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Surveys in Operations Research and Management Science SURVEYS IN OPERATIONS RESEARCH AND MANAGEMENT SCIENCE Editors Jan Karel Lenstra, Centrum Wiskunde & Informatica (CWI), Science Park 123, 1098 XG Amsterdam, Netherlands. Michael Trick, Tepper School of Business, Carnegie Mellon University, 5000 Forbes Avenue, PA 15213-3890, Pittsburg, USA. Bert Zwart, Centrum Wiskunde & Informatica (CWI), Science Park 123, 1098 XG Amsterdam, Netherlands. Editorial Board Associate Editors A. Scheller-Wolf CA 94720-1777, S. Ahmed Carnegie Mellon University, Berkeley, USA, Georgia Institute of Technology, Tepper School of Business, e-mail: [email protected] School of Industrial and Systems Engineering, 5000 Forbes Avenue, PA 15213-3890 765 Ferst Drive, GA 30332-0205, Pittsburgh, USA, G. Laporte Atlanta, USA, e-mail: [email protected] HEC Montreal, Management Department, e-mail: [email protected] GERAD, 3000 Ste-Catherine Road, PQ H3T 2A7, M. Skutella Montreal, Canada, B. Ata Technische Universität Berlin (TUB), e-mail: [email protected] Northwestern University, Inst. für Mathematik MA 8-1, Kellogg School of Management, Straße des 17. Juni 136, D-10623, G.L. Nemhauser 2001 Sheridan Rd, IL 60208, Berlin, Germany Georgia Institute of Technology, Evanston, USA, e-mail: [email protected] School of Industrial and Systems Engineering, [email protected] 765 Ferst Drive, GA 30332-0205, S. Zenios Stanford University, Atlanta, USA, S. Burer e-mail: [email protected] University of Iowa, Graduate School of Business, Dept. of Management Sciences, 518 Memorial Way, CA 94305-5015, S. Pollock Tippie College of Business, Stanford, USA, e-mail: [email protected] University of Michigan, S346 Pappajohn Building, IA 52242-1000, Dept. of Industrial and Operations Engineering, Iowa City, USA, Advisory Editors 1205 Beal Avenue, MI 48109-2117, e-mail: [email protected] Ann Arbor, USA, F. Baccelli J. Koenemann Ecole Nationale Superieure (ENS), e-mail: [email protected] University of Waterloo, ENS INRIA, 45 rue d'Ulm,75005, Canada Paris, France, e-mail:[email protected] D.B. Shmoys e-mail: [email protected] Cornell University, C. Barnhart 232 Rhodes Hall, NY 14853, V. Linetsky Massachusetts Institute of Technology, Ithaca, USA, Northwestern University, Dept. of Civil and Environmental Engineering, e-mail: [email protected] Dept. of Industrial Engineering 77 Massachusetts Avenue, MA 02139, and Management Sciences, Cambridge, USA L. Stougie McCormick School of Engineering e-mail: [email protected] VU University, Amsterdam, and Applied Sciences, Netherlands 2145 Sheridan Road, IL 60208, A. Ben-Tal e-mail: [email protected] Evanston, USA, Technion - Israel Institute of Technology, e-mail: [email protected] Fac. of Industrial Engineering and Management, L.N. Van Wassenhove 32000, Haifa, Israel INSEAD, Technology Management, A. Lodi e-mail: [email protected] boulevard de Constance, 77305, University of Bologna, Fontainebleau, France, Italy A. Geoffrion e-mail: [email protected] e-mail: [email protected] University of California at Los Angeles (UCLA), Anderson Graduate School of Management, R. Lougee 110 Westwood Plaza, Box 951481, A. Veinott Stanford University, IBM Watson Research Center, CA 90095-1481, Los Angeles, USA, Dept. of Management Science and Engineering, USA e-mail: [email protected] e-mail: [email protected] 380 Panama Way, CA 94305-4026, L. Green Stanford, USA, B.L. Nelson Columbia University, e-mail: [email protected] Northwestern University, Graduate School of Business, Dept. of Industrial Engineering 718 Uris Hall, NY 10027, P. Whittle and Management Sciences, New York, USA, University of Cambridge, McCormick School of Engineering e-mail: [email protected] Centre for Mathematical Sciences, and Applied Sciences, Dept. of Pure Math. and Math. Stat., 2145 Sheridan Road, IL 60208, D.S. Hochbaum Wilberforce Road, CB3 0WB, Evanston, USA, University of California at Berkeley, Cambridge, UK, e-mail: [email protected] College of Engineering, e-mail: [email protected] Advertising Information: If you are interested in advertising or other commercial opportunities please e-mail commercialsales@elsevier .com and your enquiry will be passed to the correct person who will respond to you within 48 hours. Publication information: Surveys in Operations Research and Management Science (ISSN 1876-7354). For 2012, volume 17 is scheduled for publication. Subscription prices are available upon request from the Publisher or from the Elsevier Customer Service Department nearest you or from this journal's website (http://www.elsevier.com/locate/sorms). Further information is available on this journal and other Elsevier products through Elsevier's website: (http://www.elsevier.com). Subscriptions are accepted on a prepaid basis only and are entered on a calendar year basis. Issues are sent by standard mail (surface within Europe, air delivery outside Europe). Priority rates are available upon request. Claims for missing issues should be made within six months of the date of dispatch. Orders, claims, and journal enquiries: Please contact the Elsevier Customer Service Department nearest you: St. Louis: Elsevier Customer Service Department, 3251 Riverport Lane, Maryland Heights, MO 63043, USA; phone: (877) 8397126 [toll free within the USA]; (+1) (314) 4478878 [outside the USA]; fax: (+1) (314) 4478077; e-mail: [email protected] Oxford: Elsevier Customer Service Department, The Boulevard, Langford Lane, Kidlington, OX5 1GB, UK; phone: (+44) (1865) 843434; fax: (+44) (1865) 843970; e-mail: [email protected] Tokyo: Elsevier Customer Service Department, 4F Higashi-Azabu, 1-Chome Bldg, 1-9-15 Higashi-Azabu, Minato-ku, Tokyo 106-0044, Japan; phone: (+81) (3) 5561 5037; fax: (+81) (3) 5561 5047; e-mail: [email protected] Singapore: Elsevier Customer Service Department, 3 Killiney Road, #08-01 Winsland House I, Singapore 239519; phone: (+65) 6349 0222; fax: (+65) 6733 1510; e-mail: [email protected] Surveys in Operations Research and Management Science 17 (2012) 69–84 Contents lists available at SciVerse ScienceDirect Surveys in Operations Research and Management Science journal homepage: www.elsevier.com/locate/sorms Review Copula-based multivariate input modeling Bahar Biller a,∗, Canan Gunes Corlu b a Tepper School of Business, Carnegie Mellon University, United States b Department of Industrial Engineering, Bilkent University, Turkey article info a b s t r a c t Article history: In this survey, we review the copula-based input models that are well suited to provide multivariate Received 7 April 2010 input-modeling support for stochastic simulations with dependent inputs. Specifically, we consider the Received in revised form situation in which the dependence between pairs of simulation input random variables is measured 13 February 2012 by tail dependence (i.e., the amount of dependence in the tails of a bivariate distribution) and review Accepted 3 April 2012 the techniques to construct copula-based input models representing positive tail dependencies. We complement the review with the parameter estimation from multivariate input data and the random- vector generation from the estimated input model with the purpose of driving the simulation. ' 2012 Elsevier Ltd. All rights reserved. Contents 1. Introduction........................................................................................................................................................................................................................ 69 2. Two measures of dependence: correlation and tail dependence ................................................................................................................................... 70 2.1. Correlation.............................................................................................................................................................................................................. 70 2.2. Tail dependence..................................................................................................................................................................................................... 71 3. Copula-based input modeling........................................................................................................................................................................................... 72 3.1. Fundamentals of copula theory ............................................................................................................................................................................ 73 3.2. Bivariate copula models ........................................................................................................................................................................................ 74 3.2.1. Elliptically symmetric copulas............................................................................................................................................................... 74 3.2.2. Archimedean copulas ............................................................................................................................................................................. 75 3.2.3. Max-infinitely divisible copulas ............................................................................................................................................................ 75 3.3.
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