Sample average approximation for the stochastic resource-constrained project scheduling problem with flexible resource profiles
针对活动工期不确定且资源分配灵活的项目调度问题，提出混合整数线性规划模型，用样本均值近似处理随机性，并开发串行调度生成方案和分散搜索算法求解，适用于项目管理者评估方案。
Abstract Despite the availability of various decision support tools for project managers, only few methods explicitly account for uncertainty in activity durations and flexibility in resource allocation. To address this issue, we consider a stochastic resource-constrained project scheduling problem with flexible resource profiles. The problem is formulated as a mixed-integer linear program with chance-constraints, aiming to minimize the project duration while ensuring a predefined confidence level. Uncertainty is modeled through workload distributions and approximated using a sample average approximation based on discrete scenario sets. While exact solutions can be obtained for small instances with standard solvers, larger instances require heuristic approaches. For this purpose, we develop a serial schedule generation scheme to create feasible solutions and apply a scatter search to improve them. Both methods check the scenarios for feasibility with respect to the confidence level. Once a feasible schedule is identified, improvements are pursued by rescheduling activities along the critical paths. The proposed methods are evaluated in a comprehensive performance analysis, focusing on solution quality, robustness across scenarios, and scalability with respect to instance size and resource configurations.