*4.1. Bilateral Beginning (1994–1998)*

The discussions on the LCA multifunctionality issue were initially developed following two parallel routes (see Figure 6). On the first route, Tillman, Ekvall and their co-authors developed different types of allocation methods for multi-output systems and open-loop recycling [58,88]. It is crucial to notice that at that time, the ISO 14041 was not yet released [25]. Tillman et al. [58] focused their article on the choice of system boundaries based on the purpose of an LCA. They defined three LCA purposes: 1) process tree (PT), today known as ALCA and applied to processes where there are one main product and some by-products, 2) technological whole system (TWS), similar to what today is known as ALCA and applied to processes delivering several co-products, and 3) socio-economic whole system (SWS), similar to current CLCA [58]. In this article, the word *expansion* was used once with

respect to SWS, indicating that such a system accounts for economic and social factors and therefore "may lead to further expansion of the system" [58]. In 1994 and 1996, two conferences were held with sessions on allocation and life cycle inventory. Clift, who was also co-author of the publications in the second parallel route, published the reports of such sessions [89,90]. These reports concluded that allocation must, when possible, be based on causal relationships. Ekvall and Tillman discussed this conclusion, arguing that causal relationships could be either cause-oriented or effect-oriented [88]. An example of the first one is the manufacture of a product that occurs because the company expects customers to be willing to pay for it (cause). An example of an effect-oriented relationship is a system delivering a recycled product, which reduces the amount of virgin product in another system (effect). This second type of relationship resembles the current CLCA thinking. To represent effect-oriented relationships, they argue that the effects of the investigated product on other life cycles can be included in the LCA through the expansion of system boundaries. As the expansion of the system boundaries, they cited the approach developed by Tillman et al. (1994), which today is known as "substitution". Moreover, they argued that when LCA is used as a tool for decision support, the allocation procedure should generally be effect-oriented rather than cause-oriented. Therefore, it is possible to identify the probable origin of the consequential school in the study of 1997 of Ekvall and Tillman [88] and the study of 1994 of Tillman et al. [58].

The four articles of the second route were authored by Azapagic and Clift. In the first article (1995), they proposed linear programming (LP) modeling to solve the multifunctionality issue and to calculate the optimized environmental impact of plastic resins production, such as polypropylene and polystyrene [91]. The inputs and outputs of the system are then allocated to each of the co- and by-products through marginal changes in its production [91]. The marginal allocation coefficients correspond to the variation of the environmental burdens associated with a marginal variation of one of the co-functions [91]. The second article (1998) focused as well on LP as a tool for solving the problem of allocation and was applied to systems producing borate products. They highlighted that 1) "the main characteristic of this kind of modeling is that it is based on physical and technical relationships between the inputs and outputs [ ... ] describing the underlying physical causation in the system" [73] and 2) that the allocation by causal relationships provided by the model is obtained ''by exploring how the burdens change when the quantity of one function is changed with the quantities of all the other functions kept constant" [73]. These changes can be marginal, incremental, or average ones; however, LP can only be applied when system behavior can be linearized, which does not usually happen in average changes (i.e., substantial changes as for example the elimination of a functional output completely) [73].

In 1996, the first draft [92] of the ISO hierarchy for solving multifunctionality was released, as reported by Ekvall and Tillman [88]. This hierarchy was very similar to the one still present in the current ISO 14044:2006. System expansion was indicated in the first level [92]: "by expanding the system boundaries so that inputs, outputs and recycles remain within the system" (retrieved from [88]). From the literal statement, it appears clear that it was intended as an enlargement of the system boundaries to include all the co-functions within the boundaries (see Figure A1 in Appendix A). Such an approach is different from the system expansion method (substitution) indicated by Tillman's SWS, where functions are avoided instead of added.

On the second level, it was stated [92]: "where allocation cannot be avoided, the allocation should be based on the way in which the inputs and outputs are changed by quantitative changes in the products or functions delivered by the system" (retrieved from [88]). There was no use of the term "physical relationships" as in ISO 14044:2006. Hence, ISO was proposing allocation methods such as the marginal allocation developed by Azapagic and Clift [91], which are based on quantitative changes in the products or functions delivered by the system.

Finally, the last level allowed the allocation of different functions based on economic relationships, excluding allocation by physical properties. This preference for economic values could be due to their cause-oriented essence (the function is provided because one is willing to pay for it). Based on the

analysis of this bilateral beginning and this ISO draft [92], it seems that the socio-economic ALCA school represents the first version of the ISO hierarchy. In fact, they distinguish themselves by applying system expansion by only adding (and not subtracting) functions, and preferring economic allocation to an allocation based on a physical parameter (excluded option by this first draft version).
