## TWO-STAGE ROBUST NETWORK FLOW AND DESIGN UNDER DEMAND UNCERTAINTY (2004)

Venue: | FORTHCOMING IN OPERATIONS RESEARCH |

Citations: | 34 - 3 self |

### BibTeX

@MISC{Atamtürk04two-stagerobust,

author = {Alper Atamtürk and Muhong Zhang},

title = {TWO-STAGE ROBUST NETWORK FLOW AND DESIGN UNDER DEMAND UNCERTAINTY},

year = {2004}

}

### OpenURL

### Abstract

We describe a two-stage robust optimization approach for solving network flow and design problems with uncertain demand. In two-stage network optimization one defers a subset of the flow decisions until after the realization of the uncertain demand. Availability of such a recourse action allows one to come up with less conservative solutions compared to single-stage optimization. However, this advantage often comes at a price: two-stage optimization is, in general, significantly harder than singe-stage optimization. For network flow and design under demand uncertainty we give a characterization of the first-stage robust decisions with an exponential number of constraints and prove that the corresponding separation problem is N P-hard even for a network flow problem on a bipartite graph. We show, however, that if the second-stage network topology is totally ordered or an arborescence, then the separation problem is tractable. Unlike single-stage robust optimization under demand uncertainty, two-stage robust optimization allows one to control conservatism of the solutions by means of an allowed “budget for demand uncertainty.” Using a budget of uncertainty we provide an upper