Ali Ghodratnama - Department of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran
Seyed Ali Torabi - Department of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran
Raza Tavakkoli-Moghaddam - Department of Industrial Engineering, College of En- gineering, University of Tehran, Tehran, Iran

This paper addresses a new version of the exible ow line prob- lem, i.e., the budget constrained one, in order to determine the required num- ber of processors at each station along with the selection of the most eco- nomical process routes for products. Since a number of parameters, such as due dates, the amount of available budgets and the cost of opting particular routes, are imprecise (fuzzy) in practice, they are treated as fuzzy variables. Furthermore, to investigate the model behavior and to validate its attribute, we propose three fuzzy programming models based upon credibility measure, namely expected value model, chance-constrained programming model and dependent chance-constrained programming model, in order to transform the original mathematical model into a fuzzy environment. To solve these fuzzy models, a hybrid meta-heuristic algorithm is proposed in which a genetic al- gorithm is designed to compute the number of processors at each stage; and a particle swarm optimization (PSO) algorithm is applied to obtain the op- timal value of tardiness variables. Finally, computational results and some concluding remarks are provided.

Budget-constrained exible ow lines, Credibility-based fuzzy pro- gramming, Meta-heuristic, Genetic Algorithm, Particle Swarm Optimization