Abstract: The safe and efficient collection of medical waste is of great significance for ensuring the smooth operation of medical institutions, preventing the secondary pollution of medical waste, and protecting the health and safety of residents. Medical waste collection requires qualified enterprises to arrange vehicles to collect medical wastes at various medical institutions and transport medical wastes to the special treatment center. Whether the arrangement of the routes of collection vehicles is reasonable or not has an important impact on the medical waste collection. If the arrangement of the routes is not appropriate, it is apt to increase the risk of collection and result in an adverse impact. The large number and great dispersion of medical institutions are the difficulties in the medical waste collection. The amount of medical waste generated by a single medical institution, especially a small one, is relatively small. If the collection and transportation of medical wastes are only carried out between medical institutions and the treatment center, the total cost of collection will be too high and bring great pressure on the transportation capacity of medical waste collection enterprises. In order to alleviate this problem, many cities have begun to build medical waste transit points. During the medical waste collection, the medical wastes collected from medical institutions are sent to the transit points first, and then to the treatment center. Although the transit points of medical waste have improved the efficiency of medical waste collection, they are likely to result in a high-risk adverse situation owing to the potential risks related to collection vehicles. Therefore, it is very important to reasonably arrange the routes of collection vehicles in the collection mode with multiple transit points, and the routing optimization for medical waste collection considering load dependent risk and multiple transit points has also become an important research problem.
This research comprehensively considers the actual situation in which the risk of medical waste collection depends on the loads of vehicles and the collection mode with multiple transit points. The entire collection process is divided into three stages for discussion. First, the total cost and maximum risk of each stage are analyzed in depth. Second, based on the analysis results, a bi-objective routing optimization model for medical waste collection considering load dependent risk and multiple transit points is developed, minimizing the maximum risk and the total cost of collection simultaneously. Third, some properties of the problem are analyzed before the solution algorithm is proposed. Fourth, an approximation algorithm is proposed based on the properties of the problem and the epsilon constraint method, and the time complexity and approximation ratio of the algorithm are analyzed. This approximation algorithm determines the routes for vehicles in three stages and includes multiple prohibited conditions. The analysis results show that the algorithm is a polynomial time algorithm. Finally, through a series of generated test instances based on Solomon's instances, the mathematical model and approximation algorithm proposed in this research are tested, and the results show that the proposed approximate algorithm can effectively solve the routing optimization problem for medical waste collection considering load dependent risk and multiple transit points.
According to the sensitivity analysis of the key parameter affecting the risks, that is, the loading capacity of vehicles, it is found that both the total cost of collection and the maximum risk show downward trends. But in some cases, when vehicles with larger loading capacity for medical waste collection are used, these downward trends are not significant. The possible reason is that the maximum risk is tightened, so the increasing loading capacity of vehicles cannot continue to bring about the downward trends of cost and risk due to the limitation of risk.
The contents worthy of further study include three aspects. First, the work of this research is completed under the condition in which the amounts of medical wastes to be collected in each medical institution are not allowed to be split. Thus, the problem that the amounts of medical wastes to be collected can be split is worth studying. Second, the possible risks of temporary storage of medical wastes at transit points have not been considered in this research, and further work is needed to analyze and control the temporary storage risks at transit points. Third, developing algorithms with better time complexities or approximation ratios is also a future research direction.

Key words: medical waste collection, routing optimization, load dependent risk, multiple transit points

摘要： 医疗废物的安全高效回收对于保障医疗机构正常运转、防止产生二次污染以及保护居民的健康安全有重要意义。医疗机构数量多且较为分散是医疗废物回收的难点之一,由此催生了多中转点回收模式。本文综合考虑医疗废物多中转点回收模式以及风险基于装载量的实际情形,将整个医疗废物回收过程分为三个阶段进行讨论,并以最大风险最小和回收成本最小为双目标,建立医疗废物回收路径优化模型。基于问题性质和ε约束法设计求解的近似算法,该算法分三个阶段决策回收车辆的路径且包含多种禁行条件,并分析了算法的时间复杂性和近似比。最后通过算例对模型和算法进行测试,验证近似算法的求解效率,并通过对影响风险的关键参数进行敏感性分析,发现使用装载量更大的车辆时回收成本和最大风险均呈现出下降趋势。

关键词: 医疗废物回收, 路径优化, 风险基于装载量, 多中转点