带有增量型价格折扣报童问题的竞争性决策方法

Competitive Decision-Making Method of Newsvendor Problem with Incremental Price Discount

弱集成算法是一种在线序列预测算法,在不对需求做任何统计假设下,可解决带有增量型价格折扣的多阶段报童问题。首先,运用弱集成算法对固定订购量的专家意见进行学习,并考虑回收价值和缺货损失费,得到所研究问题的在线决策方法;其次,修正收益函数后,从理论上证明了在线决策方法的累积收益渐近于最优专家意见的累积收益;最后,通过数值算例进一步表明该在线决策方法相对于最优专家意见具有良好的竞争性能,且竞争性能随着阶段数的增加而增强。

The weak aggregating algorithm(WAA) is an on-line sequential prediction algorithm. It can solve the multi-period newsvendor problem with incremental price discount without making any statistical assumptions about the demand. Firstly,in consideration of the recovery value and shortage cost,the explicit online decision-making method was obtained by applying WAA to learn the expert advice who suggested fixed order quantities. Then,by modifying the gain function,it was theoretically proved that the cumulative gains of the proposed method asymptotically approached those of the best expert advice. Finally,the numerical examples illustrated that the proposed method showed better competitive performance comparing with the best expert advice,and the larger the number of the stage was,the better the performance of the strategy owns.