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Title: Algorithm to solve a chance-constrained 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 real-world 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 minimum-cost 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 chance-constrained version of the problem in which α% of the scenarios must be feasible under the chosen capacity, where α is a user-defined parameter and the specific scenarios to be satisfied are not predetermined. We describe an algorithm which utilizes a separation routine for identifying violated cut-sets 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:
 [1] ;  [2] ;  [3] ;  [3]
  1. General Motors, Warren, MI (United States)
  2. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
  3. Univ. of Michigan, Ann Arbor, MI (United States)
Publication Date:
Report Number(s):
SAND-2016-9223J
Journal ID: ISSN 0894-069X; 647498
Grant/Contract Number:
AC04-94AL85000
Type:
Accepted Manuscript
Journal Name:
Naval Research Logistics
Additional Journal Information:
Journal Volume: 63; Journal Issue: 3; Journal ID: ISSN 0894-069X
Publisher:
Office of Naval Research - Wiley
Research Org:
Sandia National Lab. (SNL-NM), 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 Li-Yang, Cohn, Amy E. M., and Castaing, Jeremy. Algorithm to solve a chance-constrained 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 Li-Yang, Cohn, Amy E. M., & Castaing, Jeremy. Algorithm to solve a chance-constrained network capacity design problem with stochastic demands and finite support. United States. doi:10.1002/nav.21685.
Schumacher, Kathryn M., Chen, Richard Li-Yang, Cohn, Amy E. M., and Castaing, Jeremy. 2016. "Algorithm to solve a chance-constrained 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 chance-constrained network capacity design problem with stochastic demands and finite support},
author = {Schumacher, Kathryn M. and Chen, Richard Li-Yang 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 real-world 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 minimum-cost 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 chance-constrained version of the problem in which α% of the scenarios must be feasible under the chosen capacity, where α is a user-defined parameter and the specific scenarios to be satisfied are not predetermined. We describe an algorithm which utilizes a separation routine for identifying violated cut-sets 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}
}