On a multiple item replenishment problem in the presence of carbon emissions

Abstract

Motivated by the increasing popularity of sustainability issues, and the opportunities to create positive value through collaboration, the purpose of the study is to investigate a joint replenishment model in the presence of carbon emissions. The joint replenishment problem here is one where there is a deterministic demand rate over an infinite time horizon where there are major fixed, minor fixed, holding, and per unit costs and emissions. Since extensive research has been done on carbon caps and carbon tax, in order to differentiate the thesis from the existing work, a novel objective function is implemented. Through this, the optimality of the objective function has been investigated and the obtained results prove the concavity of the objective function for the common order interval and joint concavity for the item-specific order intervals. Relationships between the parameters of the variables are obtained to decrease the computational complexity. Lastly, basic numerical analysis is conducted to compare the performance of the objective function to traditional objective functions.