2134/26456 Wendy Jiao Wendy Jiao Ju-Liang Zhang Ju-Liang Zhang Hong Yan Hong Yan The stochastic lot-sizing problem with quantity discounts Loughborough University 2017 Inventory Stochastic lot-sizing problem All-unit quantity discounts Polynomial time algorith Business and Management not elsewhere classified 2017-09-12 10:06:14 Journal contribution https://repository.lboro.ac.uk/articles/journal_contribution/The_stochastic_lot-sizing_problem_with_quantity_discounts/9503441 This paper addresses the stochastic lot-sizing problem with quantity discounts. In particular, we examine the uncapacitated finite-period economic lot-sizing problem in which the parameters in each period are random and discrete. When an order is placed, a fixed cost is incurred and an all-unit quantity discount is awarded based on the quantity ordered. The lead time is zero and the order is delivered immediately. First we study the case with overstocks by which the excess inventory incurs a holding cost. The objective in this case is to minimize the expected total cost including ordering and holding costs. The stochastic dynamics is modeled with a scenario tree. We characterize properties of the optimal policy and propose a polynomial time algorithm with complexity O ( n 3 ) for single discount level, where n is the number of nodes in the scenario tree. We extend the results to cases allowing stockout and multi-discount levels. Numerical experiments are conducted to evaluate the performance of the algorithm and to gain the man- agement insights.