The rank pricing problem: Models and branch-and-cut algorithms
The rank pricing problem: Models and branch-and-cut algorithms
复制标题
排名定价问题：模型和分支切割算法
DOI：
10.1016/j.cor.2018.12.011
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Alfredo Marín
中科院分区：
文献类型：
--
作者：
Herminia I. Calvete;Concepción Domínguez;C. Galé;M. Labbé;Alfredo Marín
在管理和经济规划中，主要关注的问题之一是以合适的价格将合适的产品出售给合适的客户。零售业和制造业的公司采用定价策略来最大限度地提高收入。等级定价问题考虑的是一个具有无限供给和统一预算的单位需求模型，其中顾客具有等级购买行为。在这些假设下，首先从双层定价模型的角度分析了该问题，并将其表示为一个具有多个独立跟随者的非线性双层规划。我们还提出了一个直接的非线性单级制定铭记问题的目的。两种不同的线性化的模型进行，并获得两个家庭的有效的不等式，嵌入在配方中，通过实施一个分支和切割算法，使我们能够收紧由线性松弛的模型给出的上限。我们还研究了模型的多面体结构，利用一个事实，即它们的约束的子集构成了一个特殊的情况下的集合包装问题，并表征所有的集团方面。此外，我们开发了一个预处理过程，以减少实例的大小。最后，我们通过大量的计算实验，证明了配方，分支和切割算法和预处理的效率。
One of the main concerns in management and economic planning is to sell the right product to the right customer for the right price. Companies in retail and manufacturing employ pricing strategies to maximize their revenues. The Rank Pricing Problem considers a unit-demand model with unlimited supply and uniform budgets in which customers have a rank-buying behavior. Under these assumptions, the problem is first analyzed from the perspective of bilevel pricing models and formulated as a non linear bilevel program with multiple independent followers. We also present a direct non linear single level formulation bearing in mind the aim of the problem. Two different linearizations of the models are carried out and two families of valid inequalities are obtained which, embedded in the formulations by implementing a branch-and-cut algorithm, allow us to tighten the upper bound given by the linear relaxation of the models. We also study the polyhedral structure of the models, taking advantage of the fact that a subset of their constraints constitutes a special case of the Set Packing Problem, and characterize all the clique facets. Besides, we develop a preprocessing procedure to reduce the size of the instances. Finally, we show the efficiency of the formulations, the branch-and-cut algorithms and the preprocessing through extensive computational experiments.
影响因子：
1.1
作者：
Chen, Xi;Diakonikolas, Ilias;Paparas, Dimitris;Sun, Xiaorui;Yannakakis, Mihalis
通讯作者：
Yannakakis, Mihalis