Discount pricing for a family of items: The supplier's optimal decisions

Consider a family of SKUs for which the supplier will offer a quantity discount, according to the aggregate purchases of the product group. Management of those items is based on the modified periodic policy. From the supplier's point of view, what are the optimal parameters (breakpoint and discount percentage)? For deterministic demand, we discuss the cases in which demand is both constant and price-sensitive. First as a noncooperative Stackelberg game, and then when the two parties make the discount and replenishment decisions jointly, we illustrate the impact of price-sensitivity and joint decision making on the supplier's discount policy.