具有内生需求学习的二阶段随机设施选址问题

中文摘要 AI 辅助

在设施选址问题中，规划者可以通过收集数据来降低需求不确定性，但这些行动成本高昂。本文探讨规划者应如何联合决策在何处开设设施以及投资于需求学习（该学习伴随成本）。挑战在于，学习会改变未来随机成本的评估方式，从而形成一个在选址决策中既内生又非线性的模型。我们将此问题建模在二阶段随机框架内，其中选址和学习决策均须在当下（here-and-now）做出。在若干温和假设下，我们获得了闭式重构，这进一步支持了对学习决策对模型参数敏感性的理论分析，以及设计了在更新选址和学习决策之间交替进行的收敛求解算法。在基准实例上的数值实验表明，当初始需求不确定性高、学习有效且学习成本低时，学习的价值最大。此外，所提出的求解算法比穷举搜索和标准商业非线性求解器更快地找到高质量解。这些发现表明，信息获取决策可以直接纳入战略性设施规划中，帮助决策者将有限的学习资源投向需求信息价值最大的地方。

英文摘要

In facility location problems, planners can reduce demand uncertainty by collecting data, but these actions are costly. In this paper, we ask how a planner should jointly decide where to open facilities and invest in demand learning, which comes with a cost. The challenge is that learning changes how future random costs should be evaluated, creating a model that is both endogenous and nonlinear in location decisions. We model this problem within a two-stage stochastic framework, where both location and learning decisions have to be made here-and-now. Under some mild assumptions, we obtain a closed-form reformulation, which further enables a theoretical analysis of the sensitivity of learning decisions to model parameters and design of convergent solution algorithms that alternate between updating location and learning decisions. Numerical experiments on benchmark instances show that learning is most valuable when initial demand uncertainty is high, learning is effective, and learning costs are low. Moreover, the proposed solution algorithms find high-quality solutions much faster than exhaustive search and a standard commercial nonlinear solver. These findings show how information-acquisition decisions can be built directly into strategic facility planning. They help decision makers target limited learning resources where better demand information has the greatest value.

发表机构

• Clemson University（克莱姆森大学）

机构由 AI 辅助整理，请以论文原文为准。