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

Kathryn M. Schumacher, Richard Li‐Yang Chen, Amy E.M. Cohn and Jeremy Castaing

Naval Research Logistics (NRL), 2016, vol. 63, issue 3, 236-246

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

Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:wly:navres:v:63:y:2016:i:3:p:236-246

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