Advertising and forecasting investments of a newsvendor

We consider a newsvendor that can increase the mean demand with advertising and reduce the variability in the demand by forecasting or market research. We analyze the problem under uniform and normal demand distributions. We also study the distribution-free case by using a lower bound on the newsvendor profit function. We show that when the budget is unlimited, the forecasting expenditure increases with the production cost until the cost of holding an inventory is equal to the cost of a lost sales. Although both expenditures increase with the product price, it turns out that the advertising expenditure is more important for the newsvendor: it allocates more to the advertising for products with higher prices if the budget is limited. It turns out that a newsvendor can benefit more from advertising (forecasting) if the market size (variability) is larger. Moreover, it is more profitable to allocate the expenditures into a single large market rather than allocating it to small segmented markets. The numerical studies show that the ability of forecasting makes a newsvendor more robust to the variance, i.e., the variability level is reduced significantly with the forecasting expenditure.