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•A bi-level programming model to model a market regulation situation is presented.•The government intervenes by regulating the raw material given to the competitors.•Two equivalent single-level reformulations are proposed.•Three heuristics that exploit characteristics of the bi-level model are developed.•A case-study based on the Mexican petrochemical industry is presented.
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 profit by deciding the amount of raw material bought from the a state-owned firm. Two equivalent single-level reformulations are proposed to solve the problem. The first reformulation is based on the strong duality condition of the lower level and results in a continuous non-linear model. The second reformulation resorts to the complementarity slackness optimality constraints yielding a mixed-integer linear model. Additionally, three heuristic algorithms are designed to obtain good-quality solutions with low computational effort. In this problem, the feasible region of the dual problem associated to the follower is independent from the leader’s decision. Therefore, the proposed heuristics exploit this particular characteristic of the bilevel model. Moreover, the third heuristic hybridizes the other two algorithms to enhance its performance. 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. Numerical results indicate that the hybrid algorithm outperforms the other two heuristics. However, all of them demonstrate to be good alternatives for solving the problem. Additionally, optimal solutions of all the instances are obtained by using good quality solutions (given by the hybrid algorithm) as initial solutions when solving the second reformulation via a general purpose solver.