An integer programming approach for linear programs with probabilistic constraints

• 成果类型: Article
• 署名作者: Luedtke, James; Ahmed, Shabbir; Nemhauser, George L.
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; University System of Georgia; Georgia Institute of Technology
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-008-0247-4
• 发表日期: 2010
• 页码: 247-272
• 关键词: discrete-distributions; optimization; simulation; STABILITY; bounds; sets

摘要

Linear programs with joint probabilistic constraints (PCLP) are difficult to solve because the feasible region is not convex. We consider a special case of PCLP in which only the right-hand side is random and this random vector has a finite distribution. We give a mixed-integer programming formulation for this special case and study the relaxation corresponding to a single row of the probabilistic constraint. We obtain two strengthened formulations. As a byproduct of this analysis, we obtain new results for the previously studied mixing set, subject to an additional knapsack inequality. We present computational results which indicate that by using our strengthened formulations, instances that are considerably larger than have been considered before can be solved to optimality.