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A market regulation bilevel problem: A case study of the Mexican petrochemical industry

机译：市场监管队列问题：墨西哥石化工业的案例研究

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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 mixedinteger 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. (C) 2019 Elsevier Ltd. All rights reserved.
机译：本文旨在通过政府干预研究市场监管问题。本文问题的主要特征之一是分析的是，政府垄断了一个行业的原材料，并参与另一个行业，其中包括私营企业生产商品。根据本计划，政府控制一个国有企业来平衡市场;也就是说，为了最大限度地减少所生产和要求的商品之间的差异。另一方面，协调私营企业的监管组织旨在通过决定从国有公司购买的原材料量来最大限度地利润。提出了两个等同的单级重新级别来解决问题。第一个重构是基于较低水平的强型状况，并导致连续的非线性模型。第二个重构度假胜地，互补松弛最优性约束，产生了混合体线性模型。此外，三种启发式算法旨在获得具有低计算工作的高质量解决方案。在这个问题中，与跟随者相关的双重问题的可行区域与领导者的决定无关。因此，拟议的启发式利用彼得二的这种特征。此外，第三启发式杂交其他两种算法以提高其性能。进行了广泛的计算实验，以衡量提出的解决方案方法的效率。提出了基于墨西哥石化工业的案例研究。从案例研究生成的附加实例被认为是验证所提出的启发式算法的鲁棒性。数值结果表明，混合算法优于其他两个启发式算法。然而，所有这些都证明是解决问题的好替代品。另外，通过使用通用求解器解决第二重构时，通过使用良好的质量解决方案（混合算法给出）获得所有实例的最佳解决方案。 （c）2019 Elsevier Ltd.保留所有权利。

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