价格数量折扣下多阶段报童问题的在线策略

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

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.

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 decisionmaking 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 multiperiod 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.