A Mathematical Model for Dynamic Cell Formation Problem Based on Scheduling, Worker Allocation, and Financial Resources Constraint

Cellular production is one of the important applications of group technology in production. With the development of modern industrial technology, many manufacturers use it as a solution to implement complex and realistic scenarios that increase the productivity and flexibility of a production system. Cellular production includes cell formation, cellular and intracellular arrangement, operation scheduling, and resource allocation. The process of formation and grouping of machines to produce families of parts to minimize the cost of moving materials among cells is called cell formation. In other words, cell formation in cell production systems and assignment of machine groups and family of parts to these cells is done to minimize the total cost and increase flexibility and productivity in production. The layout design is also related to the position of the cells relative to each other and the position of the machines in each cell relative to each other. In some production units, the placement of cells in relation to each other and even the placement of devices in each cell is not done properly, which increases the movement of materials, semi-finished parts, and consequently, production costs. On the other hand, with changes in customer needs and demand and competitive market conditions, the combination of existing cells and their arrangement in one period may not be appropriate for another period, and it is necessary to make changes to reply to customer needs and remain competitive. The possibility of making changes in cells combination, placement inside and between cells is called dynamic cell formation. In other words, dynamic cell formation involves changing the position of the cells relative to each other and the proper placement of the machines in one cell so that it is possible to move the machines to a new position or another cell and increase or decrease them.

Operation scheduling and assigning human resources incurring a notable proportion of expenses in the cell formation. These issues seem more important when financial resources are limited. In this research, dynamic cell formation problems based on scheduling, allocation of workers, and constraints of financial resources on machines and workers are simultaneously investigated, Accordingly, the present study seeks to minimize the total costs, including the costs of machines, workers, and transportation of parts. At first, a mathematical model was presented. The model was then linearized and validated. After that, a genetic algorithm was proposed to solve the problem where the parameters were adjusted and selected by using the Taguchi method. Sensitivity analysis was also performed based on the related parameters in constraints of financial resources of machines and workers.

The results showed the accuracy of the model and its validation. It was also shown that the proposed algorithm is highly efficient and can be used for medium and large-sized problems where it is not impossible to find the optimal solution.

Sensitivity analysis showed that the constraints of financial resources for purchasing machines have a greater impact on the objective function than workers' financial constraints, which is of high importance.