Optimal capacity design under $$k$$ k -out-of- $$n$$ n and consecutive $$k$$ k -out-of- $$n$$ n type probabilistic constraints

Merve Unuvar (), Eren Ozguven () and András Prékopa ()

Annals of Operations Research, 2015, vol. 226, issue 1, 643-657

Abstract: We formulate and solve probabilistic constrained stochastic programming problems, where we prescribe lower and upper bounds for $$k$$ k -out-of- $$n$$ n and consecutive- $$k$$ k -out-of- $$n$$ n reliabilities in the form of probabilistic constraints. Problems of this kind arise in many practical situations where stockout in a number of consecutive or a certain fraction of all periods causes irreparable damage. Examples are determination of reservoir capacities used for irrigation or capital reserves of banks. The optimal solution is typically obtained by the solution of a“reliability equation” involving discrete or continuous random variables. The reliability here is approximated by the use of binomial Boolean probability bounds. For $$k$$ k -out-of- $$n$$ n reliability, the properties of Gamma distribution are used to approximate the reliability equation. For the consecutive $$k$$ k -out-of- $$n$$ n case, Binomial probability bounds ( $$S_1, S_2, S_3$$ S 1 , S 2 , S 3 sharp lower bounds, Hunter’s upper bound and Cherry tree upper bound) are used to create lower and upper bounds for the reliability constraint and therefore to solve the reliability equation. A bi-section algorithm is finally applied to determine the optimal capacity level. Copyright Springer Science+Business Media New York 2015

Keywords: Probabilistic modeling; Optimization; Bounding; Bi-section algorithm (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1007/s10479-014-1712-5 (text/html)
Access to full text is restricted to subscribers.

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:226:y:2015:i:1:p:643-657:10.1007/s10479-014-1712-5

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

DOI: 10.1007/s10479-014-1712-5

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 ().