Optimization model for perishable items under inspection and carbon tax policy

Transportation, holding inventory and deterioration of perishable goods are the main producers of carbon emissions, raising worries about their impact on the environment. This article develops an inventory model for perishable goods under inspection and carbon tax policy. The demand rate of the product is a function of stock level and advertisement frequency. This model seeks to obtain the optimal cycle length and number of inspections which lower overall costs. The model is solved using Mathematica 11.2. Numerical analysis is provided to validate the model and sensitivity analysis investigates the impact of key parameters on the optimal solution. The findings show that total cost decreases as the number of inspection and cycle time increase upto a certain point and then eventually increases beyond that point. Sensitivity analysis reveals that total cost is highly sensitive to purchasing cost and basic demand. Also, increasing frequency of advertisement increases total cost but it boosts product demand for perishable items.