Using System Modularity to Simplify Viability Studies: An Application to a Farm-Restaurant Interaction
Résumé
Viability theory is a relevant framework for modeling environmental and sustainability problems, looking for satisficing solutions rather than optimal ones. In particular, it can be adapted to model the management of agroecological farming systems. However, numerical applications related to the computation of the viability kernel are very sensitive to the state space and control space dimensions, as computation time and memory requirement increase exponentially with the number of state and control variables. In this study, we relied on the modularity of a system representing a collective installation of a market gardening activity and a restaurant to split the model into two interconnected modules of smaller size, each one corresponding to an activity. Different organizations of collective management have been tested. To reduce the range of uncertainty on each activity outcomes while keeping low communication costs, the algorithm considers that the two managers agree on commitments about vegetable production and economic results. In each organization, only a limited set of commitment level values enables simultaneous viability of both activities. These commitment values are an instance of essential information to share between the managers of both activities and guarantee in order to ensure collective functioning. Moreover, guaranteed viability kernels in the case of modular organizations are included into the viability kernel of an equivalent non-modular model. The modular algorithm captures most viable states while drastically reducing computing time. Beside its applied interests, the methodological developments presented here constitute a major step forward in overcoming the dimensionality curse faced by most viability problems.