This paper studies the online multiple time series search problem with interrelated prices (MTSS-ip). This perspective narrows the distance between the problem and the reality of market prices with limited variation. In MTSS-ip, the products arrive periodically, and the decision maker has a limited storage size without knowing future prices. The prices of two adjacent periods are interrelated. This study proposes an online zero-inventory algorithm (ZIA) and proves an upper bound of \(K+1-\frac{K}{\theta _2}\) on the competitive ratio of ZIA. In addition, a lower bound on the competitive ratio of problem MTSS-ip for any deterministic online algorithm is established. For the case with a large storage size K, a lower bound of \(\frac{K}{48\log _{\theta _2} K}\) on the competitive ratio for MTSS-ip is proved.

本文研究了具有相互关联价格的在线多时间序列搜索问题 （MTSS-IP）。这种观点缩小了问题与变化有限的市场价格现实之间的距离。在 MTSS-ip 中，产品会定期到达，决策者在不知道未来价格的情况下拥有有限的存储大小。两个相邻期间的价格是相互关联的。本研究提出了一种在线零库存算法 （ZIA），并证明了 ZIA 竞争比率的上限 \（K+1-\frac{K}{\theta _2}\）。此外，对于任何确定性在线算法，问题 MTSS-ip 的竞争比率都建立了下限。对于大存储大小 K 的情况，证明了 MTSS-ip 竞争比率的下限 \（\frac{K}{48\log _{\theta _2} K}\）。