An Integer Grey Goal Programming For Project Time, Cost and Quality Trade-Off

Project management (PM) is one of the prominent fields in business and industry. Every task of an organization can be imagined as a project, being a coordinated set of activities toward a common goal. One important aspect of PM is analysing the information related to the optimum balance among the project's objectives. Each project is a combination of different activities, being connected to each other and having several success criteria, among which the time, cost and quality of the project completion are more significant, due to their significant effect on obtained results. Accordingly, the time might lead to delay and penalty which means more cost; and cost may be underestimated than real required funds. They both will lead to failure in project management. On the other hand, quality is the final key which confirms the success. The aim of a time-cost-quality trade-off problem (TCQTP) is to select a set of activities and an appropriate execution mode for each activity; the cost and time of the project is minimized while the project quality is maximized. The purpose of this paper is to present a model for TCQTP in which these parameters are approximated by grey numbers. Since there are various modes to accomplish each activity, the trade-off problem is formulated based upon a multiobjective integer grey programming model. Afterwards, a goal programming-based approach is designed to solve this model. The model's results provide a framework for the project manager to manage his/her project successfully, in acceptable time, with the lowest cost and the highest quality. The main originality of the proposed model is the approximation of time, cost and quality parameters of activities mode with grey numbers and the development of a two phase goal programming-based approach to solve this problem. Ultimately, the proposed model is applied in two different cases and results are illustrated to clarify the outstanding capabilities of the model.