A multi-objective linear programming model for scheduling part families and designing a group layout in cellular manufacturing systems

Different industries compete to attract customers in different ways. In the field of production, group technology (GT) is defined by identifying and grouping similar parts based on their similarities in design and production. Cellular manufacturing (CM) is an application of GT to reconfigure the factory and job shop design. A manufacturing cell is a group of independent machines with different functions put together to produce a family of parts. Designing a cellular manufacturing system involves three major decisions: cell formation (CF), group layout (GL), and group scheduling (GS). Although these decisions are interrelated and can affect each other, they have been considered separately or sequentially in previous research. In this paper, CF, GL, and GS decisions are considered simultaneously. Accordingly, a multi-objective linear programming (MOLP) model is proposed to optimize weighted completion time, transportation cost, and machine idle time for a multi-product system. Finally, the model will be solved using the ϵ-constraint method, representing different scales solutions for decision-making. The proposed model is NP-hard. Therefore, a nondominated sorting genetic algorithm II (NSGA-II) is presented to solve it since GAMS software is unable to find optimal solutions for large-scale problems. Besides, to evaluate the performance of NSGA-II, the problem is solved by three metaheuristic algorithms.