Algorithm to solve a chance-constrained network capacity design problem with stochastic demands and finite support

Journal Article · Fri Apr 15 00:00:00 EDT 2016 · Naval Research Logistics

DOI:https://doi.org/10.1002/nav.21685· OSTI ID:1326636

Schumacher, Kathryn M. ^[1]; Chen, Richard Li-Yang ^[2]; Cohn, Amy E. M. ^[3]; Castaing, Jeremy ^[3]

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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)

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.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE; USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC04-94AL85000
• OSTI ID: 1326636
• Alternate ID(s): OSTI ID: 1786508
• Report Number(s): SAND--2016-9223J; 647498
• Journal Information: Naval Research Logistics, Journal Name: Naval Research Logistics Journal Issue: 3 Vol. 63; ISSN 0894-069X
• Publisher: Office of Naval Research - Wiley
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING