A polyhedral study of the static probabilistic lot-sizing problem

Xiao Liu () and Simge Küçükyavuz ()
Additional contact information
Xiao Liu: The Ohio State University
Simge Küçükyavuz: University of Washington

Annals of Operations Research, 2018, vol. 261, issue 1, No 10, 233-254

Abstract: Abstract We study the polyhedral structure of the static probabilistic lot-sizing problem and propose valid inequalities that integrate information from the chance constraint and the binary setup variables. We prove that the proposed inequalities subsume existing inequalities for this problem, and they are facet-defining under certain conditions. In addition, we show that they give the convex hull description of a related stochastic lot-sizing problem. We propose a new formulation that exploits the simple recourse structure, which significantly reduces the number of variables and constraints of the deterministic equivalent program. This reformulation can be applied to general chance-constrained programs with simple recourse. The computational results show that the proposed inequalities and the new formulation are effective for the static probabilistic lot-sizing problems.

Keywords: Chance constraints; Lot sizing; Valid inequalities; Facets; Branch and cut; Simple recourse reformulation (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10479-017-2641-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:261:y:2018:i:1:d:10.1007_s10479-017-2641-x

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-017-2641-x

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().