Applying fuzzy multi-objective linear programming to a project management decision with nonlinear fuzzy membership functions

This paper investigates a multi-objective project management problem where the goals of the decision maker are fuzzy. Prior research on this topic has considered linear membership functions to model uncertain project goals. Linear membership functions, however, are not much flexible to model uncertain information of projects in many situations, and therefore, fuzzy models with linear membership functions are not suitable to be applied in many practical situations. Hence, the purpose of this paper is to apply nonlinear membership functions in order to develop a better representation of fuzzy project planning in practice. This approach supports managers in examining different solution strategies and in planning projects more realistically. In doing so, a fuzzy mathematical project planning model with exponential fuzzy goals is developed first which takes account of (a) the time between events, (b) the crashing time for activities, and (c) the available budget. Following, a weighted max–min model is applied for solving the multi-objective project management problem. The performance of the developed solution procedure is compared with the literature that applied linear membership functions to this problem, and it is shown that the model developed in this paper outperforms the existing solution.