A piecewise linear upper bound on the network recourse function

We consider the optimal value of a pure minimum cost network flow problem as a function of supply, demand and arc capacities. We present a new piecewise linear upper bound on this function, which is called the network recourse function. The bound is compared to the standard Madansky bound, and is shown computationally to be a little weaker, but much faster to find. The amount of work is linear in the number of stochastic variables, not exponential as is the case for the Madansky bound. Therefore, the reduction in work increases as the number of stochastic variables increases. Computational results are presented.