Stochastic choice-based discrete planning is a broad class of decision-making problems characterized by a sequential decision-making process involving a planner and a group of customers. The firm or planner first decides a subset of options to offer to the customers, who, in turn, make selections based on their utilities of those options. This problem has extensive applications in many areas, including assortment planning, product line design, and facility location. A key feature of these problems is that the firm cannot fully observe the customers' utilities or preferences, which results in intrinsic and idiosyncratic uncertainties. Most works in the literature have studied a specific type of uncertainty, resulting in customized decision models that are subsequently tackled using ad-hoc algorithms designed to exploit the specific model structure.
In this paper we propose a modeling framework capable of solving this family of sequential problems that works for a large variety of uncertainties. We then leverage an approximation scheme and develop an adaptable mixed-integer linear programming method. To speed up the solution process, we further develop an efficient decomposition approach. We show that our solution framework can yield solutions proven to be (near-)optimal for a broad class of problems. We illustrate this by applying our approach to three classical application problems: constrained assortment optimization and two facility location problems. Through extensive computational experiments, we demonstrate the performance of our approach in terms of both solution quality and computational speed, and provide computational insights. In particular, when we use our method to solve the constrained assortment optimization problem under the Exponomial choice model, it improves the state-of-the-art.
Towards a Sustainable Power Grid: Stochastic Hierarchical Planning for High Renewable Integration
在雄心勃勃的可再生能源组合标准的推动下，大规模纳入可变能源（如风能和太阳能）预计将给电力系统运行带来前所未有的不确定性。目前采用确定性优化模型的作战计划实践可能不适合具有大量不确定性的未来。为了克服潜在的可靠性和经济挑战，我们提出了一个随机分层规划（SHP）框架。该框架捕捉了前一天、短期和前一小时的时间尺度上的操作，以及随机过程和决策之间的相互作用。与早期的研究不同，在早期的研究中，个体问题的随机优化（例如，机组组合、经济调度）的研究，本文研究了一个集成的\emph{planning under uncertainty}框架，其中随机优化模型被缝合在一个层次设置中，这与电力工业中广泛采用的确定性分层规划方法相平行。我们的实验，基于NREL-118数据集，揭示了在高可再生能源渗透率下，通过过渡到小水电模式，可以预期显著的运营改善。特别是，计算结果表明，显着的改善，可以实现在几个指标，包括系统的可靠性，环境的可持续性和系统的经济性，仅仅通过战略选择，采用新的小水电范例。
