A global optimization strategy for the 1 environmentally conscious design of chemical 2 supply chains under uncertainty in the 3 damage assessment model

10 This paper addresses the optimal design and planning of sustainable chemical supply 11 chains (SCs) in the presence of uncertainty in the damage model used to evaluate 12 their environmental performance. The environmental damage is assessed through 13 the Eco-indicator 99, which includes recent advances made in Life Cycle Assess14 ment (LCA). The overall problem is formulated as a bi-criterion stochastic non15 convex mixed-integer nonlinear program (MINLP). The deterministic equivalent of 16 such a model is obtained by reformulating the joint chance-constraint employed to 17 calculate the environmental performance of the SC in the space of uncertain pa18 rameters. The resulting bi-criterion non-convex MINLP is solved by applying the 19 epsilon constraint method. To guarantee the global optimality of the Pareto solu20 tions found, we propose a novel spatial branch and bound method that exploits the 21 specific structure of the problem. The capabilities of our modeling framework and 22 the performance of the proposed solution strategy are illustrated through a case 23 study. 24