Robust schedule for the bi-objective discrete time/resource trade-off problem

The Discrete Time/Resource Trade-Off Problem (DTRTP), a subproblem of the multi-mode resource-constrained project scheduling problem, is prevalent in fields such as construction and software development, where project uncertainties often impact schedule stability. This paper proposes a bi-objective DTRTP model designed both to minimize project duration and to enhance robustness against disruptions. To solve this model, we develop several optimization algorithms, including the Non-Dominated Sorting Genetic Algorithm II (NSGA-II), Variable Neighborhood Search (VNS) and three hybrid algorithms that combine NSGA-II with VNS to improve robustness and solution quality. The performance of these algorithms is evaluated through computational experiments, which involve algorithm performance analysis, Pareto optimality analysis and uncertainty analysis. The results show that both NSGA-II and the hybrid algorithms generate robust schedules that effectively minimize project duration and maximize robustness, providing a promising approach for managing uncertainties in complex project scheduling.