*Appendix A.1. Type of Products*

In this article, three definitions are used for different types of products and services: *co-products*, *by-products and wastes*.

Co-products are the ones satisfying the main (primary) function that a production system or process is intended to deliver. As highlighted by Majeau-Bettez et al. [35], co-products have also been defined with the term ''primary", ''determining", and others. Conversely, by-products represent only secondary functions of the system. A by-product is a substance resulting from a production process whose primary function is not the production of that item but either it is inevitably produced or could, in principle, be avoided by the system without altering the main functionality of the process (e.g., a farm with tourist accommodation services).

The primary function of a product system is identified by evaluating the purpose of such a system. For example, for the internal combustion engine of a car, the primary product is the mechanical power needed by the car to carry people (primary function). A secondary function of the same engine can be the production of heating (by-product) to keep a proper temperature in the car. Nevertheless, the distinction between primary and secondary functions can be particularly difficult for some unit processes (e.g., sunflower oil vs meal). When such difficulty is encountered, the primary function should be selected by assessing what function of the multifunctional process generates more revenues for the investigated process [27,35,63], within the temporal scope of the LCA. Nevertheless, there are processes whose aim is the generation of several functions of comparable value. In such a case, there can be multiple primary functions. For example, a biorefinery can produce various chemicals and fuels as primary functions (co-products) and provide district heating as a secondary function (by-product).

The shared environmental impact of a process shall be apportioned between co-products and by-products, but not to wastes [2]. According to ISO 14044:2006, wastes are "substances or objects which the holder intends or is required to dispose of" [2]. There is, however, a fine line between wastes and by-products. For example, manure is nowadays used as feedstock for biogas plants, used cooking oil is used for biodiesel production, and residues of the potato industry are used for animal feed. When these alternative uses make these wastes find a market demand represented by market values, they should be considered, therefore, as by-products. We adopt the distinction waste/by-product provided by the Waste Directive Framework [105]. A "waste" becomes a by-product when the "following conditions are met: (1) further use of the substance or object is certain; (2) the substance or object can be used directly without any further processing other than normal industrial practice; (3) the substance or object is produced as an integral part of a production process; (4) further use is lawful, i.e., the substance or object fulfills all relevant product, environmental and health protection requirements for the specific use and will not lead to overall adverse environmental or human health impacts" [105].
