A linear mathematical model for a transportation-inventory problem in a two-stage supply chain with different types of fuels for vehicles

Transportation and inventory challenges are classic problems which have been taken into consideration by researchers in the past regularly. On the other hand, energy is a recent critical challenge which has been considered widely. This paper addresses an integrated transportation and inventory problem in a two‐stage supply chain, including suppliers and retailers, while considering the role of energy in terms of fuel's type selection. An approach of ranking fuels based on relevant criteria is described here in order to help decision makers in quantifying these factors. Moreover, a mathematical model is developed to show all goals and constraints in such a framework and to find optimum solutions for the combined problem. The model is then tested through a number of generated numerical examples and respective results are presented.