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.