A sustainable multi-objective multi-mode resource-constrained project scheduling problem solved by a new Reduced Bucket Search matheuristic algorithm

A Sustainable Multi-Objective Multi-Mode Resource-Constrained Project Scheduling Problem (Sustainable MO-MRCPSP) is proposed in this research, as a reformulation of the well-known NP-hard Multi-Mode Resource-Constrained Project Scheduling Problem (MRCPSP). The MRCPSP has several practical applications in industrial and business situations. In the traditional MRCPSP, the objective is usually to minimise the project makespan. Our proposal, however, incorporates economic, environmental, and social factors as simultaneous objectives, in order to provide a sustainable approach to the decision-making process, which is essential in the current competitive landscape. An Improved Augmented Epsilon-Constraint (AUG2) solution method and a new Reduced Bucket Search (RBS) matheuristic method are developed and tested on adapted benchmark instances of different sizes obtained from well-known libraries. Performance metrics show that the RBS matheuristic performs faster for larger instances, and provides similar convergence and solution diversity than the AUG2 method. Both the reformulation of the problem to incorporate the sustainable approach and the development of a new, efficient RBS solution method, designed to fit well for sequencing problems, provide valuable contributions to the scientific knowledge.