Optimal multiple-breakpoint quantity discount schedules for customers with heterogeneous demands: all-unit or incremental?

The supplier's problem of designing a quantity discount schedule is much more complicated when she faces customers who vary in size. This article considers both all-unit and incremental discount schedules with multiple breakpoints that maximize the supplier's net savings. Specifically, we assume that the distribution of customers' demand belongs to the general family of Bender's Pareto curves, which generalizes the well-known "80-20" rule from A-B-C inventory analysis. For any number of breakpoints, we prove that the supplier is at least as well off under the optimal incremental discount schedule as she would be under the optimal all-unit discount schedule. Numerical study shows that most of the savings can be captured by a modest number (five) of breakpoints and that the advantage of incremental schedules over all-unit schedules goes to zero as the number of breakpoints grows large.