Bi-objective optimization of biomass supply chains considering carbon pricing policies

Bi-objective optimization models considering carbon pricing policies are developed in this paper to obtain the trade-off between cost and emissions of biomass supply chain models, which is important for decision making. Solving bi-objective optimization models to obtain the set of trade-off solutions can be time consuming. To avoid the computational effort, in this paper, a new algorithm is developed to obtain the solutions for the bi-objective models with carbon pricing policies using the solutions of the bi-objective model without carbon pricing. The algorithm is based on mathematical properties of optimum solutions of bi-objective models with and without carbon pricing policies. These properties are proved mathematically. The developed algorithm is applied to a case study of a biomass-fed district heating system. Results indicate that the number of optimum solutions to the bi-objective models decrease when emissions are priced compared to when emissions are not priced. The increase in total cost for mitigating a given quantity of emission is more for the carbon offset model compared to the carbon tax and the carbon cap-and-trade models. Pair-wise comparison of the models indicates that the carbon tax model has more cost than the carbon cap-and-trade and the carbon offset models. The algorithm and results of this study are independent of the case study; therefore, they can be applied to other cases and industries.