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Pythagorean Fuzzy Storage Capacity with Controllable Carbon Emission Incorporating Green Technology Investment on a Two-Depository System

Global warming is mainly caused by carbon emissions. Currently, fewer countries are concentrating on reducing carbon emissions. The primary strategy utilized by numerous countries to achieve carbon emissions reduction is the carbon tax policy. With this in mind, a sustainable two-warehouse inventory model was taken carbon tax into account for a controllable carbon emissions rate by investing in green technology initiatives under uncertain emission and cost parameters. The globe is currently experiencing an eco-friendly period. Many individuals are interested in purchasing natural or herbal items since they are made from natural sources and do not affect the environment. The demand for products made with herbal or natural ingredients is considered eco-friendly demand. This study examines a two-warehouse inventory model of deteriorating commodities with price and marketing-dependent eco-friendly demand. The inventory system is presented to handle the inventory in the depository with last-in-first-out and first-in-first-out strategies. After comparing both the policies under deterioration rate and holding cost, this study recommended a suitable dispatch policy. Interval-valued numbers and fuzzy numbers are the mathematical techniques that deal with uncertainties, so this model’s emission and cost parameters are taken as interval-valued numbers, and the storage capacity of the owned warehouse is a Pythagorean fuzzy number. The optimal solution for the two-warehouse inventory system is evaluated by taking the parametric form of interval-valued cost parameters and the new concept of the ranking function of triangular Pythagorean fuzzy numbers. Numerical results prove that emissions are reduced by 87% under green technology investment in both policies. As a consequence, in the FIFO policy, the total cost of the two-warehouse inventory system decreases by 34.45% and cycle length increases by 5.72%, and in the LIFO policy, the total cost of the two-warehouse inventory system decreases by 34.42% and cycle length increases by 11.19%. Sensitivity analysis of the key parameters has been performed to study the effect of various parameters on the optimal solution.