The present work proposes an inventory model with negative exponential demand and instantaneous replenishment. As a natural occurrence, deterioration is crucial to inventory management and can have an impact on the overall profitability of an organization. Today, researchers are working to identify ways to slow down the rate of deterioration. To slow down the rate of deterioration, we have included preservation technology in our proposed model. Moreover, carbon emissions are considered, and it is thought that the price of carbon emissions relies on green investment. This model is different from the existing inventory models with negative exponential demand, which did not incorporate carbon emission and preservation technology. Weighted particle swarm optimization (WPSO) and constriction factor particle swarm optimization (CO-PSO) are used to solve the specified model, and the optimality is demonstrated by numerical values for the system parameters and a graphical depiction of convergence characteristics. The model is then verified by sensitivity analysis of the system parameters, and managerial implications are made for efficient decision-making.