# A Mathematical Model for Scheduling and Assignment of Customers in Hospital Waste Collection Routes
## 2 State of the Art
The proposed approach has been tested in the Marmara region of Turkey. The model aims to help decision-makers decide on treatment centers' locations utilizing different technologies, routing different types of industrial hazardous wastes to compatible treatment centers, locations of recycling centers and routing hazardous waste and waste residues to those centers, and locations of disposal centers and routing waste residues there. Three criteria are considered: minimizing the total cost, minimizing total transportation risk related to the population exposure, and minimizing total risk for the population around treatment and disposal centers. A similar approach is introduced by [PERSON] and [PERSON] [13]. The proposed model aims to open treatment centers and their technologies, open disposal centers and the different route types of hazardous waste to which of the compatible treatment technologies, and route waste residues to disposal centers. Large-scale implementation of the model in the Central Anatolian region of Turkey is presented. In [PERSON] et al. [14], a multi-objective mixed integer location/routing model aiming to minimize transportation costs and risks for large-scale hazardous waste management systems is proposed. A Pareto optimal curve for two conflicting objectives is proposed as a solution scheme. The suggested model was used in a case study targeting HWMS in Turkey. A bi-objective obnoxious facility location problem that deals with the existing tradeoff between a low-cost operating network and the negative effect on the population living near the waste management facilities are introduced by [PERSON] et al. [15]--a hybrid approach combining a multi-objective evolutionary algorithm (NSGA II) with a mixed-integer program. A new mathematical model to solve the vehicle routing problem with backhauls and time windows (VRPBTW) is proposed by [PERSON] et al. [16]. In this problem, customers are divided into two subsets, for delivery and collection. The objective is to minimize the total distance and the number of vehicles to make the route is minimized. In Wichapa and Khokhajaikiat [17], a new multi-objective facility location problem model which hybridizes fuzzy AHP and goal programming (GP) has been introduced. Finally, the vehicle routing problem (VRP) for a case study was formulated, and it was tested using a hybrid genetic algorithm (HGA) which hybridizes the push forward insertion heuristic (PFIH), genetic algorithm (GA), and three local searches, including 2-opt, insertion-move, and interexchange-move. In [PERSON] [12], a mathematical model is proposed for collecting, transport, treatment, recycling, and disposal of hazardous industrial materials. The model has three objectives: minimization of total costs, including hazardous material transport costs and fixed costs from establishing waste treatment centers; minimization of total transport risks related to population exposure to the developed routes; and minimization of overall risks for populations near waste treatment centers. [PERSON] et al. [13] propose a model for the location and routing problem of hazardous waste management. The model makes decisions related to the opening and location of treatment centers and the routes developed for waste collection. The model considers total cost and transport risk minimization. In [PERSON] et al. [14], a multi-objective mixed-integer linear programming model is presented to minimize transport costs and risk for hazardous waste management systems. The model is tested in a case study in Turkey. [PERSON] et al. [15] propose a bi-objective hybrid algorithm for the location of final Hospital Waste disposal centers. The paper analyzes the conflict of objectives between the network operating costs and the adverse effect on the population living near the potential waste disposal centers by applying the algorithm to a real-life case in the Boyaca Department, Colombia. In [PERSON] et al.