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运筹学学报 ›› 2018, Vol. 22 ›› Issue (3): 37-48.doi: 10.15960/j.cnki.issn.1007-6093.2018.03.004

• 运筹学 • 上一篇    下一篇

价格数量折扣下多阶段报童问题的在线策略

张永1,*  钟惠芬1  张卫国2  徐维军2  张群3   

  1. 1. 广东工业大学管理学院, 广州 510520; 2. 华南理工大学工商管理学院, 广州 510006; 3. 广东外语外贸大学金融学院, 广州 510006
  • 收稿日期:2016-04-07 出版日期:2018-09-15 发布日期:2018-09-15
  • 通讯作者: 张永 E-mail: yq21614@163.com
  • 基金资助:

    国家自然科学基金(No. 71501049), 2015年广州市哲学社会科学``十二五"规划课题(No. 15G29), 广东省高等学校珠江学者岗位计划(2016)

On-line strategies for multi-period newsvendor problem with price quantity discount

ZHANG Yong1,*  ZHONG Huifen1  ZHANG Weiguo2  XU Weijun2  ZHANG Qun3   

  1. 1. School of Management, Guangdong University of Technology, Guangzhou 510520, China; 2. School of Business Administration, South China University of Technology, Guangzhou 510006, China; 3. School of Finance, Guangdong University of Foreign Studies, Guangzhou 510006, China
  • Received:2016-04-07 Online:2018-09-15 Published:2018-09-15

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摘要：

价格数量折扣可以提高订购量, 是库存决策中的一个重要因素. 特别地, 当订购量达到一定水平时, 价格折扣才会发生. 应用理论计算机科学兴起的弱集成算法, 研究具有这种价格数量折扣的多阶段报童问题的在线策略. 弱集成算法是一种在线序列决策算法, 其主要特点是不对未来输入做任何统计假设, 克服了报童问题研究中需要对需求做概率假设的困难. 主要将弱集成算法应用到固定订购量的专家策略, 给出了价格数量折扣下多阶段报童问题的具体在线策略；得到了该在线策略相对于最优专家策略的理论保证. 进一步将回收价值和缺货损失费引入, 给出了推广的在线策略及其理论结果. 最后应用数值算例说明了给出的在线策略具有较好的竞争性能.

关键词: 价格数量折扣, 多阶段报童问题, 弱集成算法, 在线策略, 竞争性能分析

Abstract:

The price quantity discount can increase the order quantity, which is an important factor of inventory decision making. Particularly, price discount only occurs when the order quantity reaches a fixed level. This paper uses the Weak Aggregating Algorithm (WAA) advanced in computer science to study the multi-period newsvendor problem with this kind price quantity discount. WAA is an on-line sequential decision-making algorithm; its main advantage is that it does not make statistical assumption on future inputs, which overcomes the difficulties of having to make probability hypothesis on demand in newsvendor problem research. Mainly, this paper applies WAA to experts whose strategies are fixed order quantities to present explicit online strategy for the multi-period newsvendor problem with price quantity discount. The theoretical guarantee for the proposed online strategy is obtained compared with the best expert strategy. The salvage and shortage cost are further introduced to obtain extended online strategies and their theoretical results. The numerical examples are finally used to show the good competitive performance of the proposed online strategies.

Key words: price quantity discount, multi-period newsvendor problem, weak aggregating algorithm, on-line strategy, competitive performance analysis