nsga-ii algorithm

The development of green product processes is a strategic approach to minimize the impact of organizational supply chain on the environment while simultaneously expanding its economic performance. To achieve this task, it is crucial to emphasize aspects related to performance in optimizing resource utilization and implementing sustainability principles within an organizational domain. To this end, a multi-objective mixed-integer linear programming model is presented in this study with the objective of minimizing the production time of textiles, transportation costs, and inventory of the products, as well as minimizing the environmental effects of the processes of developing green products. In this model, the constraints and problem parameters are deterministic and solved using weighted sum methods, utilizing real data obtained from the "Oyaz" industrial group. By solving the model, an optimal combination for the values of the objective functions is obtained both collectively and separately. Furthermore, the capability of the proposed model is evaluated for solving large-scale instances using the NSGA-II algorithm. This metaheuristic method has demonstrated satisfactory capabilities compared to the mathematical model because of the slight difference in modeling errors while confirming the accuracy of the developed mathematical model, proving the accuracy and efficiency of the NSGA-II algorithm. Consequently, the sensitivity analysis examines the influence of changing key parameters, such as the maximum storage capacity of production centers, on the decisions of the proposed model. This parameter change is determined through consultation with experts in the textile field. Based on the results obtained, changing the maximum storage capacity has a considerable impact on fibers and cotton. Additionally, if the capacity is changed to the maximum possible value, it has the greatest impact on the purifiers.

In this paper, developed a new multi-product, multi-period, and multi-level closed-loop green supply chain planning model under uncertain conditions. The formulated model consists of five objective functions, which minimize the cost of the supply chain, minimize the CO2 emission of transportation vehicles, maximize the reliability of manufacturing and distribution centers, maximize the reliability of the transportation system, and maximize the level of service provided. Therefore, the problem of model formulated as a multi-objective mixed integer nonlinear programming. Also, since the proposed model is complex and NP-hard in large size, therefore, for the investigation of the results, we have used a Non-Dominated Sorting Genetic II Algorithm (NSGA-II). In addition, the small of size results of the problem achieved by GAMS software. Therefore, we try to solve these problems by analyzing and comparing them with the help of these algorithm. For this purpose, various size has been considered.