Commitments between managers in order to guarantee viability of a collective installation with different activities
Résumé
Diversification of farm activities can be adopted as a way to reduce risk and improve farm resilience in
a context of climate change and increased uncertainties (Barbieri and Mahoney, 2009; Gonçalves et
al., 2021; Paut et al., 2019). However, it raises many challenges such as an increase of workload or the
necessity of knowledge and know-how acquisition (Duru et al., 2015). A solution can be found through
collective installation, sharing workload and competences among the associates. It implies finding a
way to organize individual and collective management of activities. Indeed, management decisions
about one activity can affect the others, on the short but also long term.
In our study, we used the framework of Viability Theory in order to model a collective installation of a
market gardening activity and a restaurant. In the computation of a guaranteed viability kernel of each
activity, results from the second activity are considered as tychastic uncertainty. In order to reduce
this uncertainty, the two managers can agree on commitments about vegetable production and
economic results. This results in a reduction of the range of tychastic uncertainty. Different
organizations of collective management have been implemented. Thus, our model represents a variety
of solutions in the trade-off between exhaustive knowledge, resulting in heavy mental load, and
ignorance of the other manager’s results. In the field of mathematical modelling, this trade-off can be
translated by the separation of activities into different modules, resulting in a decrease of computation
times at the cost of a loss of information.
The size of the guaranteed viability kernels depends on the way the two activities are organized, and
on the levels of commitments the two managers agree on. In other words, simultaneous viability of
both activities can be more or less difficult to achieve.
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