A Fuzzy Goal Programming Approach for Optimizing Non-normal Fuzzy Multiple Response Problems

Document Type : Research Paper


1 Department of Industrial and Systems Engineering, Isfahan University of Technology, Isfahan, Iran

2 School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran

3 Industrial Engineering Department, Faculty of Engineering, Shahed University, Tehran, Iran


In most manufacturing processes, each product may contain a variety of quality characteristics which are of the interest to be optimized simultaneously through determination of the optimum setting of controllable factors. Although, classic experimental design presents some solutions for this regard, in a fuzzy environment, and in cases where the response data follow non-normal distributions, the available methods do not apply any more. In this paper, a general framework is introduced in which NORTA inverse transformation technique and fuzzy goal programming are used to deal with non-normality distribution of the response data and the fuzziness of response targets respectively. Moreover, the presented framework uses a simulation approach to investigate the effectiveness of the determined setting of controllable factors obtained from statistical analysis, for optimization of sink mark index, deflection rate and volumetric shrinkage in plastic molding manufacturing processes. The accuracy of the proposed method is verified through a real case study.


Main Subjects

Amiri, A., Bashiri, M., Mogouie, H., Dorodyan, M. H., (2012). Non-normal Multi-Response Optimization by Multivariate Process Capability Index, Scientia Iranica, Vol. 19(6), pp. 1894–1905.
Bashiri, M., Farshbaf-Geranmayeh, A., & Mogouie, H. (2013). A neuro-data envelopment analysis approach for optimization of uncorrelated multiple response problems with smaller the better type controllable factors. Journal of Industrial Engineering International, Vol. 9(1), pp. 1-10.
Bashiri, M., Geranmayeh, A. F., & Sherafati, M. (2012). Solving multi-response optimization problem using artificial neural network and PCR-VIKOR. In Quality, Reliability, Risk, Maintenance, and Safety Engineering (ICQR2MSE), 2012 International Conference on IEEE, pp. 1033-1038.
Box, G. E. P. , Cox, D. R., (1964), An analysis of transformations, Journal of the Royal Statistical Society, Series B, Vol. 26, pp. 211-252.
Chen, C.P., Chuang, M.T., Hsiao, Y.H., Yang, Y.K. and Tsai, C.H., 2009. Simulation and experimental study in determining injection molding process parameters for thin-shell plastic parts via design of experiments analysis. Expert Systems with Applications, 36(7), pp.10752-10759. 
Chen, L.H., Tsai, F.C., (2001), Fuzzy goal programming with different importance and priorities, European Journal of Operational Research, Vol. 133(3), pp. 548–556.
Chiang, k., Chang, F., (2007), Analysis of shrinkage and warpage in an injection-molded part with a thin shell feature using the response surface methodology, The International Journal of Advanced Manufacturing Technology, Vol. 35(5-6), pp. 468-479.
Chompu-inwai, R., Jaimjit, B. and Premsuriyanunt, P., (2015). A combination of Material Flow Cost Accounting and design of experiments techniques in an SME: the case of a wood products manufacturing company in northern Thailand. Journal of Cleaner Production, Vol. 108, pp.1352-1364.
Deb, K., (2014). Multi-objective optimization. In Search methodologies, pp. 403-449. Springer US.
Giasin, K., Ayvar-Soberanis, S. and Hodzic, A., 2016. Evaluation of cryogenic cooling and minimum quantity lubrication effects on machining GLARE laminates using design of experiments. Journal of Cleaner Production, Vol. 135, pp.533-548.
Griffiths, C.A., Howarth, J., De Almeida-Rowbotham, G., Rees, A. and Kerton, R., (2016), A design of experiments approch for the optimization of energy and waste during the production of parts manufactured by 3D printing .Journal of Cleaner Production, Vol. 139, pp.74-85.
Guo, W., Hua, L. and Mao, H., (2014). Minimization of sink mark depth in injection-molded thermoplastic through design of experiments and genetic algorithm. The International Journal of Advanced Manufacturing Technology, Vol. 72(1-4), pp. 365-375.
Guzmán, A.Á., Gordillo, S.M., Delvasto, A.S., Quereda, V.M.F. and Sánchez, V.E., (2016). Optimization of the technological properties of porcelain tile bodies containing rice straw ash using the design of experiments methodology. Ceramics International, Vol. 42(14), pp.15383-15396.
Heidari, B.S., Oliaei, E., Shayesteh, H., Davachi, S.M., Hejazi, I., Seyfi, J., Bahrami, M. and Rashedi, H., (2017). Simulation of mechanical behavior and optimization of simulated injection molding process for PLA based antibacterial composite and nanocomposite bone screws using central composite design. Journal of the Mechanical Behavior of Biomedical Materials, Vol. 65, pp. 160-176.
K. Johnson, N., (1949), Systems of frequency curves generated by methods of translations, Biometrika, Vol. 36, pp. 149-176.
Korhonen, K., Poikolainen, M., Korhonen, O., Ketolainen, J. and Laitinen, R., (2016). Systematic evaluation of a spraying method for preparing thin Eudragit-drug films by Design of Experiments. Journal of Drug Delivery Science and Technology, Vol. 35, pp. 241-251.
Li, S., Hu, C., (2009), Satisfying optimization method based on goal programming for fuzzy
multiple objective optimization problem. European Journal of Operational Research, Vol. 197(3), pp. 675–684.
Marler, R.T. and Arora, J.S., (2004), Survey of multi-objective optimization methods for engineering. Structural and multidisciplinary optimization, Vol. 26(6), pp. 369-395.
Niaki S.T.A., Abbasi, B., (2009), Monitoring multi-attribute processes based on NORTA inverse transformed vectors, Communication in Statistics – Theory and Methods, Vol. 38(7), pp. 964-979.
Oliaei, E., Heidari, B.S., Davachi, S.M., Bahrami, M., Davoodi, S., Hejazi, I. and Seyfi, J., 2016. Warpage and Shrinkage Optimization of Injection-Molded Plastic Spoon Parts for Biodegradable Polymers Using Taguchi, ANOVA and Artificial Neural Network Methods. Journal of Materials Science & Technology.
Ozcelic, B., Ozbay, A., Erhan, D., (2010) Influence of injection parameters and mold materials on mechanical properties of ABS in plastic injection molding, International Communications in Heat and Mass Transfer, Vol. 37(9), pp. 1359-1365.
Pawlak, A., Rosienkiewicz, M. and Chlebus, E., )2017(. Design of experiments approach in AZ31 powder selective laser melting process optimization. Archives of Civil and Mechanical Engineering, Vol. 17(1), pp. 9-18.
Quesenberry C. P. SPC methods for quality improvement, John Wiley& Sons, New York, (1997).
Rabbani, M., Mamaghani, M. G., Farshbaf-Geranmayeh, A., & Mirzayi, M. (2016). A Novel Mixed Integer Programming Formulation for Selecting the Best Renewable Energies to Invest: A Fuzzy Goal Programming Approach. International Journal of Operations Research and Information Systems (IJORIS), Vol. 7(3), pp. 1-22.
Sintov, A., Menassa, R.J. and Shapiro, A., (2016). A gripper design algorithm for grasping a set of parts in manufacturing lines. Mechanism and Machine Theory, Vol. 105, pp. 1-30.
Tanaka, H., Okuda, T., Asai, K., (1974), on fuzzy mathematical programming. Journal of Cybernetics, Vol. 3(4), pp. 37–46.
Xie, M.,Goh, T.N., Tang, Y., (2000), Data transformation for geometrically distributed quality characteristics, Quality and Reliability Engineering International, Vol. 16(1), pp. 9-15.
Zimmermann, H. J., (1978), Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, Vol.1. pp. 45–55.