Volume 2 Issue 1 pp. 179-192 Winter, 2011


Fuzzy production planning models for an unreliable production system with fuzzy production rate and stochastic/fuzzy demand rate


K. A. Halim, B. C. Giri and K. S. Chaudhuri


In this article, we consider a single-unit unreliable production system which produces a single item. During a production run, the production process may shift from the in-control state to the out-of-control state at any random time when it produces some defective items. The defective item production rate is assumed to be imprecise and is characterized by a trapezoidal fuzzy number. The production rate is proportional to the demand rate where the proportionality constant is taken to be a fuzzy number. Two production planning models are developed on the basis of fuzzy and stochastic demand patterns. The expected cost per unit time in the fuzzy sense is derived in each model and defuzzified by using the graded mean integration representation method. Numerical examples are provided to illustrate the optimal results of the proposed fuzzy models.


DOI: 10.5267/j.ijiec.2010.05.001

Keywords: Inventory, production planning, Imperfect production, Fuzzy number, Graded mean integration representation method
References

Bellman, R. E. & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management Science, 17, B141-B164.

Chen, S. H. (1986). Operations on fuzzy numbers with function principle. Tamkang Journal of Management Science, 6 (1), 13-25.

Chen, S. H. & Chang, S. M. (2008). Optimization of fuzzy production inventory model with unrepairable defective products. International Journal of Production Economics, 113, 887-894.

Chen, S. H. & Hsieh, C. H (1999). Graded mean integration representation of generalized fuzzy number. Journal of Chinese Fuzzy Systems, 5 (2), 1-7.

Dubois, D. & Prade, H. (1980), Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York.

Gen, M., Tsujimura, Y. & Zheng, P.Z. (1997). An application of fuzzy set theory to inventory control models. Computers and Industrial Engineering, 33, 553-556.

Goni, A. & Maheswari, S. (2010). Supply chain model for the retailer’s ordering policy under two levels of delay payments in fuzzy environment. Applied Mathematical Sciences, 4, 1155-1164.

Halim, K.A., Giri, B.C. & Chaudhuri, K.S. (2008). Fuzzy economic order quantity model for perishable items with stochastic demand, partial backlogging and fuzzy deteriorating rate. International Journal of Operational Research, 3, 77-96.

Halim, K.A., Giri, B.C. & Chaudhuri, K.S. (2008). Fuzzy EPQ models for an imperfect production system. International Journal of Systems Science, 40(1), 45-52.

Halim, K.A., Giri, B.C. & Chaudhuri, K.S.(2010). Lot sizing in an unreliable manufacturing system with fuzzy demand and repair time. International Journal of Industrial and Systems Engineering, 5, 485-500.

Harris, F. (1915). Operations and Cost, Factory Management Service, Chicago: A.W. Shaw Co.

Hsieh, C.H. (2002). Optimization of fuzzy production inventory models. Information Sciences, 146, 29-40.

Ishii, H. & Konno, T. (1998). A stochastic inventory problem with fuzzy shortage cost. European Journal of Operational Research, 106, 90-94.

Kaufmann, A. & Gupta, M. M. (1992), Introduction to Fuzzy Arithmetic Theory and Applications. Van Nostrand Reinhold, New York.

Lee, H. M. & Yao, J. S. (1998). Economic production quantity for fuzzy demand quantity and fuzzy production quantity. European Journal of Operational Research, 109, 203-211.

Lo, C. Y., Leu, J. H. & Hou, C. I. (2007). A study of the EPQ model using Fuzzy AHP when flaw of the products or unreliable machineries exists, In proceeding of 2007 IEEE International Conference on Industrial Engineering and Engineering Management , pp. 1163-1170.

Mahapatra, N. K. & Maiti, M. (2006). A fuzzy stochastic approach to multi-objective inventory model of deteriorating items with various types of demand and time dependent holding cost, Journal of the Operational Research Society of India, 43 (2), 117-131.

Mahata, G. C. & Goswami, A. (2006). Production lot size model with fuzzy production rate and fuzzy demand rate for deteriorating item under permissible delay in payments. Journal of the Operational Research Society of India, 43 (4), 358-375.

Maiti, M. K. & Maiti, M. (2006). Fuzzy inventory model with two warehouses under possibility constraints, Fuzzy Sets and Systems, 157, 52-73.

Mondal, S. & Maiti, M. (2002). Multi-item fuzzy EOQ models using genetic algorithm, Computers & Industrial Engineering, 44, 105-117.

Petrovic, D. & Sweeney, E. (1994). Fuzzy knowledge-based approach to treating uncertainty in inventory control, Computer Integrated Manufacturing System, 7 (3), 147-152.

Yao, J. S. & Chiang, J. (2003). Inventory without backorder with fuzzy total cost and fuzzy storing cost defuzzified by centroid and signed distance. European Journal of Operational Research, 148, 401-409.

Zadeh, L. A. (1965). Fuzzy Sets, Information and Control, 8, 338-353.

Zimmermann, H. J. (1996), Fuzzy Set Theory and Its Applications: Third ed., Kluwer Academic Publishers, Dordrecht.