A newsboy model with consumer's surplus and substituted demand

The classic newsboy problem in management science has been paid much attention in the past three decades. This year a number of attempts have been made to enrich the factors treated in the analysis. For example, if price can be set by the newsboy, this will influence demand. Extensions in which demand is related to the price charged lose the closed form, and elegance, of the original solution. This paper will examine the case in which the demand is related to the expected value anticipated by the consumer. We define this value as the consumer's surplus times the likelihood that the consumer finds the item, in stock, where the surplus is the reservation price of the consumer less the price charged by the seller, and the reservation price means the price that the consumer is willing to pay for the product. With this assumption, we analyze the characters of. the optimal solutions to two cases: single product and two substituted products. For single product, it is proved that the probability of stocking out is equal to the ratio of the item's unit cost to the consumer's reservation at the optimal inventory. For two substituted products, we use the same method and find that the simple solution is preserved. Finally the numerical analysis is done to illustrate the model proposed. Some useful findings are. drawn.