Optimal price and lot size when the supplier offers a temporary price reduction over an interval

Manufacturers and other suppliers offer temporary reduction in the price charged to resellers for a variety of reasons. Typically the trade promotion lasts for some finite time-span. In addition, in reselling situations, the end demand tends to be sensitive to selling price. Thus, when the trade promotion takes place, there is possibility that not all the quantity purchased by the reseller at discount is passed on to the final consumers at a reduced selling price. Studies to date addressing the above problem situation have assumed that the trade promotion is offered by the supplier only at one point in time. We extend the analysis to the more realistic case where the promotion lasts a finite time interval. We consider two cases: (1) using technology (e.g. point-of-sale systems), the supplier can insure that the discount is applicable to only units resold during the promotion and (2) the discount is applicable to units purchased during the promotion.