A multi-objective resource-constrained project scheduling problem with time lags and fuzzy activity durations

The resource-constrained project scheduling problem is to find a schedule that minimizes the project duration subject to precedence relations and resource constraints. To further account for economic aspects of the project, one may add an objective of cash nature to the problem. In addition, dynamic nature and variations in real world are known to introduce uncertainties into data. Therefore, this study is aimed at proposing a multi-objective model for resource-constrained project scheduling problem, with the model objectives being to minimize makespan, and maximize net present value of the project cash flows; the proposed model has activity times expressed in fuzzy numbers where the corresponding uncertainties are taken into account. The project environment is considered to be a multi-resource environment where more than one resource is needed for the execution of any activity. Also, the proposed model comes with time lags in precedence relations between activities. The proposed model is validated by using epsilon-constraint method. The α-cut approach as well as the expression of acceptable risk level by the project manager is used to defuzzificate fuzzy activity durations. Since the problem is NP-hard, a NSGA-II meta-heuristic algorithm is proposed to solve the problem. The algorithm performance has been evaluated in terms of different criteria.