# Designing Sustainable Flexible Manufacturing Cells with Multi-Objective Optimization Models +
## 5 Conclusions and Future Studies  
In this study, three multi-objective mathematical programming models were presented that focus on the design of flexible manufacturing cells while incorporating sustainable factors. The study considers economic, environmental, and social dimensions, which are the three key dimensions of sustainability, by including various parameters. By considering these dimensions, this study aimed to develop the design of flexible manufacturing cells within a sustainable framework. In addition to minimizing the number of carbon emissions within the scope of the environmental dimension, this study aimed to minimize various cost items considering carbon emissions, inter-cellular movement, machine replacement, machine operation, worker training, and bonus wages for workers as the economic dimension. The total training time received by each worker in all periods is shown as a constraint in the model within the scope of the social dimension. Since the study involves multi-objectives, the identified problem is modeled using multi-objective optimization techniques. Firstly, the goal programming model related to the problem was developed. Then, the \(\varepsilon\)-constraint and AUGMECON models for the examined problem were presented. In all developed multi-objective models, various decision variables were considered to optimize the flexible manufacturing cells. They cover the decision variables such as determining the optimal routes between the alternative routes of parts, the number of machines to be added to or removed from cells, the number of workers assigned to cells, and the total training time of workers. In this study, all the developed multi-objective mathematical programming models were solved using the LINGO 20.0 optimization program on the developed sample problem. These global optimal solutions were reached in 12 min and 38 s, 18 min and 31 s, and 19 min and 51 s for the goal programming method, the \(\varepsilon\)-constraint method, and the AUGMECON method, respectively. When the results obtained from each of the developed multi-objective optimization models were examined, it was observed that the decision variables regarding determining optimal routes of parts, assigning optimal machines to cells, adding them to cells, and removing them from cells provide different results. While the \(\varepsilon\)-constraint and AUGMECON models provided the same results in the optimal worker assignments and the optimal number of workers in cells for each period, the goal programming model provided different results. The decision variables of the total number of workers in the system in each period and the total training times received by workers provided the same results for all developed models. The results were tested by performing sensitivity analyzes for each developed multi-objective optimization model. In future studies, metaheuristic algorithms can be proposed to solve larger-scale problems in the context of sustainable manufacturing systems. Additionally, the consideration of parameters such as machining times and demands such as fuzzy variables can enhance modeling capabilities and address uncertainties in real-world scenarios. Furthermore, the development of a decision support system specifically designed for modeling sustainable manufacturing systems holds the potential to yield valuable insights for making informed decisions. Conceptualization, E.B. and E.Y. ; methodology, E.B. and E.Y. ; software, E.B. ; validation, E.B. ; visualization, E.B. and E.Y. ; writing--original draft preparation, E.B. and E.Y. ; and writing--review and editing, E.B. and E.Y. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The data presented in this study are available in this article. Thanks to LINDO Systems Inc. for ensuring a free educational license of LINGO 20.0 software package. The authors declare no conflicts of interest.