Environmentally friendly goods are market-oriented goods that create less environmental damage. Their manufacture is related to a product development process designed to consider the environmental consequences that might develop throughout their life cycle. In reality, the global demand for herbal goods is expanding since herbal products are manufactured from plant extracts such as leaves, roots, flowers, and seeds, among others, and cause less environmental destruction. This study introduces a novel, eco-friendly demand determined by the usage of herbal and chemical substances in products. In this context, companies producing these products are encouraged. Firms are interested in producing eco-friendly products while keeping an eye on carbon emissions. This paper presents a sustainable inventory model of non-instantaneous decaying items that follow this eco-friendly demand under partially backlogged shortages. In this study, emission releases due to inventory setup, degradation, and holding were estimated, as were carbon emissions under cap and tax policies. This approach invests in green and preservation technologies to reduce carbon emissions and deterioration. To address the imprecision of the model’s cost parameters, we converted them to Pythagorean fuzzy numbers. The optimum profit of the inventory model with carbon emissions is estimated by considering the time that the inventory level takes to reach zero and the replenishment time as decision variables. Numerical examples and a sensitivity analysis of significant parameters have been conducted to examine the effect of variation in the optimal inventory policy.
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