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Impact of Carbon Emissions and Advance Payment on Optimal Decisions for Perishable Products via Parametric Approach of Interval

H. Ali1, M. A. Khan2,3, A. A. Shaikh1 *, and A. F. Alrasheedi4

  1. Department of Mathematics, The University of Burdwan, Burdwan 713104, India
  2. Department of Mathematics, Jahangirnagar University, Savar, Dhaka 1342, Bangladesh
  3. School of Engineering and Sciences, Tecnológico de Monterrey, Tecnológico, 64849 Monterrey, Nuevo Leon, Mexico
  4. Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11451, Saudi Arabia

*Corresponding author. Tel.: +918617422926. E-mail address: (A. A. Shaikh).


Under the heading of sustainability challenges, this study incorporates payment procedures and inventory selections. The article’s goal is to acquire insight into how the methods of payment affect perishable product inventory selections under the widely utilised carbon tax regime in view of policies to reduce emissions. Uncertainty arises as a natural consequence of the unpredictable behaviour of customers. Keeping these impacts in mind, an interval-valued inventory model is introduced, where all the related inventory parameters are considered interval-valued. In addition, the vendor offers an interval-valued discount rate to customers against advance payment. Due to the inventory parameters being chosen as interval-valued, the objective function is changed into an interval-valued form, and the corresponding differential equation is changed into an interval differential equation. To solve the interval-valued differential equation, a parametric approach to interval is introduced, and the corresponding interval-valued objective function is constructed. Interval order relations and the MATHEMATICA software are used to solve the objective function with interval values. To assess the validity of the proposed model, one numerical example is solved, and a sensitivity analysis of the ideal course of action is performed.

Keywords: interval differential equation, interval-valued deterioration, interval-valued discount, interval-valued carbon emission, environmental regulations, interval-valued inventory

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