For a purchase-to-order seller, there is no inventory and the seller has to purchase goods to fulfill orders already placed. For each purchase, there is a constant ordering cost. For each order, delay cost will be incurred if it is not fulfilled timely. Consequently, there is a tradeoff between the ordering cost and the delay cost for the seller to make replenishment decisions minimizing the total cost. In practice it is impossible or difficult for the seller to know demand information about future orders in advance, and thus this decision-making problem is of an online fashion. In the previous work, this online problem is classified into three cases according to capacity limit and demand quantity, and a 10-competitive online policy is proposed for the general case. In the present paper, an improved 4-competitive online policy is proposed. Besides, an asymptotic lower bound of 2 is derived for this online decision-making problem.

对于按订单采购的卖家来说，没有库存，卖家必须购买商品来履行已下的订单。每次购买都会产生恒定的订购成本。对于每一个订单，如果没有及时履行，都会产生延迟成本。因此，卖方需要在订购成本和延迟成本之间进行权衡，以最小化总成本来做出补货决策。在实践中，卖方不可能或很难提前知道未来订单的需求信息，因此这种决策问题是一种在线时尚。在之前的工作中，该在线问题根据容量限制和需求数量分为三种情况，并针对一般情况提出了10竞争的在线策略。在本文中，提出了一种改进的4竞争在线策略。除了，