Optimal sales limits in multi-stage bargain sales with shifts of customers

摘要

We consider multi-stage bargain sales in which the earlier a customer buys the goods, the more inexpensive it is. If we sell more goods in earlier stage, the earning rate becomes low. On the contrary, if we are unwilling to sell the goods in earlier stages, it may occur that the goods are unsold. Then we face the problem of determining the optimal sales limit on each stage. Furthermore we take into consideration the shifts of customers, that is, customers, who couldn't buy the goods in the earlier stage, may intend to buy them at the later stage. We formulate this problem by a dynamic programming and obtain a necessary and sufficient condition for the optimal policy. Furthermore we analyze the case of two stages in detail.