Rare-Event Simulation for Distribution Networks

Jose Blanchet (), Juan Li () and Marvin K. Nakayama ()
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Jose Blanchet: Department of Management Science and Engineering, Stanford University, Stanford, California 94305
Juan Li: Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027
Marvin K. Nakayama: Department of Computer Science, New Jersey Institute of Technology, Newark, New Jersey 07102

Operations Research, 2019, vol. 67, issue 5, 1383-1396

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.

Keywords: distribution network; linear program; rare-event simulation; importance sampling; conditional Monte Carlo (search for similar items in EconPapers)
Date: 2019
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