Designing Stochastic Cell Formation Problem Using Queuing Theory

This paper presents a new nonlinear mathematical model to solve a cell formation problem which assumes that processing time and inter-arrival time of parts are random variables. In this research, cells are defined as a queue system which will be optimized via queuing theory. In this queue system, each machine is assumed as a server and each part as a customer. The grouping of machines and parts are optimized based on the mean waiting time. For solving exactly, the proposed model is linearized. Since the cell formation problem is NP-Hard, two algorithms based on genetic and modified particle swarm optimization (MPSO) algorithms are developed to solve the problem. For generating of initial solutions in these algorithms, a new heuristic method is developed, which always creates feasible solutions. Also, full factorial and Taguchi methods are used to set the crucial parameters in the solutions procedures. Numerical experiments are used to evaluate the performance of the proposed algorithms. The results of the study show that the proposed algorithms are capable of generating better quality solutions in much less time. Finally, a statistical method is used which confirmed that the MPSO algorithm generates higher quality solutions in comparison with the genetic algorithm (GA)

Making an integrated decision in a three-stage supply chain along with cellular manufacturing under uncertain environments: A queueing-based analysis

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