Algorithm to solve a chance-constrained network capacity design problem with stochastic demands and finite support
Abstract
Abstract 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 proposedmore »
- Authors:
-
- General Motors, Warren, MI (United States)
- Sandia National Lab. (SNL-CA), Livermore, CA (United States)
- Univ. of Michigan, Ann Arbor, MI (United States)
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1326636
- Alternate Identifier(s):
- OSTI ID: 1786508
- Report Number(s):
- SAND-2016-9223J
Journal ID: ISSN 0894-069X; 647498
- Grant/Contract Number:
- AC04-94AL85000
- Resource 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
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING
Citation Formats
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., 2016.
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. https://doi.org/10.1002/nav.21685
Schumacher, Kathryn M., Chen, Richard Li-Yang, Cohn, Amy E. M., and Castaing, Jeremy. Fri .
"Algorithm to solve a chance-constrained network capacity design problem with stochastic demands and finite support". United States. https://doi.org/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 = {Abstract 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. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 236–246, 2016},
doi = {10.1002/nav.21685},
journal = {Naval Research Logistics},
number = 3,
volume = 63,
place = {United States},
year = {Fri Apr 15 00:00:00 EDT 2016},
month = {Fri Apr 15 00:00:00 EDT 2016}
}
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