Convex approximations for two-stage mixed-integer mean-risk recourse models with conditional value-at-risk

• 成果类型: Article
• 署名作者: van Beesten, E. Ruben; Romeijnders, Ward
• 署名单位: University of Groningen
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-019-01428-6
• 发表日期: 2020
• 页码: 473-507
• 关键词: logistics network design; decomposition algorithms; stochastic-dominance; PROGRAMS; uncertainty; cuts

摘要

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.