OPTIMIZATION INVENTORY MODEL FOR DETERIORATING ITEMS WITH STOCK DEPENDENT DEMAND AND CARBON TAX UNDER FUZZY ENVIRONMENTS
By
Arushi Garg, Deepika Garg and Suvankar Biswas
Discipline of Mathematics, School of Sciences, Indira Gandhi National Open University, New Delhi, India-110068
Email: g.arushi.garg@gmail.com, gargdeepika@ignou.ac.in, sbiswas@ignou.ac.in
(Received: August 01, 2025; Revised: February 17, 2026; Accepted: March 20, 2026)
DOI: https://doi.org/10.58250/jnanabha.2026.561P-2
Abstract
Inventory control models provide a structured framework for optimizing replenishment decisions under operational and economic constraints. To address the uncertainty commonly observed in realworld systems, this study proposes a fuzzy inventory control model that incorporates parameter imprecision within a fuzzy framework. The model considers deteriorating items with stockdependent demand, allowable shortages, and complete backordering. Under the fuzzy environment, key parameters are represented as trapezoidal fuzzy numbers and defuzzified using the centroid method. A total cost function is developed to determine the optimal order quantity, the time at which inventory becomes zero, and the corresponding minimum cost. Numerical illustrations are presented for both fuzzy and crisp models, and the convexity of the cost function is verified graphically. Sensitivity analysis is conducted to examine the impact of variations in fuzzy parameters on optimal inventory decisions. The results indicate that the optimal total cost under the fuzzy environment is lower than that in the crisp case, demonstrating that incorporating fuzziness enables retailers to better capture uncertainty and improve inventory planning.
2020 Mathematical Sciences Classification: 90B05, 91B55, 03E72.
Keywords and Phrases: Inventory model; deteriorating product; carbon tax policy; fuzzy set theory.