Quality evaluation of scenario-tree generation methods for solving stochastic programming problems

This paper addresses the generation of scenario trees to solve stochastic programming problems that have a large number of possible values for the random parameters (possibly infinitely many). For the sake of the computational efficiency, the scenario trees must include only a finite (rather small)...

Full description

Saved in:

Bibliographic Details
Published in:	Computational management science Vol. 14; no. 3; pp. 333 - 365
Main Authors:	Keutchayan, Julien, Gendreau, Michel, Saucier, Antoine
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2017 Springer Nature B.V
Subjects:	Business and Management Computing time Couples Decision making Decisions Extrapolation Mathematical programming Operations Research/Decision Theory Optimization Original Paper Probability theory Quality Quality assessment Stochastic programming Trees Decision policy Scenario tree Out-of-sample evaluation Stochastic programming
ISSN:	1619-697X, 1619-6988
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	This paper addresses the generation of scenario trees to solve stochastic programming problems that have a large number of possible values for the random parameters (possibly infinitely many). For the sake of the computational efficiency, the scenario trees must include only a finite (rather small) number of scenarios, therefore, they provide decisions only for some values of the random parameters. To overcome the resulting loss of information, we propose to introduce an extension procedure . It is a systematic approach to interpolate and extrapolate the scenario-tree decisions to obtain a decision policy that can be implemented for any value of the random parameters at little computational cost. To assess the quality of the scenario-tree generation method and the extension procedure (STGM-EP), we introduce three generic quality parameters that focus on the quality of the decisions. We use these quality parameters to develop a framework that will help the decision-maker to select the most suitable STGM-EP for a given stochastic programming problem. We perform numerical experiments on two case studies. The quality parameters are used to compare three scenario-tree generation methods and three extension procedures (hence nine couples STGM-EP). We show that it is possible to single out the best couple in both problems, which provides decisions close to optimality at little computational cost.
AbstractList	This paper addresses the generation of scenario trees to solve stochastic programming problems that have a large number of possible values for the random parameters (possibly infinitely many). For the sake of the computational efficiency, the scenario trees must include only a finite (rather small) number of scenarios, therefore, they provide decisions only for some values of the random parameters. To overcome the resulting loss of information, we propose to introduce an extension procedure. It is a systematic approach to interpolate and extrapolate the scenario-tree decisions to obtain a decision policy that can be implemented for any value of the random parameters at little computational cost. To assess the quality of the scenario-tree generation method and the extension procedure (STGM-EP), we introduce three generic quality parameters that focus on the quality of the decisions. We use these quality parameters to develop a framework that will help the decision-maker to select the most suitable STGM-EP for a given stochastic programming problem. We perform numerical experiments on two case studies. The quality parameters are used to compare three scenario-tree generation methods and three extension procedures (hence nine couples STGM-EP). We show that it is possible to single out the best couple in both problems, which provides decisions close to optimality at little computational cost. This paper addresses the generation of scenario trees to solve stochastic programming problems that have a large number of possible values for the random parameters (possibly infinitely many). For the sake of the computational efficiency, the scenario trees must include only a finite (rather small) number of scenarios, therefore, they provide decisions only for some values of the random parameters. To overcome the resulting loss of information, we propose to introduce an extension procedure . It is a systematic approach to interpolate and extrapolate the scenario-tree decisions to obtain a decision policy that can be implemented for any value of the random parameters at little computational cost. To assess the quality of the scenario-tree generation method and the extension procedure (STGM-EP), we introduce three generic quality parameters that focus on the quality of the decisions. We use these quality parameters to develop a framework that will help the decision-maker to select the most suitable STGM-EP for a given stochastic programming problem. We perform numerical experiments on two case studies. The quality parameters are used to compare three scenario-tree generation methods and three extension procedures (hence nine couples STGM-EP). We show that it is possible to single out the best couple in both problems, which provides decisions close to optimality at little computational cost.
Author	Gendreau, Michel Keutchayan, Julien Saucier, Antoine
Author_xml	– sequence: 1 givenname: Julien orcidid: 0000-0002-9987-7456 surname: Keutchayan fullname: Keutchayan, Julien email: julien.keutchayan@polymtl.ca organization: Department of Mathematics and Industrial Engineering, École Polytechnique de Montréal, Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT) – sequence: 2 givenname: Michel surname: Gendreau fullname: Gendreau, Michel organization: Department of Mathematics and Industrial Engineering, École Polytechnique de Montréal, Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT) – sequence: 3 givenname: Antoine surname: Saucier fullname: Saucier, Antoine organization: Department of Mathematics and Industrial Engineering, École Polytechnique de Montréal
BookMark	eNp9kF1LwzAUhoNMcJv-AO8CXleTNmuSSxl-gSCCgnchX90y2mYm6WD_3syKiKAXIYec8-Q9PDMw6X1vATjH6BIjRK8iRiWjBcL5lJQX5AhMcY15UXPGJt81fTsBsxg3CJEFoWwK1PMgW5f20O5kO8jkfA99A6O2vQzOFylYC1e2t2HsdTatvYmw8QFG3-5cv4Ixeb2WMTkNt8Gvguy6w3OuVWu7eAqOG9lGe_Z1z8Hr7c3L8r54fLp7WF4_FrpiKBXaVqXildGVpKhmyhCONKFcU2MMkljqmhpkakpUY2qkmGKUmIWsGqxUpZpqDi7Gf3Pw-2BjEhs_hD5HCswxoRTxEuUpPE7p4GMMthHb4DoZ9gIjcVApRpUiqxQHlYJkhv5itEufPlKQrv2XLEcy5pR-ZcOPnf6EPgBt7Y1b
CitedBy_id	crossref_primary_10_3390_a16100479 crossref_primary_10_1287_moor_2019_1043 crossref_primary_10_1007_s10287_023_00446_2 crossref_primary_10_1080_00207543_2018_1431415 crossref_primary_10_1007_s10287_019_00348_2 crossref_primary_10_1111_itor_13317
Cites_doi	10.1007/PL00011398 10.1023/A:1021853807313 10.1287/ijoc.1120.0516 10.1007/s10107-005-0597-0 10.1137/S0036142901393942 10.1080/02331931003700756 10.1023/A:1018961525394 10.1287/educ.1090.0065 10.1016/0022-247X(74)90157-7 10.1007/s10107-002-0331-0 10.1016/S0377-2217(00)00261-7 10.1007/s10107-015-0958-2 10.1287/mnsc.47.2.295.9834 10.1007/s10107-004-0557-0 10.1007/s10589-015-9758-0 10.1007/s10589-015-9751-7 10.1515/9781400831050 10.1137/110825054 10.1287/moor.1040.0114 10.1007/s10107-015-0898-x 10.1007/s10107-003-0445-z 10.1287/mnsc.46.9.1214.12231 10.1007/BF01580086 10.1007/978-3-642-55753-8_48 10.1007/BF02592156 10.1007/s10107-007-0197-2 10.1016/S0167-6377(98)00054-6 10.1007/978-3-662-03514-6_11
ContentType	Journal Article
Copyright	Springer-Verlag Berlin Heidelberg 2017 Computational Management Science is a copyright of Springer, 2017.
Copyright_xml	– notice: Springer-Verlag Berlin Heidelberg 2017 – notice: Computational Management Science is a copyright of Springer, 2017.
DBID	AAYXX CITATION 3V. 7SC 7TA 7WY 7WZ 7XB 87Z 8AL 8AO 8FD 8FE 8FG 8FK 8FL 8G5 ABUWG AFKRA ARAPS AZQEC BENPR BEZIV BGLVJ CCPQU DWQXO FRNLG F~G GNUQQ GUQSH HCIFZ JG9 JQ2 K60 K6~ K7- L.- L7M L~C L~D M0C M0N M2O MBDVC P5Z P62 PADUT PHGZM PHGZT PKEHL PQBIZ PQBZA PQEST PQGLB PQQKQ PQUKI PRINS PYYUZ Q9U
DOI	10.1007/s10287-017-0279-4
DatabaseName	CrossRef ProQuest Central (Corporate) Computer and Information Systems Abstracts Materials Business File ABI/INFORM Collection ABI/INFORM Global (PDF only) ProQuest Central (purchase pre-March 2016) ABI/INFORM Global (Alumni Edition) Computing Database (Alumni Edition) ProQuest Pharma Collection Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) ABI/INFORM Collection (Alumni Edition) Research Library (Alumni Edition) ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central Business Premium Collection ProQuest Technology Collection ProQuest One Community College ProQuest Central Korea Business Premium Collection (Alumni) ABI/INFORM Global (Corporate) ProQuest Central Student Research Library Prep SciTech Premium Collection Materials Research Database ProQuest Computer Science Collection ProQuest Business Collection (Alumni Edition) ProQuest Business Collection Computer Science Database ABI/INFORM Professional Advanced Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional ABI/INFORM Global Computing Database Research Library Research Library (Corporate) Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection Research Library China ProQuest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Business ProQuest One Business (Alumni) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China ABI/INFORM Collection China ProQuest Central Basic
DatabaseTitle	CrossRef Materials Research Database ProQuest Business Collection (Alumni Edition) Research Library Prep Computer Science Database ProQuest Central Student ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts SciTech Premium Collection ProQuest Central China ABI/INFORM Complete Materials Business File ProQuest One Applied & Life Sciences Research Library China ProQuest Central (New) Advanced Technologies & Aerospace Collection Business Premium Collection ABI/INFORM Global ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest Business Collection ProQuest One Academic UKI Edition ProQuest One Academic ProQuest One Academic (New) ABI/INFORM Global (Corporate) ProQuest One Business Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) ProQuest Central (Alumni Edition) ProQuest One Community College Research Library (Alumni Edition) ProQuest Pharma Collection ProQuest Central ABI/INFORM Professional Advanced ProQuest Central Korea ProQuest Research Library Advanced Technologies Database with Aerospace ABI/INFORM Complete (Alumni Edition) ProQuest Computing ABI/INFORM Global (Alumni Edition) ProQuest Central Basic ProQuest Computing (Alumni Edition) ABI/INFORM China ProQuest SciTech Collection Computer and Information Systems Abstracts Professional Advanced Technologies & Aerospace Database ProQuest One Business (Alumni) ProQuest Central (Alumni) Business Premium Collection (Alumni)
DatabaseTitleList	Materials Research Database
Database_xml	– sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Business
EISSN	1619-6988
EndPage	365
ExternalDocumentID	10_1007_s10287_017_0279_4
GrantInformation_xml	– fundername: Natural Sciences and Engineering Research Council of Canada grantid: RGPIN-2015-04696; PIN-115965 funderid: http://dx.doi.org/10.13039/501100000038
GroupedDBID	-57 -5G -BR -EM -Y2 -~C .86 .VR 06D 0R~ 0VY 1N0 203 29F 2J2 2JN 2JY 2KG 2LR 2P1 2VQ 2~H 30V 3V. 4.4 406 408 409 40D 40E 5GY 5VS 67Z 6J9 6NX 7WY 8AO 8FE 8FG 8FL 8G5 8TC 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABUWG ABWNU ABXPI ACAOD ACBXY ACDTI ACGFO ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACREN ACSNA ACZOJ ADFRT ADHHG ADHIR ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADYOE ADZKW AEBTG AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFGCZ AFKRA AFLOW AFQWF AFWTZ AFYQB AFZKB AGAYW AGDGC AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMTXH AMXSW AMYLF AMYQR AOCGG ARAPS ARMRJ ASPBG AVWKF AXYYD AYQZM AZFZN AZQEC B-. BA0 BAPOH BDATZ BENPR BEZIV BGLVJ BGNMA BPHCQ BSONS CAG CCPQU COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DWQXO EBLON EBS EIOEI EJD EOH ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRNLG FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNUQQ GNWQR GQ6 GQ7 GQ8 GROUPED_ABI_INFORM_COMPLETE GUQSH GXS H13 HCIFZ HF~ HG5 HG6 HLICF HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ IWAJR IXC IXD IXE IZIGR IZQ I~X I~Z J-C J0Z J9A JBSCW JCJTX JZLTJ K60 K6V K6~ K7- KDC KOV LAS LLZTM M0C M0N M2O M4Y MA- MK~ N2Q NPVJJ NQJWS NU0 O9- O93 O9G O9J OAM P2P P62 P9M PADUT PF0 PQBIZ PQBZA PQQKQ PROAC PT4 Q2X QOS R89 R9I ROL RPX RSV S16 S1Z S27 S3B SAP SBE SDH SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 TSG TSK TSV TUC U2A U5U UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 Z7Z Z81 ZMTXR ~A9 AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFFHD AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA CITATION PHGZM PHGZT PQGLB 7SC 7TA 7XB 8AL 8FD 8FK JG9 JQ2 L.- L7M L~C L~D MBDVC PKEHL PQEST PQUKI PRINS Q9U
ID	FETCH-LOGICAL-c380t-ce32b93dc3a7068bd490c479c7ddd0a1ac67d0d674bfd60b8b874d5a3f1bb3bf3
IEDL.DBID	RSV
ISICitedReferencesCount	7
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000411377900003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	1619-697X
IngestDate	Wed Nov 26 13:52:24 EST 2025 Tue Nov 18 22:24:31 EST 2025 Sat Nov 29 04:06:19 EST 2025 Fri Feb 21 02:40:35 EST 2025
IsPeerReviewed	true
IsScholarly	true
Issue	3
Keywords	Decision policy Scenario tree Out-of-sample evaluation Stochastic programming
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c380t-ce32b93dc3a7068bd490c479c7ddd0a1ac67d0d674bfd60b8b874d5a3f1bb3bf3
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0002-9987-7456
PQID	1914770920
PQPubID	54341
PageCount	33
ParticipantIDs	proquest_journals_1914770920 crossref_primary_10_1007_s10287_017_0279_4 crossref_citationtrail_10_1007_s10287_017_0279_4 springer_journals_10_1007_s10287_017_0279_4
PublicationCentury	2000
PublicationDate	2017-07-01
PublicationDateYYYYMMDD	2017-07-01
PublicationDate_xml	– month: 07 year: 2017 text: 2017-07-01 day: 01
PublicationDecade	2010
PublicationPlace	Berlin/Heidelberg
PublicationPlace_xml	– name: Berlin/Heidelberg – name: Dordrecht
PublicationTitle	Computational management science
PublicationTitleAbbrev	Comput Manag Sci
PublicationYear	2017
Publisher	Springer Berlin Heidelberg Springer Nature B.V
Publisher_xml	– name: Springer Berlin Heidelberg – name: Springer Nature B.V
References	Defourny B, Ernst D, Wehenkel L (2011) Multistage stochastic programming: a scenario tree based approach. In: Sucar LE, Morales EF, Hoey J (eds) Decision theory models for applications in artificial intelligence: concepts and solutions. IGI Global, pp 97–143 KoivuMVariance reduction in sample approximations of stochastic programsMath Program2005103346348510.1007/s10107-004-0557-0 ShapiroARuszczyńskiAShapiroAMonte Carlo sampling methodsHandbooks in operations research and management science: stochastic Programming2003AmsterdamElsevier353425 SchultzRNowakMPNürnbergRRömischWWestphalenMStochastic programming for power production and trading under uncertaintyMathematics key technology for the future2003BerlinSpringer62363610.1007/978-3-642-55753-8_48 BirgeJRLouveauxFIntroduction to stochastic programming1997New YorkSpringer RuszczyńskiAShapiroARuszczyńskiAShapiroAStochastic programming modelsHandbooks in operations research and management science: stochastic Programming2003AmsterdamElsevier164 HilliPPennanenTNumerical study of discretizations of multistage stochastic programsKybernetika2008442185204 DupačováJGröwe-KuskaNRömischWScenario reduction in stochastic programmingMath Program200395349351110.1007/s10107-002-0331-0 HeitschHRömischWScenario tree modeling for multistage stochastic programsMath Program2009118237140610.1007/s10107-007-0197-2 WallaceSWFletenS-ERuszczyńskiAShapiroAStochastic programming models in energyHandbooks in operations research and management science: stochastic Programming2003AmsterdamElsevier637677 Drew SS, Homem-de Mello T (2006) Quasi-Monte Carlo strategies for stochastic optimization. In: Proceedings of the 38th conference on Winter simulation. Winter Simulation Conference, pp 774–782 HøylandKWallaceSWGenerating scenario trees for multistage decision problemsManag Sci200147229530710.1287/mnsc.47.2.295.9834 MakW-KMortonDPWoodRKMonte carlo bounding techniques for determining solution quality in stochastic programsOper Res Lett1999241475610.1016/S0167-6377(98)00054-6 Chen M, Mehrotra S (2008) Epi-convergent scenario generation method for stochastic problems via sparse grid. Stoch Program E-Print Ser 7 SchultzRStochastic programming with integer variablesMath Program200397128530910.1007/s10107-003-0445-z Pennanen T, Koivu M (2002) Integration quadratures in discretization of stochastic programs. Stoch Program E-Print Ser 11 PflugGCPichlerAA distance for multistage stochastic optimization modelsSIAM J Optim201222112310.1137/110825054 Ben-TalAEl GhaouiLNemirovskiARobust optimization2009PrincetonPrinceton University Press10.1515/9781400831050 KüchlerCVigerskeSNumerical evaluation of approximation methods in stochastic programmingOptimization201059340141510.1080/02331931003700756 PflugGCScenario tree generation for multiperiod financial optimization by optimal discretizationMath Program200189225127110.1007/PL00011398 EdirisingheNBound-based approximations in multistage stochastic programming: nonanticipativity aggregationAnn Oper Res19998510312710.1023/A:1018961525394 PowellWBTopalogluHRuszczyńskiAShapiroAStochastic programming in transportation and logisticsHandbooks in operations research and management science: stochastic programming2003AmsterdamElsevier555635 Bayraksan G, Morton DP (2009) Assessing solution quality in stochastic programs via sampling. In: Oskoorouchi MR, Gray P, Greenberg HJ (eds) Tutorials in operations research: Decision technologies and applications. Informs, pp 102 –122 Chiralaksanakul A, Morton DP (2004) Assessing policy quality in multi-stage stochastic programming. Stoch Program E-Print Ser (12) FrauendorferKBarycentric scenario trees in convex multistage stochastic programmingMath Program199675227729310.1007/BF02592156 HanasusantoGAKuhnDWiesemannWA comment on computational complexity of stochastic programming problemsMath Program2016159155756910.1007/s10107-015-0958-2 HøylandKKautMWallaceSWA heuristic for moment-matching scenario generationComput Optim Appl2003242–316918510.1023/A:1021853807313 Yu L-Y, Ji X-D, Wang S-Y (2003) Stochastic programming models in financial optimization: a survey. Adv Model Optim 5(1):1–26 KautMWallaceSWEvaluation of scenario-generation methods for stochastic programmingPac J Optim200732257271 PflugGCPichlerADynamic generation of scenario treesComput Optim Appl201562364166810.1007/s10589-015-9758-0 Proulx S (2014) Génération de scénarios par quantification optimale en dimension élevée. Master’s thesis, École Polytechnique de Montréal DyerMStougieLComputational complexity of stochastic programming problemsMath Program2006106342343210.1007/s10107-005-0597-0 L’EcuyerPLemieuxCVariance reduction via lattice rulesManag Sci20004691214123510.1287/mnsc.46.9.1214.12231 LeöveyHRömischWQuasi-Monte Carlo methods for linear two-stage stochastic programming problemsMath Program2015151131534510.1007/s10107-015-0898-x ChenMMehrotraSPappDScenario generation for stochastic optimization problems via the sparse grid methodComput Optim Appl201562366969210.1007/s10589-015-9751-7 Louveaux F (1998) An introduction to stochastic transportation models. In: Labbé M, Laporte G, Tanczos K, Toint P (eds) Operations research and decision aid methodologies in traffic and transportation management. Springer, Berlin, pp 244 –263 ShapiroAHomem-de MelloTA simulation-based approach to two-stage stochastic programming with recourseMath Program199881330132510.1007/BF01580086 KouwenbergRScenario generation and stochastic programming models for asset liability managementEur J Oper Res2001134227929210.1016/S0377-2217(00)00261-7 PennanenTEpi-convergent discretizations of multistage stochastic programsMath Oper Res200530124525610.1287/moor.1040.0114 SloanIHKuoFYJoeSConstructing randomly shifted lattice rules in weighted sobolev spacesSIAM J Numer Anal20024051650166510.1137/S0036142901393942 DefournyBErnstDWehenkelLScenario trees and policy selection for multistage stochastic programming using machine learningINFORMS J Comput201325348850110.1287/ijoc.1120.0516 RockafellarRTWetsRJContinuous versus measurable recourse in n-stage stochastic programmingJ Math Anal Appl197448383685910.1016/0022-247X(74)90157-7 JR Birge (279_CR3) 1997 J Dupačová (279_CR10) 2003; 95 GA Hanasusanto (279_CR14) 2016; 159 R Kouwenberg (279_CR21) 2001; 134 A Ruszczyński (279_CR35) 2003 A Shapiro (279_CR39) 1998; 81 M Dyer (279_CR11) 2006; 106 H Heitsch (279_CR15) 2009; 118 279_CR33 T Pennanen (279_CR27) 2005; 30 279_CR28 A Ben-Tal (279_CR2) 2009 B Defourny (279_CR8) 2013; 25 GC Pflug (279_CR31) 2015; 62 RT Rockafellar (279_CR34) 1974; 48 A Shapiro (279_CR38) 2003 279_CR1 N Edirisinghe (279_CR12) 1999; 85 W-K Mak (279_CR26) 1999; 24 279_CR4 279_CR7 279_CR6 279_CR9 R Schultz (279_CR36) 2003; 97 M Koivu (279_CR20) 2005; 103 GC Pflug (279_CR30) 2012; 22 WB Powell (279_CR32) 2003 C Küchler (279_CR22) 2010; 59 H Leövey (279_CR24) 2015; 151 SW Wallace (279_CR41) 2003 P L’Ecuyer (279_CR23) 2000; 46 IH Sloan (279_CR40) 2002; 40 279_CR42 K Høyland (279_CR17) 2003; 24 K Frauendorfer (279_CR13) 1996; 75 279_CR25 K Høyland (279_CR18) 2001; 47 R Schultz (279_CR37) 2003 M Chen (279_CR5) 2015; 62 M Kaut (279_CR19) 2007; 3 P Hilli (279_CR16) 2008; 44 GC Pflug (279_CR29) 2001; 89
References_xml	– reference: SloanIHKuoFYJoeSConstructing randomly shifted lattice rules in weighted sobolev spacesSIAM J Numer Anal20024051650166510.1137/S0036142901393942 – reference: Defourny B, Ernst D, Wehenkel L (2011) Multistage stochastic programming: a scenario tree based approach. In: Sucar LE, Morales EF, Hoey J (eds) Decision theory models for applications in artificial intelligence: concepts and solutions. IGI Global, pp 97–143 – reference: EdirisingheNBound-based approximations in multistage stochastic programming: nonanticipativity aggregationAnn Oper Res19998510312710.1023/A:1018961525394 – reference: ChenMMehrotraSPappDScenario generation for stochastic optimization problems via the sparse grid methodComput Optim Appl201562366969210.1007/s10589-015-9751-7 – reference: LeöveyHRömischWQuasi-Monte Carlo methods for linear two-stage stochastic programming problemsMath Program2015151131534510.1007/s10107-015-0898-x – reference: Yu L-Y, Ji X-D, Wang S-Y (2003) Stochastic programming models in financial optimization: a survey. Adv Model Optim 5(1):1–26 – reference: HanasusantoGAKuhnDWiesemannWA comment on computational complexity of stochastic programming problemsMath Program2016159155756910.1007/s10107-015-0958-2 – reference: SchultzRStochastic programming with integer variablesMath Program200397128530910.1007/s10107-003-0445-z – reference: ShapiroAHomem-de MelloTA simulation-based approach to two-stage stochastic programming with recourseMath Program199881330132510.1007/BF01580086 – reference: HøylandKWallaceSWGenerating scenario trees for multistage decision problemsManag Sci200147229530710.1287/mnsc.47.2.295.9834 – reference: Bayraksan G, Morton DP (2009) Assessing solution quality in stochastic programs via sampling. In: Oskoorouchi MR, Gray P, Greenberg HJ (eds) Tutorials in operations research: Decision technologies and applications. Informs, pp 102 –122 – reference: Proulx S (2014) Génération de scénarios par quantification optimale en dimension élevée. Master’s thesis, École Polytechnique de Montréal – reference: L’EcuyerPLemieuxCVariance reduction via lattice rulesManag Sci20004691214123510.1287/mnsc.46.9.1214.12231 – reference: PflugGCPichlerAA distance for multistage stochastic optimization modelsSIAM J Optim201222112310.1137/110825054 – reference: PowellWBTopalogluHRuszczyńskiAShapiroAStochastic programming in transportation and logisticsHandbooks in operations research and management science: stochastic programming2003AmsterdamElsevier555635 – reference: WallaceSWFletenS-ERuszczyńskiAShapiroAStochastic programming models in energyHandbooks in operations research and management science: stochastic Programming2003AmsterdamElsevier637677 – reference: KautMWallaceSWEvaluation of scenario-generation methods for stochastic programmingPac J Optim200732257271 – reference: Ben-TalAEl GhaouiLNemirovskiARobust optimization2009PrincetonPrinceton University Press10.1515/9781400831050 – reference: RockafellarRTWetsRJContinuous versus measurable recourse in n-stage stochastic programmingJ Math Anal Appl197448383685910.1016/0022-247X(74)90157-7 – reference: PennanenTEpi-convergent discretizations of multistage stochastic programsMath Oper Res200530124525610.1287/moor.1040.0114 – reference: DefournyBErnstDWehenkelLScenario trees and policy selection for multistage stochastic programming using machine learningINFORMS J Comput201325348850110.1287/ijoc.1120.0516 – reference: FrauendorferKBarycentric scenario trees in convex multistage stochastic programmingMath Program199675227729310.1007/BF02592156 – reference: KouwenbergRScenario generation and stochastic programming models for asset liability managementEur J Oper Res2001134227929210.1016/S0377-2217(00)00261-7 – reference: DupačováJGröwe-KuskaNRömischWScenario reduction in stochastic programmingMath Program200395349351110.1007/s10107-002-0331-0 – reference: HøylandKKautMWallaceSWA heuristic for moment-matching scenario generationComput Optim Appl2003242–316918510.1023/A:1021853807313 – reference: SchultzRNowakMPNürnbergRRömischWWestphalenMStochastic programming for power production and trading under uncertaintyMathematics key technology for the future2003BerlinSpringer62363610.1007/978-3-642-55753-8_48 – reference: Chiralaksanakul A, Morton DP (2004) Assessing policy quality in multi-stage stochastic programming. Stoch Program E-Print Ser (12) – reference: BirgeJRLouveauxFIntroduction to stochastic programming1997New YorkSpringer – reference: HeitschHRömischWScenario tree modeling for multistage stochastic programsMath Program2009118237140610.1007/s10107-007-0197-2 – reference: PflugGCScenario tree generation for multiperiod financial optimization by optimal discretizationMath Program200189225127110.1007/PL00011398 – reference: KoivuMVariance reduction in sample approximations of stochastic programsMath Program2005103346348510.1007/s10107-004-0557-0 – reference: Drew SS, Homem-de Mello T (2006) Quasi-Monte Carlo strategies for stochastic optimization. In: Proceedings of the 38th conference on Winter simulation. Winter Simulation Conference, pp 774–782 – reference: MakW-KMortonDPWoodRKMonte carlo bounding techniques for determining solution quality in stochastic programsOper Res Lett1999241475610.1016/S0167-6377(98)00054-6 – reference: HilliPPennanenTNumerical study of discretizations of multistage stochastic programsKybernetika2008442185204 – reference: Pennanen T, Koivu M (2002) Integration quadratures in discretization of stochastic programs. Stoch Program E-Print Ser 11 – reference: DyerMStougieLComputational complexity of stochastic programming problemsMath Program2006106342343210.1007/s10107-005-0597-0 – reference: Chen M, Mehrotra S (2008) Epi-convergent scenario generation method for stochastic problems via sparse grid. Stoch Program E-Print Ser 7 – reference: KüchlerCVigerskeSNumerical evaluation of approximation methods in stochastic programmingOptimization201059340141510.1080/02331931003700756 – reference: Louveaux F (1998) An introduction to stochastic transportation models. In: Labbé M, Laporte G, Tanczos K, Toint P (eds) Operations research and decision aid methodologies in traffic and transportation management. Springer, Berlin, pp 244 –263 – reference: ShapiroARuszczyńskiAShapiroAMonte Carlo sampling methodsHandbooks in operations research and management science: stochastic Programming2003AmsterdamElsevier353425 – reference: PflugGCPichlerADynamic generation of scenario treesComput Optim Appl201562364166810.1007/s10589-015-9758-0 – reference: RuszczyńskiAShapiroARuszczyńskiAShapiroAStochastic programming modelsHandbooks in operations research and management science: stochastic Programming2003AmsterdamElsevier164 – volume: 89 start-page: 251 issue: 2 year: 2001 ident: 279_CR29 publication-title: Math Program doi: 10.1007/PL00011398 – volume: 24 start-page: 169 issue: 2–3 year: 2003 ident: 279_CR17 publication-title: Comput Optim Appl doi: 10.1023/A:1021853807313 – volume: 25 start-page: 488 issue: 3 year: 2013 ident: 279_CR8 publication-title: INFORMS J Comput doi: 10.1287/ijoc.1120.0516 – volume: 106 start-page: 423 issue: 3 year: 2006 ident: 279_CR11 publication-title: Math Program doi: 10.1007/s10107-005-0597-0 – start-page: 555 volume-title: Handbooks in operations research and management science: stochastic programming year: 2003 ident: 279_CR32 – ident: 279_CR6 – volume: 40 start-page: 1650 issue: 5 year: 2002 ident: 279_CR40 publication-title: SIAM J Numer Anal doi: 10.1137/S0036142901393942 – volume: 59 start-page: 401 issue: 3 year: 2010 ident: 279_CR22 publication-title: Optimization doi: 10.1080/02331931003700756 – ident: 279_CR33 – ident: 279_CR4 – volume: 85 start-page: 103 year: 1999 ident: 279_CR12 publication-title: Ann Oper Res doi: 10.1023/A:1018961525394 – ident: 279_CR1 doi: 10.1287/educ.1090.0065 – volume: 48 start-page: 836 issue: 3 year: 1974 ident: 279_CR34 publication-title: J Math Anal Appl doi: 10.1016/0022-247X(74)90157-7 – start-page: 1 volume-title: Handbooks in operations research and management science: stochastic Programming year: 2003 ident: 279_CR35 – volume: 95 start-page: 493 issue: 3 year: 2003 ident: 279_CR10 publication-title: Math Program doi: 10.1007/s10107-002-0331-0 – volume: 134 start-page: 279 issue: 2 year: 2001 ident: 279_CR21 publication-title: Eur J Oper Res doi: 10.1016/S0377-2217(00)00261-7 – volume: 159 start-page: 557 issue: 1 year: 2016 ident: 279_CR14 publication-title: Math Program doi: 10.1007/s10107-015-0958-2 – volume: 47 start-page: 295 issue: 2 year: 2001 ident: 279_CR18 publication-title: Manag Sci doi: 10.1287/mnsc.47.2.295.9834 – volume: 103 start-page: 463 issue: 3 year: 2005 ident: 279_CR20 publication-title: Math Program doi: 10.1007/s10107-004-0557-0 – volume: 62 start-page: 641 issue: 3 year: 2015 ident: 279_CR31 publication-title: Comput Optim Appl doi: 10.1007/s10589-015-9758-0 – start-page: 637 volume-title: Handbooks in operations research and management science: stochastic Programming year: 2003 ident: 279_CR41 – ident: 279_CR42 – volume: 62 start-page: 669 issue: 3 year: 2015 ident: 279_CR5 publication-title: Comput Optim Appl doi: 10.1007/s10589-015-9751-7 – volume-title: Introduction to stochastic programming year: 1997 ident: 279_CR3 – ident: 279_CR9 – volume-title: Robust optimization year: 2009 ident: 279_CR2 doi: 10.1515/9781400831050 – volume: 3 start-page: 257 issue: 2 year: 2007 ident: 279_CR19 publication-title: Pac J Optim – volume: 22 start-page: 1 issue: 1 year: 2012 ident: 279_CR30 publication-title: SIAM J Optim doi: 10.1137/110825054 – ident: 279_CR7 – volume: 30 start-page: 245 issue: 1 year: 2005 ident: 279_CR27 publication-title: Math Oper Res doi: 10.1287/moor.1040.0114 – volume: 151 start-page: 315 issue: 1 year: 2015 ident: 279_CR24 publication-title: Math Program doi: 10.1007/s10107-015-0898-x – volume: 97 start-page: 285 issue: 1 year: 2003 ident: 279_CR36 publication-title: Math Program doi: 10.1007/s10107-003-0445-z – volume: 46 start-page: 1214 issue: 9 year: 2000 ident: 279_CR23 publication-title: Manag Sci doi: 10.1287/mnsc.46.9.1214.12231 – volume: 81 start-page: 301 issue: 3 year: 1998 ident: 279_CR39 publication-title: Math Program doi: 10.1007/BF01580086 – start-page: 623 volume-title: Mathematics key technology for the future year: 2003 ident: 279_CR37 doi: 10.1007/978-3-642-55753-8_48 – volume: 44 start-page: 185 issue: 2 year: 2008 ident: 279_CR16 publication-title: Kybernetika – volume: 75 start-page: 277 issue: 2 year: 1996 ident: 279_CR13 publication-title: Math Program doi: 10.1007/BF02592156 – volume: 118 start-page: 371 issue: 2 year: 2009 ident: 279_CR15 publication-title: Math Program doi: 10.1007/s10107-007-0197-2 – volume: 24 start-page: 47 issue: 1 year: 1999 ident: 279_CR26 publication-title: Oper Res Lett doi: 10.1016/S0167-6377(98)00054-6 – start-page: 353 volume-title: Handbooks in operations research and management science: stochastic Programming year: 2003 ident: 279_CR38 – ident: 279_CR25 doi: 10.1007/978-3-662-03514-6_11 – ident: 279_CR28
SSID	ssj0045478
Score	2.1288157
Snippet	This paper addresses the generation of scenario trees to solve stochastic programming problems that have a large number of possible values for the random...
SourceID	proquest crossref springer
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	333
SubjectTerms	Business and Management Computing time Couples Decision making Decisions Extrapolation Mathematical programming Operations Research/Decision Theory Optimization Original Paper Probability theory Quality Quality assessment Stochastic programming Trees
SummonAdditionalLinks	– databaseName: ABI/INFORM Global dbid: M0C link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8QwEA6-EC--xdVVcvCkBLNNbJKTyOLiQcWDwt5KM0lV0N3VroL_3kybuiq4F69NE0JnMplvZvoNIQdacHAnMpw00IZJr4FZmQATidfSJx0JvmLXv1TX17rfNzcx4FbGssrGJlaG2g0BY-THyEOmFDcJPx29MOwahdnV2EJjlsyjZ4MlfVe821jiiqsKAVcACSw1qt9kNetf5wJWYGijAzALu_x5L02czV_50era6a38d8OrZDk6nPSs1pA1MuMH62SxqXffILZm0figE95vOiwokjwFGD1kmLWm9xU5dTVWt5wuaXB2adBbjEfQ4EDCQ46MzzTWez3j49isptwkd73z2-4Fi40XGAjNxwy8SKwRDkSueKqtk4aDVAaUc47nnRxS5bhLlbSFS7nVVivpTnJRdKwVthBbZG4wHPhtQr0O1lSnqeW5l0WuTWEAQZa1KswH3SK8-ewZRFZybI7xlE34lFFSWZBUhpLKZIscfk0Z1ZQc015uN9LJ4ukss4loWuSoke-34b8W25m-2C5ZSiqFQr1qk7nx65vfIwvwPn4sX_cr1fwEydvrpQ priority: 102 providerName: ProQuest
Title	Quality evaluation of scenario-tree generation methods for solving stochastic programming problems
URI	https://link.springer.com/article/10.1007/s10287-017-0279-4 https://www.proquest.com/docview/1914770920
Volume	14
WOSCitedRecordID	wos000411377900003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVPQU databaseName: ABI/INFORM Collection customDbUrl: eissn: 1619-6988 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0045478 issn: 1619-697X databaseCode: 7WY dateStart: 20031201 isFulltext: true titleUrlDefault: https://www.proquest.com/abicomplete providerName: ProQuest – providerCode: PRVPQU databaseName: ABI/INFORM Global customDbUrl: eissn: 1619-6988 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0045478 issn: 1619-697X databaseCode: M0C dateStart: 20031201 isFulltext: true titleUrlDefault: https://search.proquest.com/abiglobal providerName: ProQuest – providerCode: PRVPQU databaseName: Advanced Technologies & Aerospace Database customDbUrl: eissn: 1619-6988 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0045478 issn: 1619-697X databaseCode: P5Z dateStart: 20031201 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 1619-6988 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0045478 issn: 1619-697X databaseCode: K7- dateStart: 20031201 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1619-6988 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0045478 issn: 1619-697X databaseCode: BENPR dateStart: 20031201 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: Research Library customDbUrl: eissn: 1619-6988 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0045478 issn: 1619-697X databaseCode: M2O dateStart: 20031201 isFulltext: true titleUrlDefault: https://search.proquest.com/pqrl providerName: ProQuest – providerCode: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1619-6988 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0045478 issn: 1619-697X databaseCode: RSV dateStart: 20031201 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1ZSwMxEB60FfHFW6xHyYNPSiDdpJvkUYsiqLV4Vl-WzbEqaCvdKvjvTfawVVTQl8BuDpaZyWRmZ_INwJagRJsmcztNC4mZFRorFmhMAyuYDRpM2wxd_5i326LblZ3iHndaZruXIclMU49ddnPWPfZa1blSbt1JqLrTTvh6DWfnV6X6zQCqvJflPAMcSt4tQ5nfLfH5MBpZmF-CotlZczD3r6-ch9nCtES7uSwswITtLcJ0mdm-BCrHy3hDI4Rv1E-Qh3NyDnMf-_g0ustgqLO-vLh0ipxZi5yE-j8PyJmK-j722M6oyOx68q-LsjTpMlwe7F-0DnFRYgFrKsgQa0sDJanRNOYkFMowSTTjUnNjDIkbsQ65ISbkTCUmJEoowZlpxjRpKEVVQleg0uv37CogK5zeFGGoSGxZEguZSO3dKaW4m69FDUhJ60gX-OO-DMZjNEJO9rSLHO0iT7uI1WD7Y8pzDr7x2-CNkoFRsQ_TyKPXcU5kQGqwUzJsrPunxdb-NHodZoKM457xG1AZDl7sJkzp1-FDOqjDJL--qUN1b7_dOXNPRxy79oS0fBucurbTvK1nQvwOTW7niA
linkProvider	Springer Nature
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3PTxQxFH5BMOJFVCCugvagF0hDd1qm7cEYIxDIrhsPmOxtnL52kER3cWfV8E_5N9o3M3XFBG4cvE6nTdp-71df-z2Al0YK9PsqShoay1UwyJ3KkMssGBWyvsLQsOsP9WhkxmP7YQl-pbcwdK0y6cRGUfsp0hn5HvGQaS1sJt5cfONUNYqyq6mERguLQbj8GUO2-vXJQdzfV1l2dHj67ph3VQU4SiPmHIPMnJUeZalFbpxXVqDSFrX3XpT9EnPthc-1cpXPhTPOaOX3S1n1nZOuknHcO7CipNEkVwPNk-ZvuLEowItBCc-tHqcsavtUL8YmnGxCDATjqly1gwvn9p98bGPmjtb-twV6CA86h5q9bSXgESyFyWO4l-7zr4NrWUIu2YLXnE0rRiRW5ex8yikrz84a8u2mrS2pXbPozLMol3TewqKDjJ9LYrRm3X22r_S5K8ZTb8DHW5nhJixPppPwBFgw0VqYPHeiDKoqja0sUhDpnI790fRApG0usGNdp-IfX4oFXzQho4jIKAgZherBzp8uFy3lyE0_byU0FJ32qYsFFHqwm_D0V_N1gz29ebAXsHp8-n5YDE9Gg2dwP2vATJjeguX57HvYhrv4Y35ez543YsHg023D7Dciy0t3
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1NbxMxEB2VgqpeyrcaKMUHuICsOmtnbR8QQrRRq1ZRDiBFXJb12AuVaNJmQ6v-tf46PLtrAkjtrQeu67Ul2288M57xG4BXRgr0AxUlDY3lKhjkTmXIZRaMCllfYWjY9Y_0aGQmEztegav0FobSKtOZ2BzUfoZ0R75DPGRaC5uJnapLixjvDt-fnnGqIEWR1lROo4XIYbi8iO5b_e5gN-716ywb7n36uM-7CgMcpRELjkFmzkqPstQiN84rK1Bpi9p7L8p-ibn2wudaucrnwhlntPKDUlZ956SrZBz3DtzV0cekdMLx4EvSAg1PFjl70UHhudWTFFFtn-1FP4WTfohOYVyhv3Xi0tD9JzbbqLzh_f95sR7ARmdosw-tZDyElTB9BGspz_8xuJY95JIt-c7ZrGJEblXOj2ecovXsW0PK3bS1pbZrFo18FuWV7mFYNJzxe0lM16zLczuhz12RnvoJfL6VGT6F1elsGjaBBRO1iMlzJ8qgqtLYyiI5l87p2B9ND0Ta8gI7NnYqCvKjWPJIE0qKiJKCUFKoHrz53eW0pSK56eethIyiO5XqYgmLHrxN2Pqj-brBnt082EtYi-gqjg5Gh89hPWtwTfDegtXF_Gd4AffwfHFcz7cbCWHw9bZR9gv-o1Sb
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Quality+evaluation+of+scenario-tree+generation+methods+for+solving+stochastic+programming+problems&rft.jtitle=Computational+management+science&rft.au=Keutchayan%2C+Julien&rft.au=Gendreau%2C+Michel&rft.au=Saucier%2C+Antoine&rft.date=2017-07-01&rft.issn=1619-697X&rft.eissn=1619-6988&rft.volume=14&rft.issue=3&rft.spage=333&rft.epage=365&rft_id=info:doi/10.1007%2Fs10287-017-0279-4&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s10287_017_0279_4
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1619-697X&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1619-697X&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1619-697X&client=summon