# A Mathematical Model for Scheduling and Assignment of Customers in Hospital Waste Collection Routes
## 2 State of the Art  
Because of its potential environmental and public health risks, Hospital Waste Management is a significant problem. Operators must collect medical waste and control its recovery or disposal. The recovery of medical waste includes the reuse, remanufacturing, and recycling of materials and requires a specially structured reverse logistics network to collect such products efficiently. In [PERSON] [3], a mixed-integer linear programming model is proposed for recoverable Hospital Waste Management. The efficiency of the model is validated in a real-life case study involving medical waste returned by hospitals to the manufacturer of the products. [PERSON] [4] analyzes the infectious medical waste collection problem. The problem is expressed as the well-known periodic vehicle routing problem. The problem is solved with a two-phase matheuristic algorithm. In the first phase, the standard vehicle routing problem is solved. Conversely, in the second phase, a mixed-integer linear programming model assigns routes to particular days of each week. A stochastic version of the problem is analyzed by [PERSON] et al. [5]. In this study, the problem is modeled as a particular case of the routing and inventory problem with waste management. In the process of optimization and planning for a defined time frame, identification by radio-frequency technology is considered. Two similar solution strategies are proposed. [PERSON] et al. [6] present a binary programming model to support the decision-making process, addressing workforce programming in health care organizations. Therefore, the irrational allocation of resources can have various negative impacts on the financial outcome, the quality of medical services, and both patients' and employees' satisfaction. The Hospital Waste Collection problem is included in the general Routing of Waste Collection (RWC) problem. Several articles have analyzed the RWC problem. Several articles have analyzed the RWC problem. In [PERSON] et al. [7], a mathematical model is proposed to determine the minimum distance when transporting solid waste to landfills. The model uses data on population density, solid-waste generation capacity, vehicle types,and container and collection vehicle types. In [PERSON] et al. [8], an algorithm is proposed to solve the vehicle routing problem and to program the collection of hazardous waste. The proposed method enables us to limit the distance traveled by trucks and their emissions. Additionally, the proposed approach allows us to assess the possibility of future investment in fleet acquisition. In [PERSON] et al., [9], the network design problem of hazardous waste management is analyzed. The problem is solved using a mathematical model of multi-objective mixed-integer linear programming. Algorithms considering multiple objectives for the waste collection problem have been proposed by several authors. In [PERSON] et al. [10], the authors consider the design of a collection system for infectious medical waste. A multi-objective stochastic waste collection problem is formulated considering two conflicting objective functions. Social objectives, specifically the satisfaction of pharmacists and local authorities involved in the collection process and the minimization of public health risks, need to be traded off against distribution costs comprising routing costs and fixed costs incurred each time a tour is planned. Heuristic approaches have been proposed to solve the considered problem. [PERSON] et al. [11] address a new industrial hazardous waste location-routing problem by emphasizing some new aspects in its formulation, such as considering constraints about the incompatibility between some kinds of wastes and incorporating routing decisions into the model. Simultaneous minimization of three significant criterion takes place, including total cost, total transportation risk of hazardous waste related to population exposure, and site risk. A multi-objective location-routing model is developed by [PERSON] [12].