An Integer Linear Programming Model for Quality Maximization of a Multi-mode, Multi-skilled, Resource-constrained Project Scheduling Problem with Discrete Time-cost-quality-risk Trade-off

The multi-skilled, multi-mode resource-constrained project scheduling with discrete time-cost-quality-risk trade-off problem (MS-MRCPSP-DTCQRTP) was developed with quality maximization as the primary objective function. The model is an integer linear programming model that assigns available resources to project activities based on skill requirements and time-cost-risk constraints. A case study from prior literature was extended to include skills and risk and was used to illustrate the model. The open-source Python-MIP package generated schedules that optimize time, cost, quality, and risk. A fifth solution that balances the other four solutions was also developed. Project managers can select the best schedule from the solutions for their needs.