An online trading problem with an increasing number of available products

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.