Analogies Between Social Interaction Models and Supply Chains

Laurent Navoret (1) , Richard Bon (2) , Pierre Degond (1) , Jacques Gautrais (2) , David Sanchez (1) , Guy Theraulaz (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 CRCA - Centre de Recherches sur la Cognition Animale - UMR5169

Congestion is a major issue in the modeling of both animal aggregation and supply chains. Indeed, both systems face obvious physical limits : capacities of machine in supply chains [1] and non-overlapping constraints between individuals in social groups. As a paradigm of crowding and social group movement, we are interested in sheep herds. The behaviour of this gregarious animal is experimentally studied [5]. Let us focus on the displacement period of a sheep herd, where all animals move with the same speed. A macroscopic model for herds including speed and congestion constraints is derived from an individual based model. In order to enlight the congestion part in the dynamics, a singular limit of this macroscopic model is taken and leads to two phases in our herd : a congested and a non-congested one. We finally analyse the spatial transition between these two phases. Such a study of the congestion in self organized systems could be translated to supply chains context.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Laurent Navoret, Richard Bon, Pierre Degond, Jacques Gautrais, David Sanchez, et al.. Analogies Between Social Interaction Models and Supply Chains. European Consortium for Mathematics in Industry (ECMI) conference, 2008, London, United Kingdom. ⟨hal-01872081⟩