A polyhedral analysis of the synchronous management of energy production and consumption problem

Renewable energies currently appear to be an obvious and efficient solution to combat climate change. Among these, hydrogen possesses all the attributes to be the most renewable, clean, efficient and non-toxic form of energy. In this work, we focus on the numerical handling of the synchronization of the consumption of hydrogen by a vehicle performing a pick-up and delivery tour, with its production of hydrogen through photolysis and electrolysis within a micro-plant. We address this problem through a Mixed Integer Linear Program (MILP). Due to the poor behavior of the relaxation of this MILP model, we first strengthen it with families of valid inequalities. Next, we notice that the variables related to the refueling transactions may be considered as the master ones inside the model. This leads us to introduce a specific partial ordering structure on the set of feasible refueling transactions. Taking advantage of the structure of the related chain polyhedron allows us to derive additional Non-Crossing and Time-Consistent cuts that may be separated in polynomial time. Numerical experiments demonstrate that reinforcing this way the original MILP model results in a significant improvement in its numerical handling.