This work studies the multistage adaptive stochastic mixed integer optimization problem, where the aim is to find adaptive continuous and integer decision policies that optimize the expected objective. While searching for the exact optimal policy is challenging, piecewise decision rule-based solution framework is studied and two types of strategies are compared: uncertainty set partitioning and uncertainty lifting. Adaptive binary and continuous decisions are approximated through piecewise constant and affine decision rule, respectively. The original optimization problem is solved through robust counterpart optimization technique. The proposed methods are applied to an inventory control problem and a chemical process capacity planning problem. Results show that the two methods provide flexible options with the trade-off between solution quality and computational efficiency. The uncertainty set partitioning based method leads to better solution quality and is appropriate to small-scale problems. On the other hand, the lifting method provides significant computational efficiency especially for large problems.

这项工作研究了多阶段自适应随机混合整数优化问题，其目的是找到优化预期目标的自适应连续和整数决策策略。在寻找精确的最优策略时面临挑战，同时研究了基于分段决策规则的解决方案框架，并比较了两种策略：不确定性集划分和不确定性提升。自适应二进制和连续决策分别通过分段常数和仿射决策规则来近似。最初的优化问题是通过鲁棒的对应优化技术解决的。所提出的方法被应用于库存控制问题和化学过程能力计划问题。结果表明，这两种方法在解决方案质量和计算效率之间进行了权衡，从而提供了灵活的选择。基于不确定性集划分的方法可提供更好的解决方案质量，并且适合于小规模的问题。另一方面，提升方法提供了显着的计算效率，尤其是对于大问题。