Stochastic programs over trees with random arc capacities

In this paper, we study a special class of stochastic programs where the recourse problem consists of trees with random arc capacities, which we call tree recourse. We develop an efficient procedure to obtain the expected recourse function exactly for single‐stage problems. This procedure is used in a backward recursion to find the exact expected recourse function for multistage trees. We show that for large trees n‐stage networks can be solved more easily than can a single‐stage network with n‐levels. We also show that the expected recourse functions for single‐stage and n‐stage formulations of the same network can be quite similar. Finally, we illustrate the potential of using the tree recourse problems in a more general stochastic network problem. © 1994 by John Wiley & Sons, Inc.