Allocating the CO2 emissions of an oil refinery with Aumann-Shapley prices

Linear programming is widely used by multiproduct oil-refining firms, which minimize a refinery's variable cost under a set of constraints. In addition to operating costs, this variable cost can include the cost associated with the refinery's CO2 emissions. We suggest a quite general approach combining use of Aumann-Shapley cost-sharing method and breakdown of the objective function of the linear program. This approach determines an appropriate rule for the allocation of the refinery's CO2 emissions (or, in general, variable costs) among the various finished products, which can be used for purposes of Life Cycle Assessment. A numerical application to a simplified refining model is presented.