CFP last date
20 January 2025
Reseach Article

A Fuzzy Environment Inventory Model with Partial Backlogging under Learning Effect

by Isha Sangal, Anchal Agarwal, Smita Rani
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 137 - Number 6
Year of Publication: 2016
Authors: Isha Sangal, Anchal Agarwal, Smita Rani
10.5120/ijca2016908793

Isha Sangal, Anchal Agarwal, Smita Rani . A Fuzzy Environment Inventory Model with Partial Backlogging under Learning Effect. International Journal of Computer Applications. 137, 6 ( March 2016), 25-32. DOI=10.5120/ijca2016908793

@article{ 10.5120/ijca2016908793,
author = { Isha Sangal, Anchal Agarwal, Smita Rani },
title = { A Fuzzy Environment Inventory Model with Partial Backlogging under Learning Effect },
journal = { International Journal of Computer Applications },
issue_date = { March 2016 },
volume = { 137 },
number = { 6 },
month = { March },
year = { 2016 },
issn = { 0975-8887 },
pages = { 25-32 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume137/number6/24281-2016908793/ },
doi = { 10.5120/ijca2016908793 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T23:37:40.414114+05:30
%A Isha Sangal
%A Anchal Agarwal
%A Smita Rani
%T A Fuzzy Environment Inventory Model with Partial Backlogging under Learning Effect
%J International Journal of Computer Applications
%@ 0975-8887
%V 137
%N 6
%P 25-32
%D 2016
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this article we developed an inventory model for non-instantaneous decaying items is considered under crisp and fuzzy environment. In this study we have considered stock dependent demand rate and variable deterioration. It is supposed that shortages are allowed and partially backlogged with exponential backlogging rate. Holding cost follows the learning curve. The deterioration rate, ordering cost, shortage cost and deterioration cost are assumed as a triangular fuzzy numbers. The aim of our study is to defuzzify the total cost function by signed distance method. This model is developed in both crisp and fuzzy surroundings. A numerical experiment is given to demonstrate the developed crisp and fuzzy models. Sensitivity analysis is implemented to examine the effect of parameters. The convexity of the total cost function is shown by graphically.

References
  1. Balkhi, Z.T.,(2003), ‘The Effect of learning on the optimal production lot size for deteriorating and partially backordered items with time varying demand and deterioration rates’, Applied Mathematical Modeling, 27,763-779.
  2. Chang, H.J., Dye, C.Y., (1999), ‘An EOQ model for deteriorating items with time varying demand and partial backlogging’, Journal of the Operational Research Society,50, 1176–1182.
  3. De, P.K., Rawat, A.,(2011), ‘A Fuzzy Inventory Model without Shortages Using Triangular Fuzzy Number’, Fuzzy Information and Engineering, 3, 59-68.
  4. Dubois, D., Prade, H., (1978), ‘Operations on Fuzzy Numbers’ International Journal of System Science, 9, 613-626.
  5. Dutta, D., Kumar, P., (2013), ‘Optimal Ordering Policy for an Inventory Model for Deteriorating Items without Shortages by Considering Fuzziness in Demand Rate, Ordering Cost and Holding Cost’, International Journal of Advanced Innovation and Research, 2, 320-325.
  6. Dye, C.Y.(2013), ‘The effect of preservation technology investment on a non-instantaneous deteriorating inventory model’ Omega, 41(5),872 – 880.
  7. Fisk, J.C., Ballou, D.P., (1985), ‘Production lot sizing under learning effect’ AIIE Transactions, 17, 33-37.
  8. Ghare, P.M., Schrader, G. P.,(1963), ‘A model for an exponentially decaying inventory, Journal of Industrial Engineering,14, (5),248-243.
  9. 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 .
  10. Jaber, M.Y., Goyal, S.K., Imran, M. (2008), ‘Economic production quantity model for items with imperfect quality subject to learning effects’, International Journal of Production Economics, 115,143- 150.
  11. Jaggi, C.K, Sharma, A., Tiwari .S. (2015), ‘Credit financing in economic ordering policies for non-instantaneous deteriorating items with price dependent demand under permissible delay in payments’ International Journal of Industrial Engineering Computations,(6), 481–502 .
  12. Jaggi, C.K., Pareek, S., Sharma, A., Nidhi. (2012), ‘Fuzzy Inventory Model for Deteriorating Items with Time Varying Demand and Shortages’, American Journal of Operational Research,2, 81-92.
  13. Jaggi, C.k.,(2014), ‘An Optimal Replenishment Policy for Non Instantaneous Deteriorating Items with Price Dependent Demand and Time-Varying Holding Cost’ International Scientific Journal on Science Engineering & Technology, 17(03).
  14. Jain, R. (1976), ‘Decision Making in the Presence of Fuzzy Variables’ IIIE Transactions on Systems, Man and Cybernetics.17, 698-703.
  15. Jordan, R.B.(1958), ‘Learning how to use the learning curve’, N.A.A. Bull, 39 (5), 27–39.
  16. Kacpryzk, J., Staniewski, P. (1982), ‘Long Term Inventory Policy Making through Fuzzy Decision Making Methods’, Fuzzy Sets and System, 8, 117-132.
  17. Kao, C.K., Hsu, W.K. (2002), ‘A Single Period Inventory Model with Fuzzy Demand’, Computers and Mathematics with Applications, 43, 841-848.
  18. Khurana, D.,(2015), ‘Two Warehouse Inventory Model for Deteriorating Items with Time Dependent Demand under Inflation’,International Journal of Computer Applications,114,7, 0975 – 8887
  19. Kumar ,S., Rajput, U.S.(2015), ‘Fuzzy Inventory Model for Deteriorating items with Time Dependent Demand and Partial Backlogging’, Applied Mathematics, 6,496-509.
  20. Kumar, N., Singh, S.R., Kumari, K. (2013-a), ‘Learning effect on an inventory model with two-level storage and partial backlogging under inflation’, International Journal of Services and Operations Management, 16 (1), 105–122.
  21. 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.
  22. Saha, S., Chakrabarti, T.(2012), ‘Fuzzy EOQ Model with Time Dependent Demand and Deterioration with Shortages’, IOSR Journal of Mathematics, 2, 46-54.
  23. Shukla, H. S., Shukla, V., Yadav, S. K.(2013), ‘EOQ model for deteriorating items with exponential demand rate and shortages’ Uncertain Supply Chain Management, 1(2), 67-76.
  24. Singh, S., Jain, S., Pareek, S. (2103), ‘An imperfect quality items with learning and inflation under two limited storage capacity’, International Journal of Industrial Engineering Computations, 4 (4), 479-490.
  25. Singh, S.R., Sharma, S. (2014), ‘Optimal trade-credit policy for perishable items deeming imperfect production and stock dependent demand’, International Journal of Industrial Engineering Computations. 5(1), 151-168.
  26. Singh, S.R., Singh, C.(2008), ‘Optimal ordering policy for decaying items with stock dependent demand under inflation in a supply chain’ International Review of Pure and Advanced Mathematics, 1, 31-39.
  27. Singhal, S.,Singh, S. R.(2015), ‘Modelling of an inventory system with multi variate demand under volume flexibility and learning’ Uncertain Supply Chain Management, 3(2), 147-158.
  28. Sugapriya C., Jeyaraman K. (2008), ‘An EPQ model for non-instantaneous deteriorating item in which holding cost varies with time’ Electronic Journal of Applied Statistical Analysis.1, ( 1),16–23.
  29. Tayal , S., Singh, S.R., Sharma, R., Singh, A. P.(2015), ‘An EPQ model for non-instantaneous deteriorating item with time dependent holding cost and exponential demand rate’, International Journal of Operational Research, 23,(2),145-161.
  30. Wright, T. (1936), ‘Factors affecting the cost of airplanes’ Journal of Aeronautical Science, 3( 4),122–128(1936).
  31. Wu, K.S, Ouyang, L.Y., Yang, C.T.(2006), ‘An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging’ Int. J. Production Economics 101,369–384.
  32. 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.
  33. Yao, J.S., Lee, H. M.(1996), ‘Fuzzy inventory with backorder for fuzzy order quantity’ Information Sciences, 93, 283-319.
  34. Zadeh, L.A.(1965), ‘Fuzzy Set’ Information Control, 8,338-353.
  35. Zimmerman, H.J. (1983), ‘Using Fuzzy Sets in Operational Research’ European Journal of Operation Research, 13, 201-206 .
Index Terms

Computer Science
Information Sciences

Keywords

Non-instantaneous-deterioration Triangular fuzzy numbers Signed distance Learning Partial backlogging