Two Echelon Supply Chain Model with lead time and effect of carbon emission under fuzzy environment
Main Article Content
Abstract
Carbon emission has become a major challenge everywhere, such as in the production process, holding items, deteriorating items, waste disposal, and transporting items. Two warehouses are a realistic approach in inventory modeling. Inflation and lead time play a key role in making this study closer to reality. Uncertainty is also a very realistic approach for any organization. In this study, we developed a supply chain model in which there is one retailer and one supplier. The retailer holds its inventory in two warehouses. Our objective is to find the optimal total cost, cycle length, and supplier's lead time. In this study, we calculate the total cost in three different ways: first, for the crisp model; second, for the fuzzy model using the signed distance method; and third, using the graded mean integration method. We carried out the numerical solution using the software MATHEMATICA 12.0. From numerical illustration, we find that the total cost is minimum for the fuzzy model using the graded mean integration method. Sensitivity analysis is carried out to see the behavior of different parameters on the total cost.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
References
1. Ahmad, N., Sangal, I., Sharma K., Jaysawal, M. K., Kumar, S., Pal, S. K. and Alam, K. A green realistic inventory model with preservation technology for deteriorating items under carbon emission. Materials Today: Proceedings (2023). https://doi.org/10.1016/j.matpr.2023.03.017
2. Buzacott, J. A. Economic order quantities with inflation. Journal of the Operational Research Society 26 (3) 553-558 (1957).
3. Chen, X., Benjaafar, S., and Elomri, A. The carbon-constrained EOQ. Operations Research Letters 41 (2), 172-179 (2013). https://doi.org/10.1016/j.orl.2012.12.003
4. Covert, R. P. and Philip, G. C. An EOQ model for items with Weibull distribution deterioration. AIIE transactions 5 (4), 323-326 (1973). https://doi.org/10.1080/05695557308974918
5. Digiesi, S., Mossa, G, and Mummolo, G. Supply lead time uncertainty in a sustainable order quantity inventory model. Management and Production Engineering Review 4 (4), 15-27 (2013). https://doi.org/10.2478/mper-2013-0034
6. Dutta, Pankaj, Debjani Chakraborty, and Akhil R. Roy. A single-period inventory model with fuzzy random variable demand. Mathematical and computer modelling 41 (8-9) 915-922 (2005).
7. Garg, Garima, Sanjay Singh, and Vinita Singh. A two warehouse inventory model for perishable items with ramp type demand and partial backlogging. International journal of engineering research & technology (IJERT) 9 (6), 1504-1521 (2020).
8. Ghare , P. M. , and G. F. Schrader . A Model for Exponentially Decaying Inventory. Journal of Industrial Engineering , 14 (5), 238 – 243 (1963).
9. Giri, B. C., and K. S. Chaudhuri. Deterministic models of perishable inventory with stock-dependent demand rate and nonlinear holding cost. European Journal of Operational Research 105 (3), 467-474 (1998).
10. Jaggi, C. K., Pareek, S., Sharma, A., and Nidhi, A.. Fuzzy inventory model for deteriorating items with time-varying demand and shortages. American Journal of Operational Research 2 (6), 81-92 (2012).
11. Kansal, M., Tuteja, A., and Kumar, V. Environmentally sustainable fuzzy inventory model for deteriorating items for two warehouse system under inflation and backorder. Mathematical Statistician and Engineering Applications 71 (4), 6802-6818 (2022). https://doi.org/10.17762/msea.v71i4.1273
12. Kumar, B. A., and Paikray, S. K. Cost optimization inventory model for deteriorating items with trapezoidal demand rate under completely backlogged shortages in crisp and fuzzy environment. RAIRO-Operations Research 56 (3), 1969-1994 (2022). https://doi.org/10.1051/ro/2022068
13. Kumar, N., Singh, S. R., and Kumari, R. Two-warehouse inventory model of deteriorating items with three-component demand rate and time-proportional backlogging rate in fuzzy environment. International Journal of Industrial Engineering Computations 4 (4), 587-598 (2013). http://dx.doi.org/10.5267/j.ijiec.2013.05.001
14. Lee, H. M., and Yao, J. S. Economic order quantity in fuzzy sense for inventory without backorder model. Fuzzy sets and Systems 105 (1), 13-31 (1999).
15. Liao, C. J., and Shyu, C. H. Stochastic inventory model with controllable lead time. International Journal of Systems Science 22 (11), 2347-2354 (1991). https://doi.org/10.1080/00207729108910796
16. Mashud, A. H., Pervin, M., Mishra, U., Daryanto, Y., Tseng, M.L., and Lim, M. K. A sustainable inventory model with controllable carbon emissions in green-warehouse farms. Journal of Cleaner Production 298, 126777 (2021).
17. Mishra, U., Wu, J. Z., & Sarkar, B. A sustainable production-inventory model for a controllable carbon emissions rate under shortages. Journal of Cleaner Production, 256, 120268 (2020). https://doi.org/10.1016/j.jclepro.2020.120268
18. Mishra, V. K., Singh, L. S., & Kumar, R. An inventory model for deteriorating items with time-dependent demand and time-varying holding cost under partial backlogging. Journal of Industrial Engineering International, 9, 1-5 (2013).
19. Nayak, D. K., Paikray, S. K., & Sahoo, A. K. A Fuzzy Inventory Model of Deteriorating Items with Time-Dependent Demand Under Permissible Delay in Payment. In International Conference on Applied Nonlinear Analysis and Soft Computing. Singapore: Springer Nature Singapore 77-106 (2020).
20. Padiyar, S. V. S., Vandana, Singh, S. R., Singh, D., Sarkar, M., Dey, B.K., and Sarkar, B. Three-Echelon supply chain management with deteriorated products under the effect of inflation. Mathematics 11 (1), 104 (2022). https://doi.org/10.3390/math11010104
21. Park, Kyung S. Fuzzy-set theoretic interpretation of economic order quantity. IEEE Transactions on systems, Man, and Cybernetics 17 (6), 1082-1084 (1987).
22. Paul, A., Pervin, M., Roy, S.K., Maculan, N. and Weber, G.W. A green inventory model with the effect of carbon taxation. Annals of Operations Research 309 (1), 233-248 (2022). https://doi.org/10.1007/s10479-021-04143-8
23. Priyan, S., and P. Manivannan. Optimal inventory modeling of supply chain system involving quality inspection errors and fuzzy defective rate. Opsearch 54, 21-43 (2017). 24. Sett, B. Kumar, Biswajit Sarkar, and A. Goswami. A two-warehouse inventory model with increasing demand and time varying deterioration. Scientia Iranica 19 (6), 1969-1977 (2012).
25. Shabani, S., Mirzazadeh, A. and Sharifi, E. A two-warehouse inventory model with fuzzy deterioration rate and fuzzy demand rate under conditionally permissible delay in payment. Journal of Industrial and Production Engineering 33 (2), 134-142 (2016).
26. Sharma, R. S. A., and Rathore, H. An inventory model for deteriorating items with hybrid type demand and return in preservation technology investment. Proceedings of the Indian National Science Academy 1-6 (2024).
27. Sharma, S., and Singh, S.R. An inventory model for decaying items, considering multi variate consumption rate with partial backlogging. Indian Journal of Science and Technology 6 (7), 4870-4880 (2013). https://doi.org/10.17485/ijst/2013/v6i7.7
28. Sharma, S., Singh, S. and Singh, S.R. An inventory model for deteriorating items with expiry date and time varying holding cost. International Journal of Procurement Management 11 (5), 650-666 (2018).
29. Shee, Srabani, and Tripti Chakrabarti. A fuzzy two-echelon supply chain model for deteriorating items with time varying holding cost involving lead time as a decision variable. Optimization and Inventory Management 391-406 (2020).
30. Singh, Chaman, and S. R. Singh. Optimal ordering policy for deteriorating items with power-form stock dependent demand under two-warehouse storage facility. Opsearch 50 182-196 (2013).
31. Singh, D., Singh, S.R. and Rani, M. Impact of Preservation Technology Investment and Order Cost Reduction on an Inventory Model Under Different Carbon Emission Policies. In Data Analytics and Artificial Intelligence for Inventory and Supply Chain Management, 225-247. Singapore: Springer Nature Singapore, (2022). https://doi.org/10.1007/978-981-19-6337-7_13
32. Singh, S., Singh, S.R., and Sharma, S. A partially backlogged EPQ model with demand dependent production and non-instantaneous deterioration. International Journal of Mathematics in Operational Research 10 (2), 211-228 (2017).
33. Singh, S., Sharma, S. and Singh, S.R. Inventory model for deteriorating items with incremental holding cost under partial backlogging. International Journal of Mathematics in Operational Research 15 (1), 110-126 (2019). https://doi.org/10.1504/IJMOR.2019.10022834
34. Tiwari, S., Ahmed, W. and Sarkar, B. Sustainable ordering policies for non-instantaneous deteriorating items under carbon emission and multi-trade-credit-policies. Journal of Cleaner Production 240 118183 (2019).
35. Yao, J. S., and Lee, H.M. Fuzzy inventory with or without backorder for fuzzy order quantity with trapezoid fuzzy number. Fuzzy sets and systems 105, 311-337 (1999).