Mathematical Modelling for EOQ Inventory System with Advance Payment and Fuzzy Parameters

Document Type : Research Paper

Authors

1 The Gandhigram Rural Institute - Deemed University, Gandhigram - 624 302, India

2 The Gandhigram Rural Institute – Deemed University, Gandhigram - 624 302, , India

Abstract

This study considers an EOQ inventory model with advance payment policy in a fuzzy situation by employing two types of fuzzy numbers that are trapezoidal and triangular. Two fuzzy models are developed here. In the first model the cost parameters are fuzzified, but the demand rate is treated as crisp constant. In the second model, the demand rate is fuzzified but the cost parameters are treated as crisp constants. For each fuzzy model, we use signed distance method to defuzzify the fuzzy total cost and obtain an estimate of the total cost in the fuzzy sense. Numerical example is provided to ascertain the sensitiveness in the decision variables about fuzziness in the components. In practical situations, costs may be dependent on some foreign monetary unit. In such a case, due to a change in the exchange rates, the costs are often not known precisely. The first model can be used in this situation. In actual applications, demand is uncertain and must be predicted. Accordingly, the decision maker faces a fuzzy environment rather than a stochastic one in these cases. The second model can be used in this situation. Moreover, the proposed models can be expended for imperfect production process.

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References

Bjrk, K.M. (2009). An analytical solution to a fuzzy economic order quantity problem. International Journal of Approximate Reasoning, Vol. 50, pp. 485-493.
Chiang, J., Yao J.S. and Lee, H.M. (2005). Fuzzy Inventory with Backorder Defuzzification by Signed Distance Method. Journal of Information Science and Engineering, Vol. 21, pp. 673-694.
Goyal, S.K. (1985). Economic order quantity under conditions of permissible delay in payments. Journal of Operations Research Society, Vol. 36, pp. 335-338. 
Gupta, R.K., Bhunia, A.K. and Goyal, S.K. (2009). An application of genetic algorithm in solving an inventory model with advance payment and interval valued inventory costs. Mathematical and Computer Modelling, Vol. 49, pp. 893-905.
Ishii, H. and Konno, T.A. (1998). Stochastic inventory problem with fuzzy shortage cost. European Journal of Operational Research, Vol. 106, pp. 90-94.  
Liu, S.T. (2012). Solution of fuzzy integrated production and marketing planning based on extension principle. Computers and Industrial Engineering, Vol. 63, pp. 1201-1208. 
Mahata, G.C. and Goswami, A. (2013). Fuzzy inventory models for items with imperfect quality and shortage backordering under crisp and fuzzy decision variables. Computers and Industrial Engineering, Vol. 64, pp. 190-199. 
Maiti, A.K., Maiti, M.K. and Maiti, M. (2009). Inventory model with stochastic lead-time and price dependent demand incorporating advance payment. Applied Mathematical Modelling, Vol. 33, pp. 2433-2443. 
Pu, P.M. and Liu, Y.M. (1980). Fuzzy topology 1, neighborhood structure of a fuzzy point and moore-smith convergence. Journal of Mathematical Analysis and Applications, Vol. 76, pp. 571-599. 
Sadjadi, S.J. Ghazanfari, M. and Yousefli, A, (2010). Fuzzy pricing and marketing planning model: A possibilistic geometric programming approach. Expert Systems with Applications, Vol. 37, pp. 3392-3397. 
Seifert, D., Seifert, R.W. and Protopappa-Sieke, M. (2013). A review of trade credit literature:Opportunities for research in operations. European Journal of Operational Research, Vol. 231, pp. 245-256. 
Thangam, A. (2012). Optimal price discounting and lot-sizing policies for perishable items in a supply chain under advance payment scheme and two-echelon trade credits. International Journal of Production Economics, Vol. 139, pp. 459-472. 
Vijayan, T. and Kumaran, M. (2008). Inventory models with a mixture of backorders and lost sales under fuzzy cost. European Journal of Operational Research, Vol. 189, pp. 105-119. 
Yao, J.S. and 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, Vol. 148, pp. 401-409. 
Yao, J.S. and Lee, H.M. (1999). Fuzzy inventory with or without back order for fuzzy order quantity with trapezoidal fuzzy numbers. Fuzzy Sets and Systems, Vol. 105, pp. 311-337. 
Yao, J.S. and Wu, K. (2000). Ranking fuzzy numbers based on decomposition principle and signed distance. Fuzzy Sets and Systems, Vol. 116, pp. 275-288. 
Zadeh, L. (1965). Fuzzy sets. Information and Control, Vol. 8, pp. 338-353.
Zhang, Q., Tsao, Y.C. and Chen, T.H. (2014). Economic order quantity under advance payment. Applied Mathematical Modelling, Vol. 38, pp. 5910-5921. 
Zimmerman, H.J. (1991). Fuzzy Set Theory and Its Applications, second ed. Kluwer Academic Publishers, Boston. 
International Journal of Supply and Operations Management
Volume 1, Issue 3 - Serial Number 3
November 2014
Pages 260-278

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