Stochastic cellular manufacturing system design subject to maximum acceptable risk level

In this study, a non-linear mathematical model is proposed to solve the stochastic cellular manufacturing system (CMS) design problem. The problem is observed in both machine and labor-intensive cells, where operation times are probabilistic in addition to uncertain customer demand. We assume that processing times and customer demand are normally distributed. The objective is to design a CMS with product families that are formed with most similar products and minimum number of cells and machines for a specified risk level. Various experiments are carried out to study the impact of risk level on CMS design. As the risk level increases, lower number of cells and product families are formed and average cell utilization increases. However, this leads to poor performance in cells, where standard deviations of capacity requirements are high. Later, the deterministic approach proposed by Suer, Huang, and Sripathi (2010) and the proposed stochastic model with various risk levels are compared. Both of the models’ results are simulated with Arena Simulation Software. Simulation is performed to validate models and assess the performance of designed CMSs with respect to following measures: cell utilization, WIP, total waiting time and total number waiting. Stochastic CMS design with 10% risk formed a better CMS in all of the performance measures according to the results obtained from simulation experiments.

► This paper introduces a stochastic cell formation problem.
► Product demand and processing times are considered as uncertain.
► A stochastic nonlinear mathematical model is developed.
► Experimentation is performed with various design risk levels.
► Lower risk levels provided better cellular manufacturing system performance.