An Algorithm for Single-Item Capacitated Economic Lot Sizing with Piecewise Linear Production Costs and General Holding Costs
We consider the Capacitated Economic Lot Size Problem with piecewise linear production costs and general holding costs, which is an NP-hard problem but solvable in pseudo-polynomial time. A straightforward dynamic programming approach to this problem results in an O(n 2 c\bar d\bar ) algorithm, where n is the number of periods, and d\bar and c\bar are the average demand and the average production capacity over the n periods, respectively. However, we present a dynamic programming procedure with complexity O(n 2 q\bar d\bar ), where q\bar is the average number of pieces required to represent the production cost functions. In particular, this means that problems in which the production functions consist of a fixed set-up cost plus a linear variable cost are solved in O(n 2 d\bar ) time. Hence, the running time of our algorithm is only linearly dependent on the magnitude of the data. This result also holds if extensions such as backlogging and startup costs are considered. Moreover, computational experiments indicate that the algorithm is capable of solving quite large problem instances within a reasonable amount of time. For example, the average time needed to solve test instances with 96 periods, 8 pieces in every production cost function, and average demand of 100 units is approximately 40 seconds on a SUN SPARC 5 workstation.
Volume (Year): 44 (1998)
Issue (Month): 6 (June)
|Contact details of provider:|| Postal: 7240 Parkway Drive, Suite 300, Hanover, MD 21076 USA|
Web page: http://www.informs.org/
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Gabriel R. Bitran & Horacio H. Yanasse, 1982. "Computational Complexity of the Capacitated Lot Size Problem," Management Science, INFORMS, vol. 28(10), pages 1174-1186, October.
- M. Florian & J. K. Lenstra & A. H. G. Rinnooy Kan, 1980. "Deterministic Production Planning: Algorithms and Complexity," Management Science, INFORMS, vol. 26(7), pages 669-679, July.
When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:44:y:1998:i:6:p:831-838. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mirko Janc)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.