Convex approximations for two-stage mixed-integer mean-risk recourse models with conditional value-at-risk
| Autor: | Ward Romeijnders, E. Ruben van Beesten |
|---|---|
| Přispěvatelé: | Research programme OPERA |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Mean-risk models
0209 industrial biotechnology General Mathematics 0211 other engineering and technologies Stochastic dominance Stochastic programming UNCERTAINTY 02 engineering and technology DECOMPOSITION ALGORITHMS Expected value CUTS STOCHASTIC-DOMINANCE 020901 industrial engineering & automation Integer PROGRAMS Applied mathematics Convex approximations Mathematics 021103 operations research Risk measure Regular polygon Expected shortfall Mixed-integer recourse Unimodular matrix LOGISTICS NETWORK DESIGN Software Conditional value-at-risk |
| Zdroj: | Mathematical Programming, 181(2), 473-507. SPRINGER HEIDELBERG |
| ISSN: | 0025-5610 |
| Popis: | In traditional two-stage mixed-integer recourse models, the expected value of the total costs is minimized. In order to address risk-averse attitudes of decision makers, we consider a weighted mean-risk objective instead. Conditional value-at-risk is used as our risk measure. Integrality conditions on decision variables make the model non-convex and hence, hard to solve. To tackle this problem, we derive convex approximation models and corresponding error bounds, that depend on the total variations of the density functions of the random right-hand side variables in the model. We show that the error bounds converge to zero if these total variations go to zero. In addition, for the special cases of totally unimodular and simple integer recourse models we derive sharper error bounds. |
| Databáze: | OpenAIRE |
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