Short food supply chain management with matrices of sets: a new mathematical framework to visualise preferences of consumers’ products basket

In recent decades, the food system has been strongly affected by the phenomenon of globalisation. The globalisation of supply chains and crises such as the COVID-19 crisis have shown the need to rethink the current supply system. Complex supply systems with multiple actors and a multitude of intermediaries have gained ground in favor of direct relationships between consumers and producers. This results in a lack of information about the origin and quality of the products consumed, which leads to a lack of trust. Consequently, Short Food Supply Chains (SFSC) are presented as a response from consumers and producers to regain this lost link between them. The contribution of this paper is to provide a new methodological tool called Matrices of Sets (MOS) that can visualise efficiently consumers’ preferences products. The new mathematical framework of MOS considers matrices where each term at line i and column j is a set, instead of a number in classical matrices. Indeed, MOS descriptive sets including numbers (data) and text (metadata) may efficiently gather in one matrix of sets, what might have been scattered in multiple matrices of numbers and added metadata. An application of MOS for the needs of SFSC is proposed, in which, lines represent producers or hubs, columns represent hubs or consumers and each term ( i , j ) represents the set of products, their qualities, prices and organic characteristics. It has shown its efficiency in preserving structure and nature of input and output data in SFSC.