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

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Abstract

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.

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Notes

  1. FuMa is a project co-funded by the European Union (European Regional Development Fund) and the Normandy region. The aim of this project is to rethink the management of the flow of goods and to take the right turn towards a future integrating globalization, technology, digital and the well-being of the populations on their territory.

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Acknowledgements

We would like to thank the anonymous reviewers for their insightful comments, which enabled us to improve our results and manuscript.

Funding

Our article is part of the FuMa (Future de la Marchandise) collaborative project. FuMa is a project co-funded by the European Union (European Regional Development Fund) and the Normandy region.

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Authors and Affiliations

  1. Universite Le Havre: Universite Le Havre Normandie, Le Havre, France

    Mohamed Charhbili & Jaouad Boukachour

  2. Department of Economics, Savoie Mont Blanc University, Annecy, France

    Mohamed Charhbili

  3. Computer Sciences & Mathematics, JUNIA-ISEN, Lille, France

    Amina El Yaagoubi

  4. The Institution of Engineering and Technology, London, UK

    Renaud Di Francesco

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  1. Mohamed Charhbili
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Contributions

MC: Conceptualization, Methodology, Writing—Original draft, Visualization, Investigation. AE: Writing—Original draft, Validation, Investigation. RD: Methodology, Visualization, Writing—Review & Editing. JB: Writing—Review & Editing, Supervision, Validation. All authors read and approved the final manuscript.

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Correspondence to Mohamed Charhbili.

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Charhbili, M., El Yaagoubi, A., Di Francesco, R. et al. Short food supply chain management with matrices of sets: a new mathematical framework to visualise preferences of consumers’ products basket. OPSEARCH (2023). https://doi.org/10.1007/s12597-023-00695-4

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