Designing a nonlinear mathematical model of cellular production considering operator assignment in different layout scenarios

Cell production is one of the most important applications of group technology that forms production cells in such a way that each family of parts in a cell is processed by a certain group of machines related to that cell (machine cell). In order to have a suitable and coherent plan for a good and quality production, two important steps in production planning should be taken: sequence of operations and scheduling. Sequencing of operations and scheduling is a decision-making process that takes place by allocating resources over time to execute a set of activities in order to optimize one or more objectives. In fact, the main goal in operation sequence scheduling problems is determining the sequence of tasks and allocating resources to tasks in such a way that one or more objectives are optimized. In the proposed model, we intend to design an integrated model of cell formation with cell arrangement and operation scheduling in the cell production system and assigning operators with the aim of minimizing the time to complete the work in addition to paying attention to the non-overlapping of cells and specifying the position. Regarding machines, let's determine the optimal arrangement of the cells independently in our modeling and specify the optimal placement of the cells together. In this research, after nonlinear mathematical modeling and data collection and measurement, the problem is solved by a genetic algorithm, and finally, the best-proposed layout will be selected among the 3 existing scenarios according to the created cost.