Mixed-integer bilevel optimization for capacity planning with rational markets

We formulate the capacity expansion planning as a bilevel optimization to model the hier-archical decision structure involving industrial producers and consumers. The formulation isa mixed-integer bilevel linear program in which the upper level maximizes the profit of a pro-ducer and the lower level minimizes the cost paid by markets. The upper-level problem includesmixed-integer variables that establish the expansion plan; the lower level problem is an LP thatdecides demands assignments. We reformulate the bilevel optimization as a single-level problemusing two different approaches: KKT reformulation and duality-based reformulation. We ana-lyze the performance of these reformulations and compare their results with the expansion plansobtained from the traditional single-level formulation. For the solution of large-scale problems,we propose improvements on the duality-based reformulation that allows reducing the numberof variables and constraints. The formulations and the solution methods are illustrated withexamples from the air separation industry.