Ayse-Nur-Arslan

An energy community (EC) is a legal entity involving prosumers and consumers who produce, consume, and exchange energy. The members of these communities can cooperate to maximize the community’s social welfare. In practice, this naturally raises the question of cost sharing in the community, as the members may have different contributions to social welfare. In this presentation, we empirically highlight the benefits of cooperation for the community and the individual members. Then, we present some cost-sharing mechanisms that guarantee fairness and the stability of the grand coalition composed of all prosumers and consumers. Finally, we present some results on instances built with real-world data from our partner Sween’s demonstrator, Smart Lou Quila, in South France.

Robust optimization has evolved as a key paradigm for handling data uncertainty within mathematical optimization problems: it requires little historical information, can be used without characterizing probability distributions and often leads to tractable optimization problems that can be treated with existing deterministic optimization paradigms. However, the picture is more complex when some of the decisions (referred to as recourse decisions) can be adjusted after the uncertain data is known, to mitigate the effects of uncertainty, leading to adjustable robust optimization problems. Adjustable problems with discrete variables or multiple decision periods are particularly difficult to solve and, up to now, no scalable exact method has emerged. Project DROI proposes to study primal and dual approximations for such problems.

In this talk we consider two-stage linear adjustable robust optimization problems with continuous and fixed recourse. These problems have been the subject of exact solution approaches, notably, constraint generation (CG) and constraint-and-column generation (CCG). Both approaches repose on an exponential-sized reformulation of the problem which uses a large number of constraints or constraints and variables. The decomposition algorithms then solve and reinforce a relaxation of the aforementioned reformulation through the iterations which require the solution of bilinear separation problems. Here, we present an alternative approach reposing on a novel reformulation of the problem with an exponential number of semi-infinite constraints. We present a nested decomposition algorithm to deal with the exponential and semi-infinite natures of our formulation separately. We argue that our algorithm will lead to a reduced number of bilinear separation problems solved while providing a high quality relaxation. We perform a detailed numerical study that showcases the superior performance of our proposed approach compared to the state-of-the-art and evaluates the contribution of different algorithmic components.

Saint-Gobain Research Paris is an industrial research and development centre working for light and sustainable construction of the Saint-Gobain Group, the world leader in light and sustainable construction.

The collaboration is centered around the PhD thesis of Pierre Pinet.

We study the Vehicle Routing Problem with Stochastic Demands (VRPSD), which involves optimizing delivery routes for vehicles with limited capacity to serve customers whose demands are unknown when designing the routes. The routes are designed taking into account the possibility that a route may have too much demand for the capacity of a vehicle to be delivered, in that case recourse actions can be taken, inducing a cost. This problem seeks to minimize routing costs and the expected recourse costs.