A modified NSGA-II for the Multiobjective Multi-mode Resource-Constrained Project Scheduling Problem

This work studies a multiobjective version of the Multi-mode Resource-Constrained Project Scheduling Problem (MRCPSP), in which both the total time of execution and the total cost of assignment are treated as objective functions. An NSGA-II based genetic algorithm is employed for the estimation of the Pareto-optimal solution set. An encoding/decoding scheme guarantees that only feasible individuals are represented in the population, and problem-specific mutation and crossover operators are employed in order to enhance the algorithm efficiency. A case study of the engineering design of the facilities of a new mining plant located in the northern Brazilian territory illustrates the application of the proposed methodology. In this case study, several scenarios of project task assignment to a team of workers with different skills and different hiring costs are generated by the proposed algorithm. This quantitative description of the trade-off between project term and project cost can be particularly useful in the preliminary stage of price negotiation between the engineering consulting firm that develops the project and the client mining company.