Capacity planning with competitive decision-makers: Trilevel MILP formulation, degeneracy, and solution approaches

Abstract

Capacity planning addresses the decision problem of an industrial producer investing on infrastructure to satisfy future demand with the highest profit. Traditional models neglect the rational behavior of some external decision-makers by assuming either static competition or captive markets. We propose a mathematical programing formulation with three levels of decision-makers to capture the dynamics of duopolistic markets. The trilevel model is transformed into a bilevel optimization problem with mixed-integer variables in both levels by replacing the third-level linear program with its optimality conditions. We introduce new definitions required for the analysis of degeneracy in multilevel models, and develop two novel algorithms to solve these challenging problems. Each algorithm is shown to converge to a different type of degenerate solution. The computational experiments for capacity expansion in industrial gas markets show that no algorithm is strictly superior in terms of performance.