Two-Stage Optimization Problems with Multivariate Stochastic Order Constraints
提出了一种带有多元随机序约束的两阶段风险规避随机优化模型，用于处理第二阶段决策的向量值函数约束，并设计了两种基于拉格朗日松弛的分解方法，在供应链问题中验证了效率。
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.