A grey multi-objective linear model to find critical path of a project by using time, cost, quality and risk parameters

A project is a series of related activities which are organized to reach a defined goal or satisfy a certain need. Project management plays an important role in different fields of human life. The amount of resources spent on a project renders management of these resources a sensitive task. Determinant factors’ influencing the payoffs of a project mainly encompasses time, cost, quality and also the risk of each activity. Therefore, a critical path method is presented to find the longest path of a project completion time in order to draw managers’ attention to the critical activities. Critical path method is a well-known and widely accepted method to find the critical activities of a project and to concentrate on them for accomplishment of the project without any deviation. Classical critical path methods usually consider only a time factor, but growing complexity and importance of projects entail cost, quality and risk as the critical factors to be considered in project management. Due to the unavailability of certain information relating each factor of each activity, considering a novel approach to deal with such vague and unstable situations is really a controversial issue. Thus, another challenge of the project management contains uncertainty for approximating time, cost, quality, and risk factors of the project activities. Taking into account these two challenges, a grey multi-objective critical path model is proposed in this paper, where parameters of the activities are evaluated as grey numbers, dealing with their uncertainty. Meanwhile, a goal programming based method is illustrated to solve the problem of critical path identification, considering four considerable criteria including time, cost, quality, and risk. Eventually, a numerical example is represented to address applicability of the proposed method.