# A Mathematical Model for Scheduling and Assignment of Customers in Hospital Waste Collection Routes
## 2 State of the Art
[18], a new stochastic optimization model using two-stage stochastic programming for solving a closed-loop supply chain network design problem is proposed. A nature-inspired algorithm, namely Whale Optimisation Algorithm (WOA) and Particle Swarm Optimisation (PSO) algorithms, are utilized to solve the considered problem. Besides, Genetic Algorithm (GA) and Simulated Annealing (SA) as the well-known meta-heuristics are employed to have a comprehensive comparison. [PERSON] and [PERSON] [19] propose research and a method enabling the engineers to create a tool/program that facilitates making decisions about additional cargo insurance or the use of monitoring systems for the location and parameters of the cargo. [PERSON] et al. [20] focused their research on the solution of a real-world drug distribution problem with pharmacological waste collection. The authors modeled it as a multi-attribute-rich vehicle routing problem (RVRP). A Discrete and Improved Bat Algorithm (DaIBA) has been proposed to solve the considered problem. The main feature of this adaptation is using the well-known Hamming Distance to calculate the differences between the bats. An effective improvement has also been contemplated for the proposed DaIBA, which consists of two different neighborhood structures, which are explored depending on the bat's distance regarding the best individual of the swarm. [PERSON] et al. [21] conduct a two-stage reverse logistics network design for urban healthcare waste. The first stage involves the prediction of the amount of medical waste. Based on the Grey GM(1,1) prediction model, the amount of medical waste in a multi-period of the target hospitals is predicted. In the second stage, a multi-objective model aimed at minimizing operating costs and minimizing environmental impact is developed for facilities allocation decisions, which include the configuration of critical facilities such as hospitals, collection centers, transshipment centers, processing centers, and disposal sites, as well as medical waste flow control among facilities. A Periodic Load-dependent Capacitated Vehicle Routing Problem (PLCVRP) encountered by healthcare centers and medical waste collection companies to design a weekly inventory routing schedule to transport medical wastes to treatment sites is considered by [PERSON] et al. [22]. The authors propose a decomposition-based heuristic algorithm to solve this problem. [PERSON] and [PERSON] [23] propose a multi-objective robust optimization model to design a collection and disposal network of Hazardous Hospital Waste under uncertain conditions. The objectives minimize the total cost, including transportation and operations costs, and the real risk of transportation and operation. An augmented epsilon-constraint method was employed to solve the proposed model. A study of the Real-life Healthcare Waste Collection vehicle routing problem (HWCVRP) in Iran has been published by [PERSON] et al. [24]. This work considers social, environmental, and economic objective functions, aiming to achieve sustainable development. A self-adaptive multi-objective evolutionary algorithm is generated with numerous effective operators to solve the proposed model. Specific metrics are employed to compare the proposed meta-heuristic algorithm's performance with those of multiple other evolutionary algorithms. [PERSON] et al. [25] consider infectious, hazardous waste generated by individuals and hospitals during the COVID-19 pandemic. This paper proposes a mathematical model for hazardous infectious waste collection and government aid distribution to control COVID-19. The model is related to the operational decisions of contractors with limited capacities. In a stochastic programming approach, four possible scenarios are examined, depending on the outbreak's severity. In addition, as a solution approach, the Benders decomposition method is combined with Karush-Kuhn-Tucker conditions. A Biomedical Waste (BMW) problem is solved using route optimization by [PERSON] et al. [26].