Designing Flexible Systems using a New Notion of Submodularity

We study the problem of optimal flexibility capacity portfolio selection by introducing a new notion of submodularity in correspondences, which extends the classical notion of submodular functions. In particular, we prove that the correspondence that maps flexible resources to the set of demands that they can process is submodular, and use the properties of submodular correspondences to compare different flexibility configurations and derive insights into the optimal capacity portfolio.