edoc-Server der Humboldt-Universität zu Berlin

SPEPS Preprint

 Author(s): Anureet Saxena, Carnegie Mellon UniversityVineet Goyal, Carnegie Mellon UniversityMiguel Lejeune, Carnegie Mellon University Title: MIP Reformulations of the Probabilistic Set Covering Problem Date of Acceptance: 29.05.2007 Submission Date: 08.02.2007 Series Title: Stochastic Programming E-Print Series (SPEPS) Editors: Julie L. Higle; Werner Römisch; Surrajeet Sen Keywords (eng): Probabilistic Programming, Set Covering, Mixed Integer Programming, Cutting Planes in: Mathematical Programnming Metadata export: To export the complete metadata set as Endote or Bibtex format please click to the appropriate link. Endnote   Bibtex

Abstract (eng):
In this paper we address the following probabilistic version (PSC) of the set cover- ing problem: $min{cx | P(Ax ≥ ξ) ≥ p, x_j \in {0, 1}N }$ where A is a 0-1 matrix, ξ is a random 0-1 vector and $p \in (0, 1]$ is the threshold probability level. We formulate (PSC) as a mixed integer non-linear program (MINLP) and linearize the resulting (MINLP) to obtain a MIP reformulation. We introduce the concepts of p-inefficiency and polarity cuts. While the former is aimed at reducing the number of constraints in our model, the later is used as a strengthening device to obtain stronger formulations. A hierarchy of relaxations for (PSC) is introduced, and fundamental relationships between the relaxations are established culminating with a MIP reformulation of (PSC) with no additional integer constrained variables. Simpliﬁcations of the MIP model which result when one of the following conditions hold are brieﬂy discussed: A is a balanced matrix, A has the circular ones property, the components of ξ are pairwise independent, the distribution function of ξ is a stationary distribution or has the so-called disjunctive shattering property. We corroborate our theoretical ﬁndings by an extensive computational experiment on a test-bed consisting of almost 10,000 probabilistic instances. This test-bed was created using deterministic instances from the literature and consists of probabilistic variants of the set-covering model and capacitated versions of facility location, warehouse location and k-median models. Our computational results show that our procedure is orders of magnitude faster than any of the existing approaches to solve (PSC), and in many cases can reduce hours of computing time to fraction of seconds.
Access Statistics: These data concerning access statistics for individual documents have been compiled using the webserver log files aggregated by AWSTATS. They refer to a monthly access count to the full text documents as well as to the entry page.

As for format versions of a document which consist of multiple files (such as HTML) the highest monthly access number to one of the files (chapters) is shown respectivly.

To see the detailled access numbers please move the mouse pointer over the single bars of the digaram.
 Jul11 Sep11 Feb12 Apr12 May12 Jun12 Jul12 Aug12 Sep12 Oct12 Nov12 Dec12 Jan13 Feb13 Mar13 Apr13 May13 Jun13 Jul13 Aug13 Sep13 Oct13 Nov13 Dec13 Jan14 Feb14 Mar14 Apr14 May14 Jun14 Jul14 Aug14 Sep14 Oct14 Nov14 Dec14 Jan15 Feb15 Mar15 Apr15 May15 Jun15 Jul15 Aug15 Sep15 Oct15 Nov15 Dec15 Jan16 Feb16 Mar16 Apr16 May16 Jun16 Jul16 Aug16 Sep16 Oct16 Nov16 Dec16 Jan17 Feb17 Mar17 Apr17
 Monat Jul11 Sep11 Feb12 Apr12 May12 Jun12 Jul12 Aug12 Sep12 Oct12 Nov12 Dec12 Jan13 Feb13 Mar13 Apr13 May13 Jun13 Jul13 Aug13 Sep13 Oct13 Nov13 Dec13 Jan14 Feb14 Apr14 May14 Jul14 Aug14 Sep14 Oct14 Nov14 Dec14 Jan15 Feb15 Mar15 Apr15 May15 Jul15 Aug15 Oct15 Nov15 Dec15 Jan16 Feb16 Mar16 Apr16 Jun16 Jul16 Aug16 Sep16 Oct16 Dec16 Jan17 Feb17 Mar17 Startseite 1 1 1 3 1 2 1 2 2 2 3 1 1 2 2 2 2 2 13 20 27 34 9 8 12 1 2 2 2 2 1 1 4 6 2 4 17 1 4 1 5 1 1 4 3 5 PDF 2 1 2 4 3 1 8 12 19 10 19 7 9 7 4 4 4 10 11 9

Gesamtzahl der Zugriffe seit Jul 2011:

• Startseite – 223 (3.48 pro Monat)
• PDF – 146 (2.39 pro Monat)

Generated at 26.05.2017, 21:05:00