Title: An inventory system for imperfect products with the effect of carbon emission and with free transportation on a prepaid basis

Authors: Sandeep Kumar; Robin Singh; Manoj Kumar; Mukesh Kumar; Prachi Fartyal

Addresses: Department of Mathematics, Graphic Era Hill University, Dehradun, India ' Department of Mathematics, Graphic Era Hill University, Dehradun, India ' Department of Mathematics, Graphic Era Hill University, Dehradun, India ' Department of Mathematics, Graphic Era (Deemed to be University), Dehradun, India ' Department of Mathematics, Government PG College Bazpar, (US Nagar), India

Abstract: The EPQ model is a mathematical model used for inventory management in shop floor systems. However, it assumes manufacturers pay upfront costs and may have low-grade items. The classical inventory model assumes no imperfect items are manufactured, but the production process may shift from controlled to uncontrolled states due to various causes. To make the current study more realistic, we represent a model with imperfect production that accounts for random carbon emissions under continuous prepayment. We also assumed that the production process was imperfect, so we got some defective items, and out of these, some were reworked. Further, it is assumed that the producer provides free shipping to the retailers on a prepaid basis. The concept of carbon emissions is related to transportation and production decisions. Due to environment-saving rules, a tax on carbon emissions is required to be paid by the manufacturer. The model is validated using a numerical example and sensitivity analysis.

Keywords: inventory; carbon emission; imperfect products; transportation cost; prepayment.

DOI: 10.1504/IJMOR.2026.151173

International Journal of Mathematics in Operational Research, 2026 Vol.33 No.1, pp.73 - 87

Received: 30 Dec 2023
Accepted: 02 Feb 2024
Published online: 16 Jan 2026 *

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