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This paper presents a new mathematical model to solve cell formation problem in cellular manufacturing systems, where inter-arrival time, processing time, and machine breakdown time are probabilistic. The objective function maximizes the number of operations of each part with more arrival rate within one cell. Because a queue behind each machine; queuing theory is used to formulate the model. To solve the model, two metaheurstic algorithms such as modified particle swarm optimization and genetic algorithm are proposed. For the generation of initial solutions in these algorithms, a new heuristic method is developed, which always creates feasible solutions. Both metaheurstic algorithms are compared against global solutions obtained from Lingo software's branch and bound (B&B). Also, a statistical method will be used for comparison of solutions of two metaheurstic algorithms. The results of numerical examples indicate that considering the machine breakdown has significant effect on block structures of machine-part matrixes.

Today’s complicated business environment has underscored the importance of integrated decision-making in supply chains. In this paper, a novel mixed-integer nonlinear mathematical model is proposed to integrate cellular manufacturing systems into a three-stage supply chain to deal with customers' changing demands, which has been little explored in the literature. This model determines the types of vehicles to transport raw materials and final parts, the suppliers to procure, the priorities of parts to be processed, and the cell formation to configure work centers. In addition, queueing theory is used to formulate the uncertainties in demands, processing times, and transportation times in the model more realistically. A linearization method is employed to facilitate the tractability of the model. A genetic algorithm is also developed to deal with the NP-hardness of the problem. Numerous instances are used to validate the effectiveness of the modeling and the efficiency of solution procedures. Finally, a sensitivity analysis and a real case study are discussed to provide important management insights and evaluate the applicability of the proposed model.

An integrated decision in supply chain is a significant principle in order to compete in today's market. This paper proposes a novel mathematical model in a two-stage supply chain scheduling to cooperate procurement and manufacturing activities. The supply chain scheduling along with the production approach of cellular manufacturing under demand, processing time, and transportation time uncertainties makes business environment sustainably responsive to the changing needs of customers. Uncertainties are formulated by queuing theory. In this paper, a new mixed-integer nonlinear programming formulation is used to determine types of vehicles to carry raw materials, suppliers to procure, priority of each part in order to process, and cell formation to configure work centers. The goal is to minimize total tardiness. A linearization method is used to ease tractability of the model. A genetic algorithm is developed due to the NP-hard nature of the problem. The parameters of the genetic algorithm are set and estimated by Taguchi's experimental design. Numerous test problems are employed to validate the effectiveness of the modeling and the efficiency of solution approaches. Finally, a real case study and a sensitivity analysis are discussed to provide significant managerial insights and assess the applicability of the proposed model.