Hazardous wastes are likely to cause danger to humans and the environment. In this paper, a new mathematical optimization model is developed for the multi-period hazardous waste collection planning problem. The hazardous wastes generated by each source are time-varying in weight and allow incomplete and delayed collection. The aim of the model is to help decision makers determine the weight of hazardous wastes to collect from each source and the transportation routes of vehicles in each period. In the developed model, three objectives are considered simultaneously: (1) minimisation of total cost over all periods, which includes start-up fee of vehicles, transportation cost of hazardous wastes, and penalty fee for the delayed collection; (2) minimisation of total transportation risk posing to the surrounding of routes over all periods; and (3) even distribution of transportation risk among all periods, also called risk stability. The developed multi-objective model is transformed into a single-objective one based on the weighted sums method, which is finally equated to a mixed 0-1 linear programming by introducing a set of auxiliary variables and constraints. Numerical experiments are computed with CPLEX software to find the optimal solutions. The computational results and parameters analysis demonstrate the applicability and validity of the developed model. It is found that the consideration of the risk stability can reduce the total transportation risk, the uneven distribution of the transportation risk among all periods, and the maximum number of vehicles used, though increasing the total cost to some extent.

中文翻译：

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考虑风险稳定性的多期危险废物收集计划

危险废物可能对人类和环境造成危险。本文针对多期危险废物收集规划问题建立了新的数学优化模型。每个来源产生的危险废物的重量会随时间变化，并且收集不完整且延迟。该模型的目的是帮助决策者确定从每个来源收集的危险废物的重量以及每个时期的车辆运输路线。在开发的模型中，同时考虑了三个目标：（1）在所有期间使总成本最小化，其中包括车辆的启动费，危险废物的运输​​费和延误收取的罚款。（2）在所有时期内将对路线周围的总运输风险降至最低；风险稳定性。基于加权求和方法，将开发的多目标模型转换为单目标模型，通过引入一组辅助变量和约束条件，最终将其等效为混合0-1线性规划。使用CPLEX软件计算数值实验以找到最佳解决方案。计算结果和参数分析证明了所开发模型的适用性和有效性。可以发现，尽管在一定程度上增加了总成本，但考虑风险稳定性可以降低总的运输风险，所有时期之间运输风险的不均匀分布以及使用的最大车辆数量。