Cost Allocation for Inventory Problem with Transportation Discount under Carbon Tax Policy

In this paper, we deal with the problem of cost allocation among multiple retailers in an inventory system with transportation quantity discount under the widely-used carbon tax regulation. We first develop an inventory model with transportation discount under the carbon tax policy, and determine the optimal order quantity per order such that the total cost is minimized in the case of individual and joint ordering. We show that the total cost for the group of retailers can be reduced by placing joint orders while the total carbon emissions may increase. Then, we provide a sufficient condition which indicates that when the costs and carbon emissions associated with each order initiated are relatively high, enterprises can achieve dual objectives (both carbon emission reduction and cost reduction) through joint ordering. To allocate the total cost among the retailers, we introduce an inventory game and show that this game is concave. Based on this, we propose a cost allocation rule, which belongs to the core of the game.