The newsboy problem with multiple demand classes

We consider the single item newsboy problem, where the item can be sold to different demand classes at different prices. The demands are realized sequentially over time. That is, the newsboy purchases newspapers at the beginning of the day and sells them in the morning and in the afternoon with different prices. We analyze two cases where the prices are either decreasing or increasing; the former case applies, for example, to fashion goods retailing, while the latter to airlines and hotels. In the decreasing price case, we find the optimal order quantity to maximize the expected profit with independent multiple demands. We show numerically that aggregating the multiple demands with a single average price or applying the single demand newsboy model separately to multiple demand classes may lead to large sub-optimality. In the increasing price case, we analyze a two demand class model in which a fraction of the unsatisfied lower fare demand diverts to the high fare class, thus causing dependent sales. We follow a policy of protecting the sales in the higher fare class by limiting the sales in the lower fare class. We derive both the fare allocation limit and the initial capacity, and discuss managerial implications. For both models, we give bounds on the optimal order quantity.