ORIGINAL ARTICLE Designing integrated cellular manufacturing systems with scheduling considering stochastic processing time Vahidreza Ghezavati & Mohammad Saidi-Mehrabad Received: 10 July 2009 / Accepted: 15 September 2009 / Published online: 1 October 2009 # Springer-Verlag London Limited 2009 Abstract This paper addresses a new mathematical model for cellular manufacturing problem integrated with group scheduling in an uncertain space. This model optimizes cell formation and scheduling decisions, concurrently. It is assumed that processing time of parts on machines is stochastic and described by discrete scenarios enhances application of real assumptions in analytical process. This model aims to minimize total expected cost consisting maximum tardiness cost among all parts, cost of subcon- tracting for exceptional elements and the cost of resource underutilization. Scheduling problem in a cellular manu- facturing environment is treated as group scheduling problem, which assumes that all parts in a part family are processed in the same cell and no inter-cellular transfer is needed. Finally, the nonlinear model will be transformed to a linear form in order to solve it for optimality. To solve such a stochastic model, an efficient hybrid method based on new combination of genetic algorithm (GA), simulated annealing (SA) algorithm, and an optimization rule will be proposed where SA and optimization rule are subordinate parts of GA under a self-learning rule criterion. Also, performance and robustness of the algorithm will be verified through some test problems against branch and bound and a heuristic procedure. Keywords Cellular manufacturing . Uncertainty modeling . Stochastic processing time . Hybrid genetic algorithm . Cell scheduling . Stochastic programming 1 Introduction Group technology (GT) is a management theory that aims to group products with similar process or manufacturing characteristics, or both. Cellular manufacturing (CM) can be proposed as a practical application of GT that determines groups of machines based on similarity of the parts processed by them. The basic purpose of CM is to identify machine cells and part families concurrently and to assign part families to machine cells in order to minimize the intercellular and intracellular costs of parts [1]. Scheduling jobs in individual cells is an operational feature that should be determined at the design stage. Because design stages are so difficult, however, integrating scheduling decisions with CF decision is often seen as just a more complication. This review focuses on the uncertain studies that are relevant to the uncertainty planning of cellular manufactur- ing system (CMS) problems; however, a survey of certain conditions will be presented. The literature on the design of cellular manufacturing system is quite extensive in certain and determined situations. Past researches in studying CMSs design and implementation have been predominantly focused on the CF decision in certain conditions. In the context of the research reported here, research work dealing with the uncertainty aspects of CMS design is presented. A majority of cases studied CMS problem in uncertain situations can be classified into three branches: (1) fuzzy approach, (2) stochastic optimization, and (3) heuristic procedures. The most common planning approach devel- oped to resolve uncertainty in CMS problems can be introduced as fuzzy approach with many researches proposed previously. Papaioannou and Wilson [2] proposed CMS problems analysis where coefficients in objective function and constraints are considered as fuzzy coeffi- V. Ghezavati (*) : M. Saidi-Mehrabad Department of Industrial Engineering, Iran University of Science and Technology, P.C. 16844 Tehran, Iran e-mail: ghezavati@iust.ac.ir Int J Adv Manuf Technol (2010) 48:701–717 DOI 10.1007/s00170-009-2322-2