考虑碳排放的多产品竞争设施选址问题研究

Research on multi-commodity competitive facility location problem with carbon emission

传统的设施选址模型针对空间垄断,忽视市场竞争.在低碳可持续发展背景下,针对政府碳交易机制下生产多种替代和/或者互补产品的两家制造企业安置设施竞争市场份额的问题,基于定义于整个非负价格区域上的互补需求函数,构建考虑运输碳排放的多产品竞争设施选址模型.该模型为双层规划,上层是领导者企业的利润最大化模型,为带均衡约束的0-1混合整数二次规划;下层是跟随者企业的利润最大化模型,为带均衡约束的二次规划.首先利用Karush-Kuhn-Tucker条件、大M方法和McCormick外逼近方法将双层规划转化为有界闭集上的0-1混合整数凹规划,然后提出具有全局收敛性的分支提升算法,最后通过数值算例验证了所提模型和算法的有效性,并阐明了碳限额和碳交易对企业决策产生的影响.

Many traditional facility location models assume spatial monopoly where market competition is ignored.In the context of sustainable low-carbon economy,a multi-commodity competitive facility location problem involving two firms producing substitutable and/or complementary products under the carbon trading scheme is investigated.Based on complementarity demand functions defined in the whole non-negative price area,this problem is formulated as a bi-level program model.The upper level is the leader firm’s profit maximization model,which is a 0-1 mixed-integer quadratic program with equilibrium constraints;the lower level is the follower firm’s profit maximization model,which is a quadratic program with equilibrium constraints.This bi-level program is reformulated as a 0-1 mixed-integer concave program with a bounded closed set by applying the Karush-Kuhn-Tucker condition,big-M method and McCormick approximation method,and a branch-and-refine algorithm with global convergence is developed.Numerical results illustrate the impact of emission cap and carbon trading on firm decisions,as well as the validity of our model and algorithm.