A mean-variance model for the minimum cost flow problem with stochastic arc costs

This paper considers a minimum cost flow problem where arc costs are uncertain, and the decision maker wishes to minimize both the expected flow cost and the variance of this cost. We derive optimality conditions analagous to the negative cycle conditions that allow solution methods to exploit the network structure of the problem. An optimality condition based on concepts of network equilibria is also provided. A lower bound is developed on the benefit attained by learning the cost of an arc a priori; this is useful in quantifying the value of information for this problem. Finally, numerical results compare the solution methods developed earlier in this work; the minimum mean cycle cancelling algorithm outperforms the Frank-Wolfe algorithm in all networks tested, and an equilibriumbased algorithm is seen to perform well on networks of large size.

• Type: Journal
• Year: 2010
• Where: NETWORKS
• Authors: Stephen D. Boyles, S. Travis Waller
• Keywords: Computer Networks, Minimum Mean Cycle, Negative Cycle Conditions, NETWORKS 2010, Optimality Condition