Deterioration and age governed greenhouse gas emissions from the product itself: an optimum inventory control problem

Abstract

GHG emissions contribute significantly to global warming. This occurs during various operations, including the production, storage, and transportation of an inventory, but in some cases, the inventory itself becomes the emission source. The emissions from cattle dunk cakes, livestock slurry, manure, crude oil, and gasoline can be considered examples of this emission type. Other activities, such as energy consumption for warehousing, also contribute to greenhouse gas emissions. This paper proposes a mathematical formulation for a deteriorating inventory model utilizing the inventory as a source of emissions. The model is developed under inflation. The rate of emission from the product is exponentially governed by the rate of deterioration and the age of the material. The trapezoidal-type demand rate has been considered using the Heaviside step function. Shortages are permitted but partially backlogged, and the backlogging rate is supposed to be decreasing exponentially with the increased waiting time. The numerical illustration of the model is provided to illustrate the mathematical expressions, and the effect of parametric variation is also reported to give managerial insights. The results reveal that the GHG emission is proportional to the variable rate of emission cost and the deterioration rate. However, the increment in total emissions with respect to variable emission cost increases with the deterioration rate. If the deterioration rate is negligible, total carbon emissions don't fluctuate much but increase rapidly if it is relatively high. So the preservation technologies used to reduce deterioration can also help reduce the emission.