Algorithm to solve a chanceconstrained network capacity design problem with stochastic demands and finite support
Here, we consider the problem of determining the capacity to assign to each arc in a given network, subject to uncertainty in the supply and/or demand of each node. This design problem underlies many realworld applications, such as the design of power transmission and telecommunications networks. We first consider the case where a set of supply/demand scenarios are provided, and we must determine the minimumcost set of arc capacities such that a feasible flow exists for each scenario. We briefly review existing theoretical approaches to solving this problem and explore implementation strategies to reduce run times. With this as a foundation, our primary focus is on a chanceconstrained version of the problem in which α% of the scenarios must be feasible under the chosen capacity, where α is a userdefined parameter and the specific scenarios to be satisfied are not predetermined. We describe an algorithm which utilizes a separation routine for identifying violated cutsets which can solve the problem to optimality, and we present computational results. We also present a novel greedy algorithm, our primary contribution, which can be used to solve for a high quality heuristic solution. We present computational analysis to evaluate the performance of our proposed approaches.
 Authors:

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 General Motors, Warren, MI (United States)
 Sandia National Lab. (SNLCA), Livermore, CA (United States)
 Univ. of Michigan, Ann Arbor, MI (United States)
 Publication Date:
 Report Number(s):
 SAND20169223J
Journal ID: ISSN 0894069X; 647498
 Grant/Contract Number:
 AC0494AL85000
 Type:
 Accepted Manuscript
 Journal Name:
 Naval Research Logistics
 Additional Journal Information:
 Journal Volume: 63; Journal Issue: 3; Journal ID: ISSN 0894069X
 Publisher:
 Office of Naval Research  Wiley
 Research Org:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org:
 USDOE National Nuclear Security Administration (NNSA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING
 OSTI Identifier:
 1326636
Schumacher, Kathryn M., Chen, Richard LiYang, Cohn, Amy E. M., and Castaing, Jeremy. Algorithm to solve a chanceconstrained network capacity design problem with stochastic demands and finite support. United States: N. p.,
Web. doi:10.1002/nav.21685.
Schumacher, Kathryn M., Chen, Richard LiYang, Cohn, Amy E. M., & Castaing, Jeremy. Algorithm to solve a chanceconstrained network capacity design problem with stochastic demands and finite support. United States. doi:10.1002/nav.21685.
Schumacher, Kathryn M., Chen, Richard LiYang, Cohn, Amy E. M., and Castaing, Jeremy. 2016.
"Algorithm to solve a chanceconstrained network capacity design problem with stochastic demands and finite support". United States.
doi:10.1002/nav.21685. https://www.osti.gov/servlets/purl/1326636.
@article{osti_1326636,
title = {Algorithm to solve a chanceconstrained network capacity design problem with stochastic demands and finite support},
author = {Schumacher, Kathryn M. and Chen, Richard LiYang and Cohn, Amy E. M. and Castaing, Jeremy},
abstractNote = {Here, we consider the problem of determining the capacity to assign to each arc in a given network, subject to uncertainty in the supply and/or demand of each node. This design problem underlies many realworld applications, such as the design of power transmission and telecommunications networks. We first consider the case where a set of supply/demand scenarios are provided, and we must determine the minimumcost set of arc capacities such that a feasible flow exists for each scenario. We briefly review existing theoretical approaches to solving this problem and explore implementation strategies to reduce run times. With this as a foundation, our primary focus is on a chanceconstrained version of the problem in which α% of the scenarios must be feasible under the chosen capacity, where α is a userdefined parameter and the specific scenarios to be satisfied are not predetermined. We describe an algorithm which utilizes a separation routine for identifying violated cutsets which can solve the problem to optimality, and we present computational results. We also present a novel greedy algorithm, our primary contribution, which can be used to solve for a high quality heuristic solution. We present computational analysis to evaluate the performance of our proposed approaches.},
doi = {10.1002/nav.21685},
journal = {Naval Research Logistics},
number = 3,
volume = 63,
place = {United States},
year = {2016},
month = {4}
}