Enhancing tractability of mixed-integer nonlinear programming models: case studies in energy and sports

Abstract

We address three integer-programming models which are difficult to formulate and solve because, fundamentally, they are mixed-integer, nonlinear programs. These three applications are: (i) design of and dispatch for a forward operating base, or remote military installation, that possesses a microgrid consisting of diesel generators, photovoltaic cells and lithium-ion batteries; (ii) dispatch of a grid-scale hybrid system consisting of concentrated solar power and thermal energy storage, combined with photovoltaics and battery storage; and (iii) a series of models to determine when teams in the NBA have been eliminated from, or have clinched a spot in, the playoffs. We eliminate nonlinearities, remove superfluous variables, and add cuts to expedite solutions. In some cases, heuristics help either by providing an initial feasible solution from which the mixed-integer programming solver can start or as an end in and of themselves. In all three applications, we are able to solve otherwise unsolvable models and inform real-world decisions much more precisely.