A new combination of multi-mode resource-constrained project scheduling and group decision-making process with interval-fuzzy information

Multi-mode resource-constrained project scheduling problem (MRCPSP) is one of the most important extensions of the basic RCPSP. In this paper, a new mathematical model for MRCPSP is presented with a time-quality trade-off approach. The model has two objectives, the first objective minimizes the project completion time, and the second objective maximizes the project quality while the quality of activities can be increased based on the reworking. In addition, in the presented model, total available resources, including renewable and non-renewable, are decision variables. The quality and duration of project activities are interval forms. For this purpose, a new expert weighting method based on interval information is presented to unify the experts’ views. The group decision-making method applies a bi-directional projection measure to the positive ideal solution and two negative ideal solutions. Moreover, a new extended interval-fuzzy solution method based on goal programming is proposed to deal with the interval information and mathematical model objectives. The presented mathematical model and group decision-making method are solved with a dataset, and some sensitivity analyses are reported.