A discrete time/resource trade-off problem with a critical chain method under uncertainty: a hybrid meta-heuristic algorithm.

In recent years, the resource-constrained project scheduling problem and its variants have attracted wide attention from the perspective of theory and practice. In many projects, the amounts of the work content for the activities are specified, while the activities are executed in different modes of discrete duration and resource consumption per time. This paper focuses on this specific generalization of the resource-constrained project scheduling problem, known as the discrete time/resource trade-off problem (DTRTP). An efficient mathematical model for the DTRTP with renewable resource types is presented. Since this problem is NP-hard, a hybrid heuristic/meta-heuristic algorithm is proposed to solve the deterministic model in large sizes. Then, a critical chain project management approach is employed to handle the uncertainty of activities' work contents. Finally, several numerical examples based on the previous studies and generated examples are presented to demonstrate the performance of the proposed procedure. The proposed hybrid algorithm for deterministic cases is statistically compared with an existing exact optimization tool. The simulation-based statistical analyses showed that the proposed hybrid meta-heuristic algorithm could find global optimums for small-sized cases in shorter run times. While the exact solver cannot solve medium- and large-sized problems, the proposed nested algorithm reaches high-quality local solutions in suitable run times. Also, the simulations indicated that the proposed project scheduling can face uncertainty, at least in 77% of the cases. [ABSTRACT FROM AUTHOR]