In this paper, a bilevel programming model is proposed to study a problem of market regulation through government intervention. One of the main characteristics of the problem herein analyzed is that the government monopolizes the raw material in one industry, and competes in another industry with private firms for the production of commodities. Under this scheme, the government controls a state-owned firm to balance the market; that is, to minimize the difference between the produced and demanded commodities. On the other hand, a regulatory organization that coordinates private firms aims to maximize the total product by deciding the amount of raw material bought from the state-owned firm. Two equivalent single-level reformulations are proposed to solve the problem. Additionally, three heuristic algorithms are designed to obtain good-quality solutions with low computational effort. Extensive computational experimentation is carried out to measure the efficiency of the proposed solution methodologies. A case study based on the Mexican petrochemical industry is presented. Additional instances generated from the case study are considered to validate the robustness of the proposed heuristic algorithms.
A bilevel optimization problem consists in an optimization problem in which some of the constraints specify that a subset of variables must be an optimal solution to another optimization problem. This paradigm is particularly appropriate to model competition between agents, a leader and a follower, acting sequentially. In this talk I will discuss two such problems.
In the first one, called the network pricing problem, tolls must be determined on a specified subset of arcs of a multicommodity transportation network. The leader or first level corresponds to the profit maximizing owner of the subset of arcs and the follower to users traveling at minimum cost between nodes of the network.
The second problem, called the Stackelberg bimatrix game, involve a party with the capacity of committing to a given action or strategy, referred to as the leader, and a party responding to the leader’s action, called the follower. The objective of the game is for the leader to commit to a reward-maximizing strategy anticipating that the follower will best respond. This type of game finds important applications in the domain of security.
Computer Science Department, Université Libre de Bruxelles
Martine Labbé is honorary professor at the Université Libre de Bruxelles (ULB). She was Professor of Operations Research at the Computer Science Department of the Faculty of Sciences. From 2007 to 2011, she was Dean of the Faculty of sciences. Her main research area is discrete optimization, including graph theory and integer programming problems and with a particular emphasis on location and network design problems. She is also specialised in bilevel programming and studies pricing problems and Stackelberg games. She served on the editorial boards of Discrete Optimization, Journal on combinatorial Optimization, Operations Research, Operations Research Letters and Transportation Science. She is now the Editor in Chief of the EURO Journal on Computational Optimization. She is the author or coauthor more than120 papers published in international journals. In 2007-2008, she was president of EURO, the Association of European Operational Research Societies. She was, in 2014 and 2015, Vice-Chair of the SIAM Activity Group on Optimization (SIAG/OPT).