Fuzzy and stochastic mathematical programming for optimisation of cell formation problems in random and uncertain states Online publication date: Sat, 09-May-2015
by Ali Azadeh; Mohsen Moghaddam; Babak Nazari-Doust; Fatemeh Jalalvand
International Journal of Operational Research (IJOR), Vol. 22, No. 2, 2015
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.
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