The supplier’s problem of designing a quantity discount schedule is much more complicated when she faces customers who vary in size. This article by Associate Professor Rachel Chen and co-author Lawrence W. Robinson from Cornell University considers both all-unit and incremental discount schedules with multiple breakpoints that maximize the supplier’s net savings.

Specifically, the authors 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, they 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.