multi-objective mathematical model for optimizing the collection and recycling of urban waste under conditions of uncertainty(The subject of study : Karaj city) - Mohsen Bijanpoor; Reza Ehtesham Rasi; Davood Gharakhany (مدیریت بهره وری)
In this research, using the double-objective mixed integer linear programming method, an optimal supply chain network for the collection and recycling of urban waste has been presented in terms of source separation and the uncertainty of per capita waste generation by citizens. Due to the uncertainty in the parameters of the problem, the two-stage stochastic programming method has been used to model the problem. The objective functions include an economic function to minimize investment costs and a social objective function to maximize the amount of recycling. In order to accurately solve the problem on a large scale, the Lagrange release method has been used. To validate and confirm the effectiveness of the model presented in this research, the model was implemented on a case study in the city of Karaj. According to the obtained results, to increase the amount of recycling in the waste supply chain network, more infrastructural and operational investments are needed. By increasing recycling, the harmful environmental and destructive effects of burying and burning waste will be reduced. The Lagrange release solution method can be used as a suitable method to reduce problem-solving time. In this research, it was observed that the Lagrange release method can solve large-scale problems with appropriate accuracy and in less time compared to the commercial CPLEX solver.   Key Words: two-stage stochastic programming, Lagrange's release method, linear programming, supply chain, waste management    1.Introduction In Iran, 50,000 tons of waste are produced daily, of which only about 10% are recycled. In the city of Tehran, approximately 2% of daily urban waste production is separated at the source. The operation of collecting and disposing urban waste is very expensive due to the high investment costs for the waste collection and transportation fleet and the need to spend significant operational costs. Therefore, even small and partial reductions in the operating costs of waste management lead to large savings in the cost of municipalities. On average, between 60 and 80 percent of urban solid waste management costs are related to waste collection and transportation costs. While in the world, on average, 70% of the produced waste is recycled, optimistically, this figure reaches about 20% in Iran, and this means that in the country, about 16 million tons of waste are buried in the ground without being recycled. One of the important reasons for the low waste recycling in Iran is the lack of separation from the source of all types of waste produced in the country. The purpose of this research is to reduce the costs of urban waste management through separation at the source of waste and creating special hubs for each type of separated waste. 2- Literature review Among all municipal solid waste management strategies, waste recycling has received more attention than other options due to its impact on economic growth in addition to protecting the environment and human health. Given the need for investment in collection and disposal facilities along with high operating costs, conducting waste collection, recycling, or disposal operations is very costly. Therefore, a slight improvement in this process causes a significant reduction in the costs of municipalities (Babaei et al., 2017). The meaning of solid waste management is a set of coherent and systematic programs and laws related to the control of production, collection, transportation, separation, recycling and burial of waste based on the principles of public health, economy and conservation of biological resources (Akbarpour Shirazi et al., 2015). According to the conducted research, urban solid waste management can be considered as a supply chain network design problem (Mohammadi et al., 2019). This network includes facilities such as waste collection stations, transfer stations and recycling and disposal facilities. In the process of household waste collection, waste collected from local collection stations is first sent to transfer facilities where it is unloaded from municipal collection trucks and loaded into larger trucks to be transported to landfills in bulk (Habibi et al., 2017). In order to design an efficient and suitable supply chain network for urban waste collection, mathematical programming models can be used to improve the performance of this network by optimizing the location of facility locations and their allocations, and therefore, making them valuable tools for improving overall supply chain efficiency (Habibi et al., 2017). Since the parameters and information required for designing the waste supply chain network are not always certain, designing the supply chain in a deterministic way decreases its practical efficiency. Therefore, considering uncertainty in designing the model is inevitable (Rahimi & Qadavati, 2017). The findings from previous research indicate that, in the majority of studies, the issue of waste separation at the source and the establishment of hub centers for each type of the separated waste have not been taken into consideration; therefore, in the present study, both of the above mentioned issues have been taken into consideration in designing the model. 3- Methodology Building on the points mentioned, this research is an attempt to design a multi-level supply chain network for urban waste collection and recycling, focusing on source segregation and uncertainty in citizens' per capita waste generation. This supply chain network includes urban points (segregated waste collection tanks) as waste collection centers, transfer centers or hubs for separated waste, recycling centers, as well as burial centers and waste incinerators. The flow of materials in this supply chain is considered in such a way that the waste is separated at the source by the citizens and placed in the tanks specific to each type of waste. Then, these wastes are transported by collection trucks to the hub or waste transfer centers specific to each type of waste, and then, transported by larger trucks to recycling centers and disposal centers (including burying or burning waste centers). In order to design the network, a mixed integer programming problem is designed, which includes two economic and social objectives. The first objective function seeks to minimize initial investment and operating costs, while the second objective function, that is, the social objective function, focuses on maximizing urban waste recycling. In order to take into account, the uncertainty in the citizens' per capita waste generation, a two-stage random programming method has been used. In order to linearize the above two objective functions, the epsilon constraint method is used. Also, using a case study in the city of Karaj, the efficiency of the designed model has been investigated. The solution method used to solve the presented model in large dimensions is the Lagrange release method, which is classified in the group of exact problem-solving methods. 4- Results In the present study, with the aim of addressing the existing research gap, an integer linear programming mathematical model was developed for designing the waste collection and recycling network, focusing on source separation and the establishment of hubs for each type of separated waste. In this research, in addition to the concept of recycling, the concept of separation hub was also considered in the design of the supply chain. In order to validate the model, a case study was conducted in Karaj and its results were presented. Collecting suitable data to solve the problem was one of the problems of designing the model due to the high amount of required data and the difficulty of accessing some statistics. According to the obtained results, in order to increase the amount of recycling in the waste supply chain network, more infrastructural and operational investments are needed. By increasing recycling, the environmental and destructive effects of burying and burning waste will be reduced. The Lagrange release method can be used as a suitable solution method to reduce problem solving time in problems with high values. In this research, it was observed that the Lagrange release method can solve problems with high values ​​with appropriate accuracy and in less time compared to the CPLEX solver. Therefore, it can be said that the innovations of this research include the development of the waste collection and recycling supply chain model under uncertainty, considering the separation hubs, using the Lagrange release method to solve the model and the case study of Karaj city.  5- Discussion The purpose of this study was to design a multi-objective mathematical model to manage municipal and hospital waste. Hence, after reviewing the related literature, the gap in the existing studies was determined. In the studies conducted in the relevant articles, it was found that the specialized hub for each type of waste was not included, and only in a few articles, the concept of recycling was considered in the design of the supply chain. Also, to the researchers' best knowledge, no article was found in which exact solution methods were used to reduce the difficulty of solving the problem. Considering the collection and recycling supply chain network presented in this research and also based on the literature review, issues such as routing the movement of waste collection and transportation trucks in the mentioned network, production and storage planning for recycling centers,  using heuristic and meta-heuristic solution methods to solve the model which are combined with other exact mathematical solution methods such as Lagrange release, considering environmental objective functions such as pollution reduction in the waste transportation and recycling process and considering the uncertainty in the capacity of facilities can be considered as the subject of future research.