncertainty and addresses the consideration of replication of responses in experiments. After that, Kwong, Chen, Chan, and Luo (2010) addressed a generalized FLSR approach to modeling relationships in QFD is described that can be used to develop models of the relationships based on fuzzy observations and/or crisp observations. And, Chan, Kwong, and Hu (2012) proposed a new methodology to perform market segmentation based on consumers’ customer requirements with fuzziness consideration.
Besides, we found some inadequacies based on above-mentioned literatures:
To sum up, in this paper, we have discussed the issue of the interactive two-phase method with the limit owing consideration. The project managers may not have enough information to estimate the possible interval View the MathML sourceZijPIS,ZijNIS for imprecise objective values. Based on the results of examples, the proposed integrating interactive PLP model and two-phase approach can improve DM satisfaction degree and attempts to minimize total project costs, total completion time and total crashing costs. Also, we will focus on interactive satisfying method based on rebuilding the membership functions as our future research. This method can get the satisfying result according to DM without knowing the specific marginal rates of substitution. In comparison with the conventional model, our model has taken on the customer’s satisfaction into consideration. With other constraints, in reality, our model can handle more flexible and quality of the PM. The most important advantage of the proposed approach is to address a more systematic procedure, enabling a decision-maker to interactively modify the imprecise data and parameters of a set of satisfactory compromise solution is obtained. Based on our results, this article provides a practical example of a project which we get the data in the computer processing operations in less than 0.01 s to prove the validity of this method, and this method can be applied in more complex project issues.
