Joint advertising and ordering strategies for perishable product with emergency ordering

The emergency ordering plays an important role in the practical prouction and sale, and the newsvendor problem with advertising decision provides an important means to examine how operational problems interacts with marketing issues to influence decision-making at the firm level. When a newsvendor faces stochastic advertisement-sensitive demands, he has to make the advertising and inventory decisions before the demand is realized. In this paper, we combine the above two aspects to investigate the case in which advertising leads to increase in sales under general stochastic demand with emergency ordering. We assume the mean demand is strictly increasing and strictly concave in advertising premium and explore the optimal ordering and advertising decision's properties and their comparative statics with the ordering cost, emergency ordering cost, sale price and salvage value.