# Designing Sustainable Flexible Manufacturing Cells with Multi-Objective Optimization Models +
###### Abstract  
Having sustainable and flexible features is crucial for manufacturing companies considering the increasing competition in the globalized world. This study considers three aspects of sustainability, namely economic, social, and environmental factors, in the design of flexible manufacturing cells. Three different multi-objective integer mathematical programming models were developed with the objective of minimizing the costs associated with carbon emissions, inter-cellular movements, machine processing, machine replacement, worker training, and additional salary (bonus). Simultaneously, these models aim to minimize the carbon emission amount of the cells within the environmental dimension scope. The developed models are a goal programming model, an epsilon constraint method, and an augmented epsilon constraint (AUGMECON) method. In these models, alternative routes of parts are considered while assigning parts to machines. The results are obtained using the LINGO 20.0 optimization program with a developed illustrative example. The obtained results are tested and compared by performing sensitivity analyses. The sensitivity analyses include examinations of the effects of changes in part demands, machine capacity values, carbon limit value, and the maximum number of workers in cells. s +
Footnote †: This study is grounded in, under the supervision of Associate Professor Dr.  
impacts of manufacturing decisions [4]. [PERSON] and [PERSON] [5] examine social factors within manufacturing systems, addressing elements such as education budget, overtime rate, security, and labor expenditure. In the context of manufacturing system sustainability, [PERSON] and [PERSON] [6] investigate social sustainability indicators, encompassing aspects like job opportunities, health and safety applications, research and development, healthcare and education, and social cohesion. According to [PERSON] et al. [7], employee education and training emerge as significant strategies for advanced manufacturing systems. [PERSON] et al. [8] categorize social factors in manufacturing systems into diverse criteria, including work accidents, physical workload, working conditions, employee productivity, knowledge and skills, and employee satisfaction. [PERSON] and [PERSON] [9] gather a range of criteria, including employment opportunities, employee satisfaction, occupational health and safety, education, and development, and working conditions to define social factors within manufacturing systems. According to [PERSON] et al. [3], the economic dimensions of sustainability encompass various indicators that are traditionally associated with financial accounting and intangible assets. The economic dimension of sustainability is indeed interconnected with the environmental and social pillars. Economic pillars are also associated with costs and profits [3]. Sustainable manufacturing systems development efforts contemplate solving problems at all levels (product, process, and system) [10]. The dynamic cellular manufacturing system is one of the manufacturing systems that has a high degree of flexibility and agility to handle product changes [11]. Flexible manufacturing systems are computer-controlled systems that can simultaneously process various parts, including automated material handling equipment and numerically controlled machine tools [12]. The systems divided into subsystems to produce certain parts are called cellular manufacturing systems [13]. The cell formation problem addressing the design of cellular manufacturing systems aims to group parts into part families and related machines into machine cells. This problem aims to ensure grouping efficiency by minimizing inter-cellular and intra-cellular movement costs. The classification of cellular manufacturing systems is based on the geometry of each part and the similarity in the working process. This classification aims to reduce inventory, improve flow time, optimize space utilization, and enhance system efficiency [11].