Nonlinear Multifactor Safety Index (NMF-SI) for Construction Scheduling: Definition and Hybrid Optimization

Construction sites present intrinsically hazardous conditions characterized by dynamic and complex operational environments which persistently contribute to elevated rates of occupational injuries. While conventional safety management emphasizes controls during the execution phase, addressing safety considerations during the earliest phases of a project is more effective. In this work, a Nonlinear Multifactor Safety Index (NMF-SI) is developed to quantify activity-level occupational risk for use in project planning. The index synthesizes multiple risk factors, including accident probability, task severity, exposure duration, workforce size, and contextual variables, such as weekday effects, and site conditions, like waste accumulation. Additionally, it incorporates a structured questionnaire to capture the implementation of safety measures on site. Its nonlinear formulation reflects interactions among factors, penalizes temporal clustering of high-risk tasks, and prioritizes temporal distribution and proactive planning. To produce risk-aware schedules, a hybrid optimization framework that couples a tree-based constructive heuristic with the marine predators algorithm is introduced, maximizing NMF-SI subject to project-duration, precedence, and resource constraints. In simulation, the optimized schedules achieve higher NMF-SI values and a smoother risk profile over time than baseline plans. These results translate into a quantitative, data-driven contribution to safety by design, offering a practical decision-support tool for intelligent, risk-aware construction scheduling.