An EOQ Model for Defective Items Under Pythagorean Fuzzy Environment

Document Type : Original Manuscript

Authors

1 Department of Mathematics, ITER Siksha O Anusandhan, Jagmara, Khandagiri, Bhubaneswar, Odisha

2 Department of Mathematics, ITER Siksha O Anusandhan, Jagmara, Khandagiri

Abstract

Classical EOQ models can help us decide on the terms of how much to order, to manage an inventory. Any company dealing with physical products needs to manage an inventory to improve and avoid shortages occurring. Many times the lots come with defective items due to which there is a loss in the effectiveness of the model. In the present study, we consider two types of carrying costs for good and defectives items, and also proportionate discount is being considered for defective items. We use the Pythagorean fuzzy environment (PFS) and analyze the score functions with help of  cuts of the fuzzy parameters. The problem is optimized to get the best solution, utilizing Yager’s Ranking. The numerical results obtained from crisp and fuzzy environments are also compared. Lastly graphical and sensitivity illustrations are being used to justify the models.

Graphical Abstract

An EOQ Model for Defective Items Under Pythagorean Fuzzy Environment

Highlights

  • An Eoq model has been considered for defective items in which the items are discounted in a proportional method.
  • This model gives a managerial insight of getting the profit by allowing proportional discounts.
  • A Pythagorean Fuzzy environment has been considered, which is recent.

Keywords


Atanassov, K.T.(1986) ‘Intuitionistic fuzzy sets, Fuzzy sets and  Systems’ Vol.20(1), pp.87-96
Ahmadi, A., Mohabbatdar, S., & Sajadieh, M. S. (2016). Optimal manufacturer-retailer policies in a supply chain with defective products and price-dependent demand. Journal of Optimization in Industrial Engineering9(19), 37-46.
 Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in a   fuzzy environment. Management Science17(4), B-141.
 Chang, H. C. (2004). An application of fuzzy sets theory to the  EOQ model with imperfect quality items. Computers & Operations Research31(12), 2079-2092.
 Chen, S. H., & Chang, S. M. (2008). Optimization of fuzzy production inventory model with unrepairable defective products. International Journal of Production Economics113(2), 887-894.
 DE, S. K., & Mahata, G. C. (2019). A comprehensive study of an economic order quantity model under fuzzy monsoon demand. Sādhanā44(4), 1-12.
 De, S. K. (2021). Solving an EOQ model under fuzzy reasoning.  Applied Soft Computing99,  106892.
 De, S. K., & Mahata, G. C. (2021). Solution of an imperfect-quality EOQ model with backorder under fuzzy lock leadership game approach. International Journal of   Intelligent Systems36(1), 421-446.
 Harris, F. W. (1913) ‘Operations and costs (Factory Management  Series)’, A.W. Shaw Co, Chicago, pp.18-52.
 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  & Technology17(03).
 Jaggi, C., 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: A new approach.   International Journal of Industrial Engineering
 Computations6(4), 481-502.
Karlin, S. (1958). One stage inventory models with uncertainty. Studies in the mathematical theory of inventory and production, 109-134.
 Khanna, A., Gautam, P., & Jaggi, C. K. (2017). Inventory modeling for deteriorating imperfect quality items with selling price-dependent demand and shortage
back-ordering under credit financing. International   Journal of Mathematical, Engineering and  Management Sciences2(2), 110-124.
 Karmakar, S., De, S. K., & Goswami, A. (2018). A pollution-sensitive remanufacturing model with waste items: triangular dense fuzzy lock set approach. Journal of    Cleaner Production187, 789-803.
Maddah, B., & Jaber, M. Y. (2008). The economic order quantity for items with imperfect quality: revisited.  International Journal of Production Economics112(2), 808-815.
 Mohagheghian, E., Rasti-Barzoki, M., & Sahraeian, R. (2018).     Two-Echelon Supply Chain     Considering Multiple  Retailers with Price and Promotional Effort Sensitive    Non-Linear Demand. Journal of Optimization in Industrial Engineering11(2), 57-64.
 Mao, X. B., Hu, S. S., Dong, J. Y., Wan, S. P., & Xu, G. L. (2018).  Multi-attribute group decision-making based on cloud aggregation operators under interval-valued hesitant fuzzy linguistic environment. International Journal of  Fuzzy Systems20(7), 2273-     2300.
 Mohamadghasemi, A. (2020). A Note On “An Interval Type-2   Fuzzy Extension Of The TOPSIS Method Using Alpha  Cuts”. Journal of Optimization in Industrial  Engineering13(2), 227- 238.
 Maity, S., Chakraborty, A., De, S. K., Mondal, S. P., & Alam, S. (2020) A comprehensive study of a backlogging  EOQ model with the nonlinear heptagonal dense fuzzy environment. RAIRO-Operations Research,        54(1), 267-286.
 Peng, X., & Yang, Y. (2015). Some results for Pythagorean fuzzy sets. International Journal of Intelligent Systems,   30(11), 1133-1160.
 Peng, X., & Selvachandran, G. (2019). Pythagorean fuzzy set: state of the art and future directions. Artificial Intelligence  Review52(3), 1873-1927.
 Peng, X. (2019). New operations for interval-valued Pythagorean fuzzy set. Scientia Iranica.Transaction E, Industrial  Engineering26(2), 1049-1076.
 Patro, R., Nayak, M. M., & Acharya, M. (2019). An EOQ model for fuzzy defective rate with allowable proportionate discount. O psearch56(1), 191-215.
 Pal, S., & Chakraborty, A. (2020). Triangular neutrosophic-based  EOQ model for non-instantaneous deteriorating item under shortages. Am J Bus Oper Res1(1), 28-35.
 Pattnaik, S, & Nayak, M. (2021). Linearly Deteriorating EOQ  Model for Imperfect Items with Price Dependent  Demand Under Different Fuzzy Environments. Turkish  Journal of Computer and Mathematics Education (TURCOMAT)12(13), 5328-5349.
 Rosenblatt, M. J., & Lee, H. L. (1986). Economic production cycles with imperfect production processes. IIE  transactions18(1), 48-55.
 Salameh, M. K., & Jaber, M. Y. (2000). Economic production quantity model for items with imperfect quality.    International journal of production economics64(1-3),   59-64.
Singh, S. R., & Singh, C. (2008). Fuzzy inventory model for finite rate of replenishment using signed distance method.  International Transactions in Mathematical Sciences and Computer1(1), 21-30.
 Shekarian, E., Olugu, E. U., Abdul-Rashid, S. H., & Kazemi, N. (2016).    An economic order quantity model considering different holding costs for imperfect quality items subject to fuzziness and learning. Journal of  Intelligent & Fuzzy Systems30(5), 2985-2997.
 Shekarian, E., Kazemi, N., Abdul-Rashid, S. H., & Olugu, E. U. (2017). Fuzzy inventory models: A comprehensive review. Applied Soft Computing55, 588-621.
 Wee, H. M., Yu, J., & Chen, M. C. (2007). Optimal inventory model for items with imperfect quality and shortage backordering. Omega35(1), 7-11.
 Wahab, M. I. M., & Jaber, M. Y. (2010). Economic order quantity model for items with imperfect quality, different holding costs, and learning effects: A note. Computers & Industrial Engineering58(1), 186-190.
 Yager, R. R. (1981). A procedure for ordering fuzzy subsets of the unit interval. Information sciences24(2), 143-161.
 Zadeh, L.A. (1965).Fuzzy set information and control. 8(3), 338- 353.