Robust optimization for multi-project scheduling via the critical chain method

The critical chain method is often used to improve robustness in single-project scheduling, but there are two challenges when applying it to multi-project scheduling. First, the existing robustness measure focuses on time elasticity within sub-projects but neglects elasticity across sub-projects, making it difficult to balance drum resource requirements. Second, the differential evolution (DE) algorithm is adopted to solve this problem, but continuous evolutionary operators have limited flexibility, leading to numerous transformations between the continuous solution space and the discrete problem space. Therefore, we adjust the critical chain multi-project scheduling model by incorporating the drum buffer and the capacity constraint buffer and propose a robustness measure that considers both time elasticity within and among sub-projects. Meanwhile, we design an enhanced discrete DE algorithm, which not only discretizes the encoding-decoding strategy and evolutionary operators but also uses a hill-climbing algorithm to enhance local search. Experiments are conducted to verify the effectiveness of the robustness measure and the algorithm. The results indicate that, averaged over the eight instances, the enhanced discrete DE algorithm achieves an improvement of more than 3.3% in robustness compared with the overall mean of the benchmark algorithms. Furthermore, our robustness measure strengthens the stability of the scheduling plan and reduces buffer consumption and overflow during multi-project scheduling.