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)...

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Vydáno v:	Computational management science Ročník 14; číslo 3; s. 333 - 365
Hlavní autoři:	Keutchayan, Julien, Gendreau, Michel, Saucier, Antoine
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2017 Springer Nature B.V
Témata:	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
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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
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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
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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. 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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...
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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
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Title	Quality evaluation of scenario-tree generation methods for solving stochastic programming problems
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