A mathematical multi-objective model for treatment network design (physical-biological-thermal) using modified NSGA II

Today, sustainable development is one of the important issues in regard to the economy of a country. This issue magnifies the necessity for increased scrutiny towards issues such as environmental considerations and product recovery in closed-loop supply chains (CLSCs). The most important motivational factors influencing research on these topics can be considered in two general groups: environment-friendly legal requirements and cost efficiencies. The most important elements in the closed-loop supply chain include collection centers and treatment centers. This paper intended to design a network according to the mentioned principles. In this regard, three types of product treatment centers were taken into account: physical, biological, and thermal. The network design was made via a new mixed multi-objective nonlinear mathematical model of integers. In this model, three objective functions were considered that included profit maximization, pollution minimization, and the minimization of the number of facilities under construction. The model was obtained after determining the number of collection and treatment centers, the number of containers for storage of different waste materials, the amount of waste sent from collection centers to the treatment centers, and the areas covered by collection centers. Due to the conflicting objective functions, a corrected NSGAII algorithm was used to solve this model. The change applied in the mentioned algorithm was made to determine the appropriate amount of the crossover percentage. The improvement in the performance of the proposed solution algorithm is shown using a numerical example. To prove the improved performance, a T-test was used to compare the means between the two populations. To select the optimum answer from the Pareto solution set, indices of D, S, and solution time were used and solved with TOPSIS.