Int. J. Operational Research, Vol. 22, No. 2, 2015 129 Copyright © 2015 Inderscience Enterprises Ltd. Fuzzy and stochastic mathematical programming for optimisation of cell formation problems in random and uncertain states Ali Azadeh* School of Industrial and Systems Engineering, Department of Engineering Optimization and Center of Excellence for Intelligent-Based Experimental Mechanics, College of Engineering, University of Tehran, P.O. Box 11365/4563, Tehran, Iran Fax: +98218013102 Email: Aazadeh@ut.ac.ir Email: ali@azadeh.com *Corresponding author Mohsen Moghaddam School of Industrial Engineering, Purdue University, 315 N., Grant Street, West Lafayette, IN 47907-2023, USA Email: mmoghadd@purdue.edu Babak Nazari-Doust and Fatemeh Jalalvand School of Industrial and Systems Engineering, Department of Engineering Optimization and Center of Excellence for Intelligent-Based Experimental Mechanics, College of Engineering, University of Tehran, P.O. Box 11365/4563, Tehran, Iran Email: babak_nazaridoust@yahoo.com Email: fateme.jalalvand@gmail.com Abstract: Applying mathematical programming models to solve the cellular manufacturing problems is a challenging task as decision makers find it difficult to specify goals and constraints because some of the involved parameters cannot be estimated precisely. This study presents a modelling approach for design of a dynamic cellular manufacturing system with uncertain characteristics and parameters. It provides mathematical models for solving cell formation problems (CFPs) in three different conditions: 1) crisp state in which all parameters are known and fixed; 2) fuzzy state in which setup cost, outsourcing cost and capacity of machines are considered as fuzzy parameters; 3) stochastic state in which probability distributions are used to model the assumed randomness. The general algebraic modelling system (GAMS) software is used to solve all test problems by CPLEX solver. This is the first study that presents mathematical programming models for solving CMS problems in crisp, stochastic and fuzzy states.