Quantity discount and handling-charge reduction schemes for a manufacturer supplying numerous heterogeneous retailers

A "manufacturer" supplies a "staple" product to a large number of "retailers" having very different sales volumes. Many models have considered how the "manufacturer" should design a quantity-discount (QD) scheme to induce the retailers to order in larger batch sizes. Our models differ from most existing ones in three aspects. First, we consider situations with a much larger number of retailers. Second, our manufacturer does not need to coordinate her replenishment cycles with those of the retailers. Third, besides "QD" schemes, we also consider "handling-charge reduction" ("HCR") schemes (i.e., a retailer pays a lower handling charge if his order is sufficiently large). We develop models and solution procedures for designing QD and HCR schemes that maximize the manufacturer's expected gain. We consider schemes with one as well as two "price breaks" (i.e., order size(s) needed to qualify for a QD or HCR). Examples of noteworthy characteristics revealed by our analytical and numerical analyses are (i) an optimal QD scheme will have a high enough price break such that extremely few retailers will be big enough to get a "free" discount and (ii) an optimal HCR scheme produces practically the same magnitude of expected total gains as an optimal QD scheme.