A Bi-objective Pre-emption Multi-mode Resource Constrained Project Scheduling Problem with due Dates in the Activities


1 MSc, Department of industrial Engineering, K.N. Toosi University of Technology, Tehran, Iran

2 MSc, Department of industrial Engineering, Mazandaran University of Science and Technology, Mazandaran, Iran

3 Assistant professor, Department of industrial Engineering , K.N. Toosi University of Technology, Tehran, Iran


In this paper, a novel mathematical model for a preemption multi-mode multi-objective resource-constrained project scheduling problem with distinct due dates and positive and negative cash flows is presented. Although optimization of bi-objective problems with due dates is an essential feature of real projects, little effort has been made in studying the P-MMRCPSP while due dates are included in the activities. This paper tries to bridge this gap by studying tardiness MMRCPSP, in which the objective is to minimize total weighted tardiness and to maximize the net present value (NPV). In order to solve the given problem, we introduced a Non-dominated Ranking Genetic Algorithm (NRGA) and Non-Dominated Sort Genetic Algorithm (NSGA-II). Since the effectiveness of most meta-heuristic algorithms significantly depends on choosing the proper parameters. A Taguchi experimental design method was applied to set and estimate the proper values of GAs parameters for improving their performances. To prove the efficiency of our proposed meta-heuristic algorithms, a number of test problems taken from the project scheduling problem library (PSPLIB) were solved. The computational results show that the proposed NSGA-II outperforms the NRGA.