On the use of weighting in LCA: translating decision makers' preferences into weights via linear programming

The main goal of any life cycle assessment (LCA) study is to identify solutions leading to environmental savings. In conventional LCA studies, practitioners select from some alternatives the one which better matches their preferences. This task is sometimes simplified by ranking these alternatives using an aggregated indicator defined by attaching weights to impacts. We address here the inverse problem. That is, given an alternative, we aim to determine the weights for which that solution becomes optimal. We propose a method based on linear programming (LP) that determines, for a given alternative, the ranges within which the weights attached to a set of impact metrics must lie so that when a weighting combination of these impacts is optimized, the alternative can be optimal, while if the weights fall outside this range, it is guaranteed that the solution will be suboptimal. A large weight value implies that the corresponding LCA impact is given more importance, while a low value implies the converse. Furthermore, we provide a rigorous mathematical analysis on the implications of using weighting schemes in LCA, showing that this practice guides decision-making towards the adoption of some specific alternatives (those lying on the convex envelope of the resulting trade-off curve). A case study based on the design of hydrogen infrastructures is taken as a test bed to illustrate the capabilities of the approach presented. Given are a set of production and storage technologies available to produce and deliver hydrogen, a final demand, and cost and environmental data. A set of designs, each achieving a unique combination of cost and LCA impact, is considered. For each of them, we calculate the minimum and maximum weight to be given to every LCA impact so that the alternative can be optimal among all the candidate designs. Numerical results show that solutions with lower impact are selected when decision makers are willing to pay larger monetary penalties for the environmental damage caused. LP can be used in LCA to translate the decision makers' preferences into weights. This information is rather valuable, particularly when these weights represent economic penalties, as it allows screening and ranking alternatives on the basis of a common economic basis. Our framework is aimed at facilitating decision making in LCA studies and defines a general framework for comparing alternatives that show different performance in a wide variety of impact metrics.