Two-warehouse sustainable inventory models under different fuzzy environments with optimum carbon emissions

In the present era, the most delicate environmental issue is global warming, and because of this, countries across the globe are trying to manage the most hazardous emissions by making certain investments in projects to promote green industrial practices. The proposed study creates sustainable deteriorating inventory models in both crisp and fuzzy environments, with both cloudy and intuitionistic fuzzy considerations, where the demand is taken to be time-dependent. In the current study, the emission of CO2 from transportation is controlled by the optimum investments in green technology (GT). This work develops the previous research that has worked on a sustainable inventory system with controllable greenhouse facilities through green investment. The present research includes an optimum GT investment in an inventory system with two warehouses to restrict carbon emissions due to the transportation of goods from owned to rented warehouses and then to customers. To have control over the total cost, this work considers two warehouses to manage the stock-out conditions and represents models with shortages for crisp, cloudy fuzzy (CF), and intuitionistic fuzzy (IF) environments. A multiple prepayment option for the purchasing cost involving an installment is provided to the retailers. In the present research, we develop non-linear crisp and fuzzy deteriorating inventory models and suggest an algorithm for the solution process. Model problems are illustrated through numerical examples and validated through sensitivity analysis. A comparative inquiry is conducted for the optimum results obtained in all three cases.