Design of Sustainable Product Systems and Supply Chains with Life Cycle Optimization Based on Functional Unit: General Modeling Framework, Mixed-Integer Nonlinear Programming Algorithms and Case Study on Hydrocarbon Biofuels

We propose a life cycle optimization framework for the design of sustainable product systems and supply chains considering the concept of “functional unit” under economic and environmental criteria. This general modeling framework integrates the life cycle analysis methodology with multiobjective optimization and measures both the economic and environmental performances based on a standard quantity of functional unit associated with final products. The Pareto-optimal frontier returned by the multiobjective optimization problem reveals the trade-off between the economic and environmental objectives. We also present tailored optimization algorithms for efficiently solving the mixed-integer linear fractional programming problems, which result from the life cycle optimization framework. We apply the proposed life cycle optimization framework to a case study on the hydrocarbon biofuels through a spatially explicit model for the county-level supply chain in Illinois. The Pareto-optimal results show that the environmental impact of hydrocarbon biofuels ranges from 10.66 to 23.83 kg CO2 equiv per gasoline-equivalent gallon (GEG), corresponding to the unit cost ranging from $4.63 to $3.58/GEG.