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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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
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Summary: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.
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content type line 14
ISSN:1619-697X
1619-6988
DOI:10.1007/s10287-017-0279-4