Mixed-integer bilevel optimization for capacity planning with rational markets

• Published in: Computers & chemical engineering Vol. 86; pp. 33 - 47
• Main Authors: Garcia-Herreros, Pablo, Zhang, Lei, Misra, Pratik, Arslan, Erdem, Mehta, Sanjay, Grossmann, Ignacio E.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 04-03-2016
• Subjects: Air separation; Bilevel optimization; Capacity planning; Chemical engineering; Computer simulation; Cost engineering; Marketing; Markets; Mathematical models; Optimization; Rational markets; Bilevel optimization; Rational markets; Capacity planning
• ISSN: 0098-1354; 1873-4375
• DOI: 10.1016/j.compchemeng.2015.12.007

•Capacity expansion planning formulated as a bilevel optimization problem.•Higher level involves industrial company, lower level the market.•Formulation is a mixed-integer bilevel linear program with an LP at lower level.•Reformulation single-level problem with KKT or duality-based reformulation.•Application industrial gases shows duality-based reformulation much faster.
We formulate the capacity expansion planning as a bilevel optimization to model the hierarchical decision structure involving industrial producers and consumers. The formulation is a mixed-integer bilevel linear program in which the upper level maximizes the profit of a producer and the lower level minimizes the cost paid by markets. The upper-level problem includes mixed-integer variables that establish the expansion plan; the lower level problem is an LP that decides demands assignments. We reformulate the bilevel optimization as a single-level problem using two different approaches: KKT reformulation and duality-based reformulation. We analyze the performance of these reformulations and compare their results with the expansion plans obtained 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 number of variables and constraints. The formulations and the solution methods are illustrated with examples from the air separation industry.