Effects of green packaging and preservation on deteriorating products with Weibull distribution

¹ Department of Mathematics and Statistics, Kanya Gurukul Campus (KGC), Gurukul Kangri (Deemed to be University), Haridwar 249408, Uttarakhand, India
² Department of Mathematics, Chaudhary Charan Singh University, Meerut 250004, India
³ Department of Industrial Engineering, Yonsei University, 50 Yonsei-ro, Sinchon-dong, Seodaemun-gu, Seoul 03722, South Korea
⁴ Department of Mathematics, Lovely Professional University, Phagwara, Punjab 144411, India
⁵ Center for Global Health Research, Saveetha Medical College, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, Tamil Nadu 600077, India

^* Corresponding author: bsbiswajitsarkar@gmail.com

Received: 18 March 2024
Accepted: 3 April 2025

Abstract

In today’s environment, sustainability without including eco-friendly products is becoming a challenge for industries. Global warming and greenhouse emissions pose significant concerns worldwide. Activities such as burning fossil fuels, deforestation, renovation of industries, transportation, and green- house emissions contribute to global warming. This study presents a green integrated production system with a constant demand rate for controllable deterioration. The shortage has occurred with partially back- logged with a constant rate of backlogging. The strategy is to develop a production quantity system with three different production rates for deteriorating products that follow a three-parameter Weibull distri- bution. This model incorporates pollution control costs, disposal costs, green transportation costs, green packaging costs, and green technology costs. A solution methodology is proposed to determine the optimal investment for preservation technology and cycle time. A numerical experiment underpins this study. Sen- sitivity analysis explains the mathematical model’s results using essential parameters. This study aims to determine the optimal cost for preservation technology investment that minimizes the total average cost of the green inventory model. The findings reveal that the proposed three-rate green production economic quantity model offers superior cost efficiency, yielding the lowest preservation technology cost and cycle time compared with other models. The analysis demonstrates the practicality and applicability of the optimal results in optimizing total inventory costs for green packaging businesses.