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The stochastic lot-sizing problem with quantity discounts

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posted on 12.09.2017 by Wendy Jiao, Ju-Liang Zhang, Hong Yan
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.

Funding

This work is supported in part by the National Natural Science Foundation of China (grant no. 71390334 ) and supported by the Program for New Century Excellent Talents in University (NCET-13-0660). This work is also supported by the NSFC/RGC Joint Research Scheme (3-RAA7, 7161101015).

History

School

  • Business and Economics

Department

  • Business

Published in

Computers & Operations Research

Volume

80

Pages

1 - 10

Citation

JIAO, W., ZHANG, J-L. and YAN, H., 2017. The stochastic lot-sizing problem with quantity discounts. Computers & Operations Research, 80 pp. 1-10.

Publisher

© Elsevier

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date

14/11/2016

Publication date

2017-11-15

Notes

This paper was published in the journal Computers & Operations Research and the definitive published version is available at https://doi.org/10.1016/j.cor.2016.11.014.

ISSN

0305-0548

Language

en

Exports