solving the mrcpsp/max with the objective of minimizing tardiness costs and maximizing earliness rewards of activities with a two-stage genetic algorithm

in this study, we present a mrcpsp/max (multi-mode resource-constrained project scheduling problem with minimum and maximum time lags) model with minimization tardiness costs and maximization earliness rewards of activities as objective. the proposed model is nearby to real-world problems and has wide applications in various projects. this problem is not available in the literature exactly and we developed it for the first time. in order to solve this problem, we developed a two-stage genetic algorithm. in the first stage, the main problem is simplified, through applying a genetic algorithm, in which each activity has only one executive mode.  in the second phase, with developing another genetic algorithm, the best answer of the problem is achieved. each phase has its own codification, fitness function, crossover operator and mutation operator. finally, the computational results obtained from the algorithms of this research, which was written in matlab programming language, was compared with the results existing in the project scheduling problems library (psplib). the findings show that, our algorithm improved some of the best solutions, recorded in the psplib.