The joint optimization of transportation and inventory replenishment related decisions promises to yield significant cost savings coupled with higher customer satisfaction levels. This paper investigates a supply chain system consisting of a single supplier replenishing a single retailer, where the primary focus is on the retailer's decision-making process, aimed at determining the most efficient operational policy. This includes identifying the optimal replenishment quantity from the supplier and selecting the appropriate mix and size of the truck fleet under different situations. At first, the scenario whereby the retailer exclusively operates its limited fleet of trucks for inbound transportation is considered. An efficient solution procedure along with closed form expressions for the optimal ordering quantity and the number of trucks are devised. Subsequently, the problem is extended to incorporate environmental considerations under carbon tax and carbon cap policies. We propose a computationally efficient algorithm for generating the optimal operational policy following the carbon cap policy. Finally, to better resemble reality, the scope of the operational optimization model is extended via allowing the retailer the option to lease trucks from the external market. The conducted numerical experiments demonstrate that this flexibility can lead to significant cost reductions that are increasing with demand.
Hariga et al. (Tue,) studied this question.