On Finite Adaptability in Two-Stage Distributionally Robust Optimization
研究两阶段分布鲁棒优化中如何通过“平移象限”划分不确定性集合，构造可解释且易实施的有限适应性策略，并给出性能边界和数值验证。
The paper by Han, Bandi, and Nohadani on “On Finite Adaptability in Two-Stage Distributionally Robust Optimization” studies finite adaptability with the goal to construct interpretable and easily implementable policies in the context of two-stage distributionally robust optimization problems. To achieve this, the set of uncertainty realizations needs to be partitioned. The authors show that an optimal partitioning can be accomplished via “translated orthants.” They then propose a nondecreasing orthant partitioning and binary approximation to obtain the corresponding “orthant-based policies” from a mixed-integer optimization problem of a moderate size. For these policies, they provide provable performance bounds, generalizing the existing bounds in the literature. For more general settings, they also propose optimization formulations to obtain posterior lower bounds that can serve to evaluate performance. Two numerical experiments support these findings. A joint inventory-routing problem highlights the practical applicability for large-sized instances with mixed-integer recourse. A case study from a pharmacy retailer demonstrates that the orthant-based policies are less sensitive to cost parameters than optimal solutions, enabling these policies to outperform comparable methods when the realized cost ratio deviates from its nominal value.