Deterioration and age governed greenhouse gas emissions from the product itself: an optimum inventory control problem

¹ Department of Mathematics, Meerut Institute of Engineering and Technology, Meerut, India
² Department of Industrial Engineering, Yonsei University, 50 Yonsei-ro, Sinchon-dong, Seodaemun-gu, Seoul 03722, South Korea
³ Department of Mathematics, Keral Verma Subharti College of Sciences (KVSCOS), Swami Vivekanand Subharti University, Meerut, India
⁴ Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, India
⁵ Center for Global Health Research, Saveetha Medical College, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, Tamil Nadu 600077, India
⁶ Department of Mathematics, Lovely Professional University, Phagwara, Punjab 144411, India
⁷ Department of Mathematics, Institute of Applied Sciences & Humanities, GLA University, Mathura, India

^* Corresponding author: bsbiswajitsarkar@gmail.com

Received: 16 October 2022
Accepted: 17 November 2023

Abstract

Greenhouse gas emissions contribute significantly to global warming. This occurs during various operations, including the production, storage, and transportation of an inventory, but in some cases, the inventory itself becomes the emission source. Emissions from cattle dunk cakes, livestock slurry, manure, crude oil, and gasoline can be considered examples of this type of emissions. This paper proposes a mathematical formulation for a deteriorating inventory model utilizing the inventory as a source of emissions. The model is developed under inflation. Other activities, such as energy consumption for warehousing, are considered to be contributing to greenhouse gas emissions here. The rate of emissions from the product is exponentially governed by the rate of deterioration and the age of the material. The trapezoidal-type demand rate is considered using the Heaviside step function. Shortages are permitted but partially backlogged, and the backlogging rate is supposed to be decreasing exponentially with the increased waiting time. The numerical illustration of the model is provided to illustrate the mathematical expressions, and the effect of parametric variation is reported to give managerial insights. The results reveal that the greenhouse gas emissions are proportional to the variable rate of emissions cost and the deterioration rate. However, the increment in total emissions with respect to variable emissions cost increases with the deterioration rate. If the deterioration rate is negligible, total carbon emissions do not fluctuate much, but it increases rapidly if it is relatively high. The preservation technology is used to reduce deterioration and helps reduce emissions.