Document Type : Research Paper


1 PhD student of Industrial Management, Faculty of Management, Islamic Azad University, Firuzkoh Branch, Iran

2 Associate Professor, Department of Industrial Engineering, Faculty of Industrial Engineering, Mazandaran University of Science and Technology, Babol, Iran

3 Associate Professor, Department of Industrial Management, Faculty of Management, Islamic Azad University, Firuzkoh Branch, Iran

4 Associate Professor, Department of Industrial Engineering, Faculty of Management, Islamic Azad University, Firuzkoh Branch, Iran


This paper presents a multi-objective mathematical model for the reverse supply chain of hospital waste management in Iran during the COVID-19 pandemic, incorporating dimensions of sustainability. The objectives of the model are as follows: 1) Minimizing the costs associated with building facilities and waste treatment centers, vehicle fuel costs, and environmental costs due to pollutant emissions; 2) Maximizing the energy generated from the waste combustion process; 3) Minimizing the risk of virus transmission resulting from inadequate waste management; and 4) Maximizing the number of job opportunities in the established centers. It is important to note that existing uncertainties are addressed through the application of fuzzy set theory. Given the multi-objective nature of the model, two multi-objective algorithms, namely the Pareto archive-based Krill Herd Algorithm and Non-dominated Sorting Genetic Algorithm II (NSGA-II), are employed to solve the defined problem. The results indicate that the proposed Krill Herd Algorithm converges to a solution with higher quality and dispersion compared to NSGA-II. Additionally, through a comparison of the spacing index and running time of the two algorithms, it is observed that NSGA-II explores the solution space with higher uniformity and solves the model in less time.
Hospital waste encompasses a broad spectrum of both hazardous and non-hazardous materials. The management of hospital waste involves the development of a suitable supply chain network for handling waste generated in the healthcare sector. Improper disposal or mishandling of contaminated waste not only contributes to environmental pollution but also poses a risk of transferring viral pathogens to healthcare and recycling personnel. Research has shown that inadequate disposal of medical waste can lead to the transmission of up to 30% of hepatitis B, 1-3% of hepatitis C, and 0.3% of HIV infections from patients to healthcare workers. This paper aims to design a multi-objective mathematical model for the reverse supply chain of hospital waste management in Iran during the COVID-19 pandemic while considering the dimensions of sustainability.
Literatur Review
In recent years, various studies have delved into the complexities of medical and hospital waste management, proposing mathematical models to address this intricate issue. The current study is built upon the work of Valizadeh et al. (2021). In their paper, a hybrid mathematical modeling approach was introduced, featuring a Bi-level programming model specifically tailored for infectious waste management during the COVID-19 pandemic. The outcomes revealed that, at the higher level of the model, governmental decisions aiming to minimize total costs associated with infectious waste management were crucial. This involved the conversion of collected infectious waste into energy, with the generated revenue being reinvested back into the system. The findings indicated that, through energy production from waste during the COVID-19 pandemic, approximately 34% of the total costs related to waste collection and transportation could be offset. The uniqueness of this study lies in its consideration of three sustainability dimensions: risk, vehicle routing, energy production, employment, and emission of polluting gases. Consequently, the novelty of this research, when compared to previous studies and the article by Valizadeh et al. (2021), is evident in several aspects. It introduces an integrated multi-objective positioning-routing model for the supply chain of waste management under pandemic conditions, taking into account sustainability dimensions, notably the economic aspect, and employs meta-heuristic algorithms for model resolution.
To ensure the proper management of hospital waste, the waste is categorized into two groups: infectious and non-infectious waste. It is assumed that waste in hospitals and health centers is segregated and placed in infectious and non-infectious waste bins. The collected waste undergoes further processing: infectious waste is transported to incineration centers, where it is burned and converted into electrical energy, while non-infectious waste is sent to waste recycling centers, where it is reprocessed and returned to the production cycle in the industry. A multi-objective mathematical model is presented to integrate location-routing decisions in the supply chain of hospital waste management, with the following modeling assumptions:

Waste segregation at the source helps prevent all waste from becoming viral, reducing the spread of viruses through waste.
The risk of spreading viruses is assumed to be relatively equal for each type of waste.
Two types of vehicles are considered for transporting waste: the first type carries non-infectious waste, while the second type carries infectious waste.
The number of cars, waste collectors, and the capacity of waste incinerators are considered constant in this study.
The mathematical model is multi-objective, with the objectives being to optimize the three dimensions of sustainability (economic, social, and environmental).
The economic goal is to minimize system costs, including the cost of site location, recycling, collection, segregation of non-infectious waste, and incineration.
The environmental goal is to minimize the emission of pollutants in the transportation and processing system in various facilities, as well as to maximize the production of electrical energy.
The social goal is to minimize the risk of virus transmission and maximize the employment rate.

Results and Discussion
This research presents a multi-objective mathematical model for the reverse supply chain of hospital waste management during the COVID-19 pandemic in Iran and solves it. The pandemic period is considered a time of maximum utilization of health centers and waste disposal. In this context, a three-objective mathematical model was initially introduced. To solve the model, the krill herd optimization algorithm was employed. The performance of the krill herd optimization algorithm was scientifically and practically evaluated by comparing it with the well-known NSGA-II algorithm. After designing the model, both the multi-objective krill herd algorithm based on Pareto Archive and the NSGA-II algorithm were utilized to solve the model. The results of solving the model demonstrated that the proposed krill herd algorithm, designed in combination with VNS, effectively solved the model and determined the optimal solution within a boundary. Comparing the results of this algorithm with those obtained by the renowned NSGA-II algorithm revealed that the krill herd algorithm produced solutions of much higher quality.
The comparison of the Index of dispersion between the two algorithms indicates that the krill herd optimization algorithm explores more points in the solution space, leading to a lower probability of getting stuck in local optima compared to the NSGA-II algorithm. On the other hand, the index of uniformity for the NSGA-II algorithm is lower than that of the krill herd algorithm (lower values are better), suggesting that the multi-objective genetic algorithm explores the solution space more uniformly. Considering the execution time of the two algorithms, it was observed that the NSGA-II algorithm solved the model in less time. Additionally, the increasing trend of execution time in both algorithms confirms the NP-HARD nature of the hospital waste management problem. According to the output of the MATLAB software, considering the presented model, the results affirm the capability to optimally select hospital waste recycling centers.


Main Subjects

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