Dynamic lot sizing with all-units discount and resales

We consider a single-product dynamic lot-sizing model with an all-units quantity discount pricing scheme available to the buyer, where the discount price breakpoints are stationary. To capture the real-life behavior of a typical buyer who often takes advantage of quantity discounts through purchasing in excess of the anticipated demand, our model allows the buyer to resell or dispose of any leftover inventory that he/she does not need. We show that the general problem with an arbitrary number of discount price breakpoints is NP-hard. We then develop a polynomial algorithm for the problem with an O(T m+3) running time when the number of price breakpoints, m, is fixed, where T is the number of time periods in the planning horizon. We further develop an O(T 2) algorithm for the special case with a single price breakpoint.