Optimal design and planning of sustainable chemical supply chains under uncertainty

This paper addresses the design of sustainable chemical supply chains (SCs) in the presence of uncertainty in the life cycle inventory associated with the network operation. The design task is mathematically formulated as a bi-criterion stochastic mixed-integer nonlinear program that simultaneously accounts for the maximization of the net present value (NPV) and the minimization of the environmental impact for a given probability level. The environmental performance is measured through the Eco-indicator 99, which incorporates the recent advances made in Life Cycle Assessment (LCA). The stochastic model is converted into its deterministic equivalent by reformulating the probabilistic constraint required to calculate the environmental impact in the space of uncertain parameters. The resulting deterministic bi-criterion MINLP is further reformulated as a parametric MINLP, which is solved by decomposing it into two sub-problems and iterating between them. The capabilities of the proposed model and solution procedure are illustrated through two case studies for which the set of Pareto optimal, or efficient solutions that trade-off environmental impact and profit, are calculated. These solutions provide valuable insights into the design problem and are intended to guide the decision maker towards the adoption of more sustainable design alternatives.