Two-stage robust optimization for public health emergency project scheduling with uncertain activity durations

The utilization of emergency projects, which can facilitate the coordinated scheduling of medical resources and rescue activities, offers a promising approach for absorbing disturbances, mitigating damage and achieving restoration from public healthcare catastrophes. However, the complex implementation environment in public health emergencies significantly impacts the preventive effectiveness and rescue efficiency of emergency projects. Considering the substantial uncertainty in activity durations, this study models resource allocation and schedule generation of an emergency project as a two-stage robust optimization formulation to reduce economic expenditure and minimize delayed rescue. Specifically, the preparedness stage is to minimize the pre-deployment cost of emergency resources, and a max–min objective is introduced in the response stage to optimize the deprivation cost affected by random activity durations. Then, as the robust optimization model could be reformulated in a master-submodel framework, we develop a customized column-and-constraint generation (C&CG) algorithm with enhancements based on the structure of the problem and decision variables for rapid problem-solving. Besides, the algorithms are tested on randomly generated datasets, and the influences of key parameters on the algorithm performance, the resource cost and the deprivation cost of the emergency project are analyzed. Based on the computational results, the customized C&CG algorithm with enhancements outperforms others and sensitivity analysis of key parameters is presented. This research provides effective decision support for public health emergency scheduling and draws management insights, validated through a real-world case study that demonstrates the model's practical effectiveness in enhancing emergency response resilience and efficiency.