Stochastic cellular manufacturing system design subject to maximum acceptable risk level

Abstract

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.

Introduction

Manufacturing strategies and approaches have significantly changed in recent decades in comparison to the first half of the 20th century. One of the changes that has been employed and implemented by numerous companies in recent decades is the Group Technology (GT) and Cellular Manufacturing (CM) concepts. Group technology is a general philosophy, where similar items are brought together considering a critical attribute and the same solution is applied to the entire group thus improving the productivity of the system.

Cellular manufacturing is an application of GT to the manufacturing world. In a cellular manufacturing system (CMS), similar products are grouped into product families and the required machines are assigned to manufacturing cells to produce the corresponding product families. In this respect, a cell is a small manufacturing unit designed to have people, dissimilar equipment and machines together to produce like products resulting in lower leadtimes, work-in-process inventory (WIP), setup times and workforce (Wemmerlov & Johnson, 1997). See Burbidge and Wei (1992) for more detailed explanation of the benefits of implementing CMS. Although there are significant benefits that can be achieved when CMS is employed, there are some disadvantages of CMS implementation such as being less flexible to rapid changes in product mix and demand (Ang and Willey, 1984, Wei and Gaither, 1990, Satoglu and Suresh, 2009). In addition to these cons, the major concern about Cellular Manufacturing (CM) is the reduced machine utilization due to the dedication of machines and cells to certain product families (Suer & Ortega, 1996). Moreover, overutilization or underutilization of cells can be another complicated issue when demand of each product is uncertain. Due to such difficulties as inefficient cell and machine utilization and poor production control associated with highly probabilistic demand (Suer et al., 2010), stochastic behavior of demand should be taken into consideration prior to CMS design.

Manufacturing cells can be defined as either machine-intensive cell or labor-intensive. In machine-intensive cells, the operator involvement is limited and the operation is mostly influenced by the machine performance. The operators usually load the raw material or semi-product, unload it from the machine and perform quality control. In these environments, processing times may not greatly vary from one unit of the job to the next unit of the same job as the machines increasingly have a better repeatability feature. On the other hand, in labor- intensive manufacturing cells, operations are mainly carried out by the operators and the processing time of an operation can vary significantly from one unit of the job to the next unit depending on the operator and even for the same operator.

In this paper, both demand and processing times are considered as probabilistic. A non-linear stochastic mathematical model is developed for CMS design. Experimentation is carried out with deterministic model given by Suer et al. (2010) and the proposed stochastic mathematical model. Subsequently, the results are simulated with Arena software to validate the mathematical model and observe performance of CMS in terms of cell utilization, WIP, waiting times and total number of units waiting.

The remainder of the paper is organized as follows. In Section 2, literature is reviewed. In Section 3, the manufacturing system studied is explained. In Section 4, the calculation of similarity coefficients and capacity requirements and the deterministic capacitated P-median model are discussed. In Section 5, stochastic CMS design is introduced, where bottleneck machine identification and probabilistic capacity requirements are discussed and the proposed non-linear stochastic mathematical model is described. An example problem is solved and provided in Section 6. In Section 7, the validation of models and performance analysis are explained. The experimentation and the results are presented in Section 8. Finally, the concluding remarks are made and the future work is given in Section 9.