A joint chance-constrained programming approach for the single-item capacitated lot-sizing problem with stochastic demand
Céline Gicquel () and
Jianqiang Cheng
Additional contact information
Céline Gicquel: Université Paris Sud
Jianqiang Cheng: University of Arizona
Annals of Operations Research, 2018, vol. 264, issue 1, No 5, 123-155
Abstract:
Abstract We study the single-item single-resource capacitated lot-sizing problem with stochastic demand. We propose to formulate this stochastic optimization problem as a joint chance-constrained program in which the probability that an inventory shortage occurs during the planning horizon is limited to a maximum acceptable risk level. We investigate the development of a new approximate solution method which can be seen as an extension of the previously published sample approximation approach. The proposed method relies on a Monte Carlo sampling of the random variables representing the demand in all planning periods except the first one. Provided there is no dependence between the demand in the first period and the demand in the later periods, this partial sampling results in the formulation of a chance-constrained program featuring a series of joint chance constraints. Each of these constraints involves a single random variable and defines a feasible set for which a conservative convex approximation can be quite easily built. Contrary to the sample approximation approach, the partial sample approximation leads to the formulation of a deterministic mixed-integer linear problem having the same number of binary variables as the original stochastic problem. Our computational results show that the proposed method is more efficient at finding feasible solutions of the original stochastic problem than the sample approximation method and that these solutions are less costly than the ones provided by the Bonferroni conservative approximation. Moreover, the computation time is significantly shorter than the one needed for the sample approximation method.
Keywords: Stochastic lot-sizing; Chance-constrained programming; Joint probabilistic constraint; Sample approximation approach; Mixed-integer linear programming (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)
Downloads: (external link)
http://link.springer.com/10.1007/s10479-017-2662-5 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:264:y:2018:i:1:d:10.1007_s10479-017-2662-5
Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479
DOI: 10.1007/s10479-017-2662-5
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 ().