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

Julien Keutchayan (), Michel Gendreau and Antoine Saucier
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Julien Keutchayan: École Polytechnique de Montréal
Michel Gendreau: École Polytechnique de Montréal
Antoine Saucier: École Polytechnique de Montréal

Computational Management Science, 2017, vol. 14, issue 3, No 3, 333-365

Abstract: 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.

Keywords: Stochastic programming; Scenario tree; Decision policy; Out-of-sample evaluation (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10287-017-0279-4

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