In this paper, we study a multiple time series search problem in which at the first n periods, one product is produced in each period and becomes sellable. The total length of the trading horizon N (\(N>n\)), i.e., the total number of trading periods (which includes the first n periods when the products are produced), is unknown beforehand. All the n products are homogeneous. At each period, a price is observed and the player must decide immediately the number of available products to sell at this period, without the knowledge of future prices and when the trading horizon ends. The objective is to maximize the total revenue from selling the n products. We present an online algorithm ON for this problem and prove its competitive ratio. A lower bound on the competitive ratio for this online problem is also proved. Numerical results for the theoretical competitive ratio of algorithm ON and the lower bound are also reported.

在本文中，我们研究了一个多时间序列搜索问题，其中在前n 个时期，每个时期都生产一种产品并可以销售。交易区间的总长度N（\(N>n\)），即交易周期的总数（包括产品生产的前n个周期），事先是未知的。所有n 个产品都是同质的。在每个时期，都会观察到一个价格，玩家必须立即决定在此时期出售的可用产品数量，而不知道未来价格和交易期限何时结束。目标是最大化销售n的总收入产品。我们针对这个问题提出了一个在线算法，并证明了它的竞争力。还证明了该在线问题的竞争比的下界。还报告了算法ON的理论竞争比和下限的数值结果。