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• This research proposes a method for scheduling medical supplies in major public health emergencies. • The method of the allocation of medical materials per vehicle to each hospital is proposed. • The method of the supply sequence per vehicle to each hospital is proposed. • The problems can obtain the optimal solution while the time complexity is within an acceptable range. In the early days of the COVID-19 pandemic in Wuhan, there was an unreasonable allocation between hospitals and a lack of timely transportation of medical supplies, which reduced the cure rate of infected cases. To solve the problem, this research proposes a method for scheduling medical supplies in major public health emergencies to develop a rapid and accurate supply scheme for medical materials, including the allocation of medical materials per vehicle to each hospital and the supply sequence per vehicle to each hospital. Specifically, this paper solves the following two sub-problems: (1) calculating the shortest transportation times and the corresponding routes from any distributing center(s) to any hospital(s); (2) calculating the medical supplies per vehicle transporting to each hospital. The method of solving sub-problem 1 is performed by multiple iterations, each of which calculates the shortest route from a distributing center, through one or more hospitals, and back to the distributing center. According to sub-problem 2, this research proposes a distribution model of medical supplies in major public health emergencies. A multiple dynamic programming algorithm which is a combination of some separated dynamic programming operations is proposed to solve this model. This algorithm also realizes the rapid updating of the scheme in the context of the changing number of vehicles. The first sub-problem can be solved in normal times, while the second one should be solved on the premise of obtaining the corresponding data after the occurrence of a major public health emergency. In the case study section, the whole method proposed in this research is employed in the medical supplies scheduling in the early stage of the COVID-19 outbreak in Wuhan, which proves the availability of the method. The main innovation of the method proposed in this research is that the problems can obtain the optimal solution while the time complexity is within an acceptable range. [ABSTRACT FROM AUTHOR]

• A novel two-stage robust optimization model is developed for the line planning with passenger demand uncertainty. • A Lagrange relaxation-based heuristic as well as some strengthening techniques is introduced to solve the robust model. • The model and algorithm are tested for case studies of a Chinese high-speed railway line. A railway line-planning problem is one of the fundamental problems in the strategic planning of railway operations. Operation zone, frequency, stop schedule, and passenger distribution for each train based on passenger demand are determined to minimize both the operation cost of the railway enterprise and the total travel cost to the passengers. However, passenger demand uncertainty makes balancing transport capacity and fluctuating demand challenging. Therefore, this paper proposes a two-stage robust optimization model wherein the nominal line plan is determined in the first stage (i.e., the case in which passenger demand has no fluctuation) and the rescheduled line plan based on the nominal line plan is determined according to the demand realization in the second stage. A Lagrangian relaxation algorithm and some strengthening techniques are designed. The model and algorithm are tested on real-world instances of the Wuhan–Guangzhou high-speed railway line under uncertain passenger demands. Computational results indicate that the proposed solution algorithm can yield a high-quality solution in 3600 s. In addition, the proposed two-stage robust solution can help minimize both operation and travel costs on average when compared with the nominal solution under uncertainty realization. [ABSTRACT FROM AUTHOR]