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Multi-period hazardous waste collection planning with consideration of risk stability

  • * Corresponding author: Xiang Li

    * Corresponding author: Xiang Li
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  • 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.

    Mathematics Subject Classification: Primary: 90B06, 90B50; Secondary: 90C30.


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  • Figure 1.  The results of period 1

    Figure 2.  The influence of $ \lambda_3 $

    Figure 3.  The influence of $ W $

    Table 1.  The weight of hazardous wastes generated by each factory in each period (Tons)

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    Table 2.  The transportation cost ($/Ton) and the number of population exposed (Pop/Ton) of transporting a unit weight of hazardous wastes from one node to another

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    Table 3.  The computational results

    $ \lambda_1 = 1, \lambda_2 = 2, \lambda_3 = 0 $$ \lambda_1 = 1, \lambda_2 = 2, \lambda_3 = 5 $
    Period 1Period 2Period 3Period 1Period 2Period 3
    No. of vehicles644555
    Transportation cost($)6373527847045399.85134.75445
    Penalty fee($)0001415.712500
    Transportation risk (Pop)2442227917261971.71971.71955
    Total cost($)1635518645.2
    Total transportation risk (Pop)64475898.4
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