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Advances in Fuzzy Systems
Volume 2016 (2016), Article ID 6132768, 10 pages
http://dx.doi.org/10.1155/2016/6132768
Research Article

A Novel Method for Optimal Solution of Fuzzy Chance Constraint Single-Period Inventory Model

Department of Mathematics, ITER, Siksha ‘O’ Anusandhan University, Bhubaneswar, Odisha 751030, India

Received 16 July 2016; Accepted 11 October 2016

Academic Editor: Erich Peter Klement

Copyright © 2016 Anuradha Sahoo and J. K. Dash. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. A. Zadeh, “Fuzzy sets,” Information and Computation, vol. 8, no. 3, pp. 338–353, 1965. View at Google Scholar · View at MathSciNet
  2. J. J. Buckley, Fuzzy Probabilities. New Approach and Applications, Physica, Heidelberg, Germany, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  3. H. Kwakernaak, “Fuzzy random variables—I. definitions and theorems,” Information Sciences, vol. 15, no. 1, pp. 1–29, 1978. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. H.-J. Zimmermann, “Fuzzy mathematical programming,” Computers & Operations Research, vol. 10, no. 4, pp. 291–298, 1983. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. S. Nanda and K. Kar, “Convex fuzzy mappings,” Fuzzy Sets and Systems, vol. 48, no. 1, pp. 129–132, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. M. L. Puri and D. A. Ralescu, “Fuzzy random variables,” Journal of Mathematical Analysis and Applications, vol. 114, no. 2, pp. 409–422, 1986. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. D. Petrović, R. Petrović, and M. Vujošević, “Fuzzy models for the newsboy problem,” International Journal of Production Economics, vol. 45, no. 1–3, pp. 435–441, 1996. View at Publisher · View at Google Scholar
  8. K. Das, T. K. Roy, and M. Maiti, “Multi-item stochastic and fuzzy-stochastic inventory models under two restrictions,” Computers and Operations Research, vol. 31, no. 11, pp. 1793–1806, 2004. View at Publisher · View at Google Scholar · View at Scopus
  9. S. Nanda, G. Panda, and J. K. Dash, “A new methodology for crisp equivalent of fuzzy chance constrained programming problem,” Fuzzy Optimization and Decision Making, vol. 7, no. 1, pp. 59–74, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. N. K. Mahapatra and M. Maiti, “Decision process for multiobjective, multi-item production-inventory system via interactive fuzzy satisficing technique,” Computers & Mathematics with Applications, vol. 49, no. 5-6, pp. 805–821, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. H.-C. Chang, J.-S. Yao, and L.-Y. Ouyang, “Fuzzy mixture inventory model involving fuzzy random variable lead time demand and fuzzy total demand,” European Journal of Operational Research, vol. 169, no. 1, pp. 65–80, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. Z. Shao and X. Ji, “Fuzzy multi-product constraint newsboy problem,” Applied Mathematics and Computation, vol. 180, no. 1, pp. 7–15, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. C.-M. Lee, “A Bayesian approach to determine the value of information in the newsboy problem,” International Journal of Production Economics, vol. 112, no. 1, pp. 391–402, 2008. View at Publisher · View at Google Scholar · View at Scopus
  14. J. C. Hayya, T. P. Harrison, and D. C. Chatfield, “A solution for the intractable inventory model when both demand and lead time are stochastic,” International Journal of Production Economics, vol. 122, no. 2, pp. 595–605, 2009. View at Publisher · View at Google Scholar · View at Scopus
  15. J. K. Dash, G. Panda, and S. Nanda, “Chance constrained programming problem under different fuzzy distributions,” International Journal of Optimization. Theory Methods and Applications, vol. 1, no. 1, pp. 58–71, 2009. View at Google Scholar · View at MathSciNet
  16. J.-S. Hu, H. Zheng, R.-Q. Xu, Y.-P. Ji, and C.-Y. Guo, “Supply chain coordination for fuzzy random newsboy problem with imperfect quality,” International Journal of Approximate Reasoning, vol. 51, no. 7, pp. 771–784, 2010. View at Publisher · View at Google Scholar · View at Scopus
  17. G. Zhang, “The multi-product newsboy problem with supplier quantity discounts and a budget constraint,” European Journal of Operational Research, vol. 206, no. 2, pp. 350–360, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. R.-H. Su, D.-Y. Yang, and W. L. Pearn, “Decision-making in a single-period inventory environment with fuzzy demand,” Expert Systems with Applications, vol. 38, no. 3, pp. 1909–1916, 2011. View at Publisher · View at Google Scholar · View at Scopus
  19. K. A. M. Kotb and H. A. Fergany, “Multi-item EOQ model with both demand-dependent unit cost and varying leading time via geometric programming,” Applied Mathematics, vol. 2, no. 5, pp. 551–555, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  20. O. Dey and D. Chakraborty, “A fuzzy random continuous review inventory system,” International Journal of Production Economics, vol. 132, no. 1, pp. 101–106, 2011. View at Publisher · View at Google Scholar · View at Scopus
  21. R. Banerjee and S. Banerjee, “Solution of a probabilistic inventory model with chance constraints: a general fuzzy programming and intuitionistic fuzzy optimization approach,” International Journal of Pure and Applied Sciences and Technology, vol. 9, no. 1, pp. 20–38, 2012. View at Google Scholar
  22. M. Nagare and P. Dutta, “On solving single-period inventory model under hybrid uncertainty,” International Journal of Economics and Management Sciences, vol. 6, no. 4, pp. 290–295, 2012. View at Google Scholar
  23. M. A. Jahantigh, S. Khezerloo, A. A. Hosseinzadeh, and M. Khezerloo, “Solutions of fuzzy linear systems using ranking function,” International Journal of Applied Operational Research, vol. 2, pp. 67–75, 2012. View at Google Scholar
  24. A. Karpagam and P. Sumathi, “New approach to solve fuzzy linear programming problems by the ranking function,” Bonfring International Journal of Data Mining, vol. 4, no. 4, pp. 22–25, 2014. View at Publisher · View at Google Scholar
  25. D. Dutta and P. Kumar, “Fuzzy inventory model without shortage using trapezoidal fuzzy number with sensitivity analysis,” IOSR Journal of Mathematics, vol. 4, no. 3, pp. 32–37, 2012. View at Publisher · View at Google Scholar
  26. S. Ding, “Uncertain multi-product newsboy problem with chance constraint,” Applied Mathematics and Computation, vol. 223, pp. 139–146, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. H. Zolfagharinia and K. P. S. Isotupa, “Erratum on ‘Optimal inventory control of empty containers in inland transportation system’ Int. J. Prod. Econ. 133(1) (2011) 451–457,” International Journal of Production Economics, vol. 141, no. 1, pp. 43–436, 2013. View at Publisher · View at Google Scholar
  28. P. Majumder, U. K. Bera, and M. Maiti, “An EPQ model of deteriorating items under partial trade credit financing and demand declining market in crisp and fuzzy environment,” Procedia Computer Science, vol. 45, pp. 780–789, 2015. View at Google Scholar
  29. S. M. Mousavi, J. Sadeghi, S. T. A. Niaki, N. Alikar, A. Bahreininejad, and H. S. C. Metselaar, “Two parameter-tuned meta-heuristics for a discounted inventory control problem in a fuzzy environment,” Information Sciences, vol. 276, pp. 42–62, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. H. N. Soni and M. Joshi, “A periodic review inventory model with controllable lead time and backorder rate in fuzzy-stochastic environment,” Fuzzy Information and Engineering, vol. 7, no. 1, pp. 101–114, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  31. R. S. Kumar and A. Goswami, “A fuzzy random EPQ model for imperfect quality items with possibility and necessity constraints,” Applied Soft Computing, vol. 34, pp. 838–850, 2015. View at Publisher · View at Google Scholar · View at Scopus
  32. N. Kazemi, E. Shekarian, L. E. C. Barrón, and E. U. Olugu, “Incorporating human learning into a fuzzy EOQ inventory model with backorders,” Computers & Industrial Engineering, vol. 87, pp. 540–542, 2015. View at Publisher · View at Google Scholar · View at Scopus
  33. J. K. Dash and A. Sahoo, “Optimal solution for a single period inventory model with fuzzy cost and demand as a fuzzy random variable,” Journal of Intelligent & Fuzzy Systems. Applications in Engineering and Technology, vol. 28, no. 3, pp. 1195–1203, 2015. View at Google Scholar · View at MathSciNet
  34. M. Nagare, P. Dutta, and N. Cheikhrouhou, “Optimal ordering policy for newsvendor models with bidirectional changes in demand using expert judgment,” OPSEARCH, vol. 53, no. 3, pp. 620–647, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  35. P. Raula, S. K. Indrajitsingha, P. N. Samanta, and U. K. Misra, “A Fuzzy Inventory Model for constant deteriorating item by using GMIR method in which inventory parameters treated as HFN,” Open Journal of Applied and Theoretical Mathematics (OJATM), vol. 2, no. 1, pp. 13–20, 2016. View at Google Scholar
  36. I. Sangal, A. Agarwal, and S. Rani, “A fuzzy environment inventory model with partial backlogging under learning effect,” International Journal of Computer Applications, vol. 137, no. 6, pp. 25–32, 2016. View at Publisher · View at Google Scholar