Online multiple one way non-preemptive time series search with interrelated prices

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 \(K+1-\frac{K}{\theta _2}\) $K+1-\frac{K}{{\theta }_2}$ 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 \(\frac{K}{48\log _{\theta _2} K}\) $\frac{K}{48{log}_{{\theta }_2}K}$ on the competitive ratio for MTSS-ip is proved.