Development of a fuzzy multi-objective mathematical model for hazardous waste location-routing problem

Industries and manufacturers produce hazardous waste that causes long-term harm to human health, animal life, and the environment. Hazardous waste management (HWM) involves the collection, transportation, recycling, treatment, and disposal of hazardous waste under safe, efficient, and cost effective manner. Researchers have presented different framework to illustrate required facilities and connection between these facilities for hazardous waste management. In the most of previous studies some important facilities such as recycling centers and connection between different facilities were neglected. Aforementioned in HWM definition, risk and cost are the most important criteria. Using total cost and total risk as objectives for the mathematical model present a good trade-off between environmental and economic aspects. Until recently, there have been some studies that used both objectives together. Uncertainty is one of the important issues to deal with the real world problems. The generated hazardous waste quantity is not predictable precisely. Therefore, amount of waste is uncertain parameter. However, no research has been found that use fuzzy theory to address uncertainty of hazardous waste quantity. A multi-objective location-routing problem is a NP-Hard problem. It is difficult to find Pareto optimal solution for these problems. This indicates a need to apply a Metaheuristic method to solve these problems. However, far too little attention has been paid to use Meta-heuristic method in this field. In this research, a fuzzy multi-objective mixed integer programming location–routing model for the hazardous waste is developed. This study considers uncertainty in generated hazardous waste quantity by using fuzzy parametric programming. The proposed model has two objectives: to minimize total costs, including transportation, operation, and initial investment costs as well as the saved costs from selling recycled waste; to minimize total risk including transportation risk and site risk by considering population exposure along the route and around each facility respectively. The aim of the model is to help decision makers to locate optimum number of facilities and finding set of routes. The results of the applied model show, it is possible to decrease the cost value by marginally increasing the total risk value. Hence, two objectives are conflicting to each other. Two objectives can give a good trade-off between environmental (calculating total risk) and economic (calculation total cost) factors. Using fuzzy parametric programing proved that the waste quantity uncertainty has effect on the objectives function values, the optimum number of facilities and location of facilities. To solve the model a (fast elitist Non-Dominated Sorting Genetic Algorithm (NSGAII)) and also the (weighted sum method (WSM)) were used and their results were compared to each other. MATLAB software is utilized for coding NSGA-II and GAMS software is utilized for coding WSM. The solved model demonstrates that NSGA-II can provide good efficient solutions in one time run than WSM. The model was applied for three different case studies. Also, a benchmark example was used to verify NSGA_II. To validate the model, a real case study of Klang city at Malaysia was applied. The results of the solved model show around 41% improvement of cost objective value in compare to the current method. However, there is not any method to measure hazardous waste transportation risk in current situation at Malaysia. Hence, value of the total risk objective can help to choose optimal set of routes and facilities under safe manner.

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