Jose Blanchet, Juan Li, Marvin K. Nakayama (2019) Rare-Event Simulation for Distribution Networks. Operations Research 67(5):1383-1396. https://doi.org/10.1287/opre.2019.1852

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Abstract

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.

Authors
Jose Blanchet, Juan Li, Marvin K Nakayama
Publication date
2019/9
Journal
Operations Research
Volume
67
Issue
5
Pages
1383-1396
Publisher
INFORMS