Algorithm to Solve a Chance-Constrained Network Capacity Design Problem with Stochastic Demands and Finite Support

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 alpha% of the scenarios must be feasible under the chosen capacity, where a 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. (C) 2016 Wiley Periodicals, Inc.