Vol. 24 No. 3 (2025): Mapana Journal of Sciences
Research Articles

Optimizing a Single-Vendor Multi-Purchaser for Multi-Item Fuzzy Inventory System along Lead Time with Carbon Emission Cost

  • R. Vithyadevi,
  • K. Annadurai
R. Vithyadevi
Department of Mathematics, SSM Institute of Engineering and Technology, Dindigul , Tamil Nadu, India
K. Annadurai
Department of Mathematics, M.V. Muthiah Government Arts College for Women, (Affiliated to Mother Teresa Women’s University) Dindigul, Tamil Nadu, India;

Published 2025-10-11

Keywords

  • Fuzzy multi-item with multi-purchaser,
  • Minimum integrated total cost,
  • Graded mean integration technique,
  • Optimal order quantity,
  • Kuhn-Tucker conditions

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Abstract

Multi-item investigation with a multi-purchaser inventory system exposes remarkable perceptions of improved demand enhancement in overall income and manufacturing time proficiency.  Similarly, lower transporting costs for multiple items positively influence minimum integrated total cost by lead time suitability.  The objective seems to be inaccurate due to the imprecision of several factors.  As the development of fuzzy objective is uncertain, a model is formulated to suit assured problems and doubtful earnings with some indecision.  The model is solved by means of graded mean integration technique with the addition of Kuhn-Tucker method when the fuzzy equivalent of the problem remains available.  An algorithm is established to attain each item's optimal order quantity for each purchaser and the minimum integrated total cost for a whole inventory system.  The evaluation of a fuzzy multi-item, multi-purchaser inventory system through crisp multi-item, multi-purchaser inventory system is completed utilizing mathematical illustrations.  

References

  1. A.A. Taleizadeh, S.T.A. Niaki and F. Barzinpour, Multiple-Buyer Multiple-Vendor Multi-Product Multi-Constraint Supply Chain Problem with Stochastic Demand and Variable Lead-Time: A Harmony Search Algorithm. Applied Mathematics and Computation, 217(22): 9234–9253, (2011).
  2. A.I. Malik and B. Sarkar, Optimizing a Multi-Product Continuous-Review Inventory Model with Uncertain Demand, Quality Improvement, Setup Cost Reduction and Variation Control in Lead Time. IEEE Access, 6: 36176–36187, (2018).
  3. A.J. Kamble, Some Notes on Pentagonal Fuzzy Numbers. International Journal of Fuzzy Mathematical Archive, 13(2): 113-121, (2017).
  4. B. C. Giri, A. Dash and A. K. Sarkar, A Single-Manufacturer Multi-Retailer Integrated Inventory Model with Price Dependent Demand and Stochastic Lead Time, International Journal of Supply and Operations Management,7( 4): 384-409, (2020).
  5. B. Malleeswaran and R. Uthayakumar, An Integrated Vendor–Buyer Supply Chain Model for Backorder Price Discount and Price-Dependent Demand using Service Level Constraints and Carbon Emission Cost. International Journal of Systems Science: Operations & Logistics, (2020).
  6. D. Barman and G. C. Mahata, A Single-Manufacturer Multi-Retailer Integrated Inventory Model for Items with Imperfect Quality, Price Sensitive Demand and Planned Back Orders. RAIRO Operations Research, 55: 3459–3491, (2021).
  7. D. M. Utama, I. R. Kusuma, I. Amallynda, T. Baroto and W. A. Jauhari, A Single-Vendor Multi-Buyer Inventory Model with Multiple Raw Material and Quality Degradation: A Case Study on Agri-Food Industry. Results in Control and Optimization, 14: 100353, (2024).
  8. D. Yadav, R. Kumari and N. Kumar, Sustainable Supply Chain Model for Multi-stage Manufacturing with Partial Backlogging Under the Fuzzy Environment with the Effect of Learning in Screening Process. International Journal of Applied and Computational Mathematics, 7(40): (2021).
  9. G. Chavarroa, M. Fresena, E. R. Gonzálezb, D. B. Ferroa and H. López-Ospinab, Solving the One-Warehouse N-retailers Problem with Stochastic Demand: An Inter-Ratio Policies Approach. International Journal of Industrial Engineering Computations, (2020).
  10. H. A. Taha, Operations Research. Prentice Hall, New Jersey, USA, 1997.
  11. H. J. Pan and J. S. Yang, A Study of An Integrated Inventory with Controllable Lead Time. International Journal of Production Research, 40(5): 1263-1273, (2002).
  12. H. Nagar and P. Surana, Fuzzy Inventory Model for Deteriorating Items with Fluctuating Demand and using Inventory Parameters as Pentagonal Fuzzy Numbers. Journal of Computer and Mathematical Sciences, 6(2): 55-66, (2015).
  13. H.J. Zimmerman, Using Fuzzy Sets in Operational Research. European Journal of Operational Research, 13(3): 201-216, (1983).
  14. K. Annadurai, Minimax Distribution-Free Procedure for Mixture Inventory Model with Variable Lead Time and A Service Level Constraint by Reducing Order Cost. American Journal of Mathematical and Management Sciences, 35(1): 1-14, (2016).
  15. K. Dey, B. Sarkar, M. Sarkar and S. Pareek, An Integrated Inventory Model Involving Discrete Setup Cost Reduction, Variable Safety Factor, Selling Price Dependent Demand, and Investment. RAIRO-Operations Research, 53(1): 39–57, (2019).
  16. K. Maiti, Multi-Item Fuzzy Inventory Model for Deteriorating Items in Multi-Outlet under Single Management. Journal of Management Analytics, 7(1): 44–68, (2020).
  17. M. Esmaeili and M. Nasrabadi, An Inventory Model for Single - Vendor Multi - Retailer Supply Chain under Inflationary Conditions and Trade Credit. Journal of Industrial and Production Engineering, (2020).
  18. M. Vijayashree and R. Uthayakumar, A Single-Vendor and A Single-Buyer Integrated Inventory Model with Ordering Cost Reduction Dependent on Lead Time. Journal of Industrial Engineering International, 13(3): 393–416, (2017).
  19. M.S. Kim and B. Sarkar, Multi-Stage Cleaner Production Process with Quality Improvement and Lead Time Dependent Ordering Cost. Journal of Cleaner Production, 144: 572–590, (2017).
  20. R. Setiawan, Salmah, Widodo, I. Endrayanto and Indarsih, Analysis of the Single-Vendor-Multi-Buyer Inventory Model for Imperfect Quality with Controllable Lead Time. International Journal of Applied Mathematics, 51(3): (2021).
  21. R. Uthayakumar and M. Ganesh Kumar, Single-Vendor Multi-Buyer Integrated Inventory System for Multi-Item. International Journal of Mathematics in Operational Research, 14(3): 359–376 (2019).
  22. R. Vithyadevi and K. Annadurai, Optimization of Fuzzy Integrated Inventory Model with Ordering Cost Reduction Dependent on Lead Time. International Journal of Operations Research, 18(4): 79-96, (2021).
  23. R. Vithyadevi and K. Annadurai, Optimization of Fuzzy Two-Level Production Inventory System with Persuasive Exertion Reliant Demand. Ratio Mathematica, 48: (2023).
  24. S. H. Chen, Operations on Fuzzy Numbers with Function Principle. Tamkang Journal of Management Sciences, 6(1): 13–26, (1985).
  25. S. Tiwari, Y. Daryanto and H. M. Wee. Sustainable Inventory Management with Deteriorating and Imperfect Quality Items Considering Carbon Emission. Journal of Cleaner Production, 192: 281–292, (2018).
  26. T. Demizu, Y. Fukazawa and H. Morita, Inventory Management of New Products in Retailers using Model-Based Deep Reinforcement Learning, Expert Systems With Applications 229: 120256, (2023).
  27. Z. Hen and B.R. Sarker, Integrated Production-Inventory and Pricing Decisions for A Single-Manufacturer Multi-Retailer System of Deteriorating Items under JIT Delivery Policy. The International Journal of Advanced Manufacturing Technology, 89(5–8): 2099–2117, (2017).