Optimizing substitution of two products model for exponentially increasing demand under inflation and shortages

¹ Department of Mathematics, Hansraj College, University of Delhi, Delhi 110 007, India
² Department of Mathematics, Acharya Narendra Dev College, University of Delhi, New Delhi 110019, India
³ Department of Industrial Engineering, Yonsei University, 50 Yonsei-ro, Sinchon-dong, Seodaemun-gu, Seoul 03722, South Korea
⁴ Center for Global Health Research, Saveetha Medical College, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, Tamil Nadu 600077, India
⁵ Department of Mathematics, Lovely Professional University, Phagwara, Punjab 144411, India

^* Corresponding author: bsbiswajitsarkar@gmail.com

Received: 24 November 2023
Accepted: 2 April 2024

Abstract

This study addresses the limited attention given to product substitution in inventory models. Incorporating product substitution is crucial for determining reorder points, and safety stock, enabling businesses to optimize inventory levels, reduce costs, and maintain customer satisfaction. This study introduces an economic order quantity model tailored to an inflationary environment with shortages and one-way substitution between two deteriorating product types. Through comprehensive testing, this study evaluates the model under various substitution scenarios, including partial substitution. Findings highlight the significance of product substitution in inventory management, allowing businesses to optimize inventory levels, manage costs, and ensure customer satisfaction in dynamic environments with inflation and fluctuating product availability. This model provides the firm with the necessary information to determine the optimal ordering quantity of both products to optimize total benefit and enhance supply chain efficiency. The model demonstrates substantial cost advantages, with partial substitution resulting in an average cost reduction of approximately 9% compared to no substitution and about 45% compared to full substitution. Numerical experiments validate the applicability of the proposed model.