Rare-Event Simulation for Distribution Networks

• 成果类型: Article
• 署名作者: Blanchet, Jose; Li, Juan; Nakayama, Marvin K.
• 署名单位: Stanford University; Columbia University; New Jersey Institute of Technology
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2019.1852
• 发表日期: 2019
• 页码: 1383-1396
• 关键词: distribution network; linear program; rare-event simulation; importance sampling; conditional Monte Carlo

摘要

We model optimal allocations in a distribution network as the solution of a linear program (LP) that minimizes the cost of unserved demands across nodes in the network. The constraints in the LP dictate that, after a given node's supply is exhausted, its unserved demand is distributed among neighboring nodes. All nodes do the same, and the resulting solution is the optimal allocation. Assuming that the demands are random (following a jointly Gaussian law), our goal is to study the probability that the optimal cost of unserved demands exceeds a large threshold, which is a rare event. Our contribution is the development of importance sampling and conditional Monte Carlo algorithms for estimating this probability. We establish the asymptotic efficiency of our algorithms and also present numerical results that illustrate strong performance of our procedures.