The stochastic lot-sizing problem with quantity discounts

Wen Jiao, Ju Liang Zhang, Hong Yan

Research output: Journal article publicationReview articleAcademic researchpeer-review

11 Citations (Scopus)


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(n3) 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 management insights.
Original languageEnglish
Pages (from-to)1-10
Number of pages10
JournalComputers and Operations Research
Publication statusPublished - 1 Apr 2017


  • All-unit quantity discounts
  • Inventory
  • Polynomial time algorithm
  • Stochastic lot-sizing problem

ASJC Scopus subject areas

  • General Computer Science
  • Modelling and Simulation
  • Management Science and Operations Research


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