Modeling framework and computational algorithm for hedging against uncertainty in sustainable supply chain design using functional-unit-based life cycle optimization

In this work, we address the life cycle economic and environmental optimization of a supply chain network considering both design and operational decisions under uncertainty. A modeling framework is proposed that integrates the functional-unit-based life cycle optimization methodology and the two-stage stochastic programming approach for sustainable supply chain optimization under uncertainty. We develop a stochastic mixed-integer linear fractional programming (SMILFP) model to tackle multiple uncertainties regarding feedstock supply and product demand. To address the computational challenge of solving the resulting large-scale SMILFP problems, an efficient solution algorithm is developed that takes advantage of the efficiency of parametric algorithm and the decomposition-based multi-cut L-shaped method. We present a case study based on a spatially explicit model for the optimal design and operations of a county-level hydrocarbon biofuel supply chain in Illinois to demonstrate the applicability of the proposed modeling framework and the efficiency of the solution algorithm.