مطلبی در مورد: "اثر تبلیغات بهینه در مسئله پسر روزنامه فروش بدون توزیع معین "

Recently, Lee and Hsu (2011) study the advertising effect on the distribution-free newsboy problem. In one of their results, they show that the optimal expenditure on advertising, the optimal order quantity and the optimal lower bound on the expected profit increase with the advertising effect parameters. Although this result holds in general, it requires additional assumptions. In this note we provide the necessary and sufficient conditions under which the statements of Lee and Hsu (2011) hold. These conditions are shown to be violated if the advertising expenditure is too low or there is a very small difference between the optimal profit and the profit without advertising.

The effect of advertising on the single period inventory problem, or the newsboy problem, has been first addressed by Khouja and Robbins (2003). They assume that the mean demand is increasing and concave in advertising expenditure and study three cases of demand variation as a function of advertising expenditure: (i) demand has constant variance, (ii) demand has a constant coefficient of variation, and (iii) demand has an increasing coefficient of variation. Lee and Hsu (2011) study the effect of advertising on the distribution-free newsboy problem. Using the bounds on the expected profit of the newsvendor problem given by Alfares and Elmorra (2005), they provide closed form solutions for the optimal order quantities and the optimal advertising policy for the three cases given in Khouja and Robbins (2003). They also provide sensitivity analysis of the optimal decisions to the parameters. One of their results is the following: the optimal advertising policy, the optimal order quantity and the optimal lower bound on the expected profit increase with the advertising effect parameters. In this study, we show that this result of Lee and Hsu (2011) requires additional assumptions on the cost parameters and advertising parameters. We also show that these assumptions are violated if the advertising expenditure is too low, or if the difference between the optimal profit and the profit without advertising is too small.

Lee and Hsu (2011) state that the optimal expenditure on advertising, the optimal order quantity and the optimal lower bound on the expected profit increase with the advertising effect parameter α. In this note we show that this result does not hold without further assumptions and provide the necessary and sufficient conditions under which their statements hold. Finally we show that their statements hold in general by showing that they are violated only if the optimal advertising expenditure is too low or if the difference between the optimal profit and the profit without advertising is too small.