Abstraction of heterogeneous supplier models in hierarchical resource allocation

Abstract

Resource allocation problems such as finding a production schedule given a set of suppliers’ capabilities are generally hard to solve due to their combinatorial nature, in particular beyond a certain problem size. Large-scale instances among them, however, are prominent in several applications relevant to smart grids including unit commitment and demand response. Decomposition constitutes a classical tool to deal with this increasing complexity.We present a hierarchical “regio-central” decomposition based on abstraction that is designed to change its structure at runtime. It requires two techniques: (1) synthesizing several models of suppliers into one optimization problem and (2) abstracting the direct composition of several suppliers to reduce the complexity of highlevel optimization problems. The problems we consider involve limited maximal and, in particular, minimal capacities along with on/off constraints. We suggest a formalization termed supply automata to capture suppliers and present algorithms for synthesis and abstraction. Our evaluation reveals that the obtained solutions are comparable to central solutions in terms of cost efficiency (within 1% of the optimum) but scale significantly better (between a third and a half of the runtime) in the case study of scheduling virtual power plants.