Two-Stage Optimization Problems with Multivariate Stochastic Order Constraints

• 成果类型: Article
• 署名作者: Dentcheva, Darinka; Wolfhagen, Eli
• 署名单位: Stevens Institute of Technology
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2015.0713
• 发表日期: 2016
• 页码: 1-22
• 关键词: dominance constraints; Duality; PROGRAMS

摘要

We propose a two-stage risk-averse stochastic optimization problem with a stochastic-order constraint on a vector-valued function of the second-stage decisions. This model is motivated by a multiobjective second-stage problem. We formulate optimality conditions for the problem and analyse the Lagrangian relaxation of the order constraint. We propose two decomposition methods to solve the problems and prove their convergence. The methods are based on Lagrangian relaxation of the order constraints and on a construction of successive risk-neutral two-stage problems. Additionally, we propose a new combinatorial method for verification of the multivariate order relation, which is a key part of both methods. We analyse a supply chain problem using our model and we apply our methods to solve the optimization problem. Numerical results confirm the efficiency of the proposed methods.