*Appendix A.2. Type of Multifunctional Processes*

As highlighted by several authors, the terminology reported in the literature for distinguishing the different types of multifunctional processes is not harmonized [5,35]. This article follows the terminology defined by Majeau-Bettez et al. [35], who differentiated between *full-joint production*, *partial joint production*, and *combined production*. *Full joint production* takes place when the co-products are produced simultaneously, with a fixed ratio of production (e.g., fixed by the stoichiometry of a chemical reaction, or by natural processes such as the proportions between wheat grains and wheat straw). *Partial joint production* occurs when there is an intermediate level of technological linkage between the different co- and by-products (e.g., an oil refinery as a whole or the production of milk and meat or the transportation of two different products) and *combined production* when there is not technological linkage (e.g., a gasoline station also offering shop services). According to this definition, the ratio of production of the co- and by-products could be varied in every case except for the full joint production.

#### *Appendix A.3. Type of Modeling Approaches*

The selection of the modeling approach is based on the goal of the study and the decision context. Generally, when the goal of a study is to describe the status of a system, an attributional LCA (ALCA) approach is followed to calculate the environmental impact of providing a specific amount of the functional unit [5]. When the goal is to describe the effect of a change due to a decision, a consequential LCA (CLCA) approach is followed to estimate how this environmental impact would change in response to a *change* in the output of the functional unit (i.e., it is change-oriented) [98]. The current conceptualization of the CLCA approach was first publicly discussed in the 2001 international workshop on electricity data for life cycle inventories [106].

One of the main principles of ALCA is the so-called 100% additivity [35]. This principle means that "results of a separate analysis of all economic activities should add up to the result of an analysis of the total economic activity" [39], so ALCA is suitable for attributing the total impacts to a defined function (product or service), but, for example, it does not indicate to policy makers the impact of policy changes, when these cause an incremental change from the *status quo*.

By contrast, CLCA determines the *change* in impacts due to a *change* in the production of the product or service, or to a change in policy. So it attempts to consider *all* the impacts of the change, also on other sectors that are influenced, for example as a consequence of the use of by-products [35]. CLCA is therefore preferred to ALCA for estimating the impact of policy changes [107]. CLCA usually uses market-driven modeling to forecast what will happen once the product or service of interest is introduced [59]. This means that in CLCA, marginal processes are considered, rather than average ones, including the activities displaced by by-products. This is typically modeled through the so-called substitution approach, whereby CLCA considers only the activities reacting to the change in demand for the functional unit, keeping the total of other services constant. Therefore, the quantification of displaced activities depends on the market characteristics of competing products [14].
