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An Exact Algorithm for Two-stage Robust Optimization with Mixed Integer Recourse Problems

Long Zhao(longzhao***at***mail.usf.edu)
Bo Zeng(bzeng***at***usf.edu)

Abstract: In this paper, we consider a linear two-stage robust optimization model with a mixed integer recourse problem. Currently, this type of two-stage robust optimization model does not have any exact solution algorithm available. We first present a set of sufficient conditions under which the existence of an optimal solution is guaranteed. Then, we present a nested column-and-constraint generation algorithm that can derive an exact solution in nite steps. The algorithm development also yields novel solution methods to solve general mixed integer bi-level programs and some four-level programs. Finally, the proposed framework is demonstrated through an application of a robust rostering problem with part-time staff scheduling in the second stage.

Keywords: two-stage robust optimization, mixed integer recourse problem, tri-level program, bi-level program

Category 1: Robust Optimization

Category 2: Applications -- OR and Management Sciences

Category 3: Applications -- OR and Management Sciences (Scheduling )


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Entry Submitted: 01/10/2012
Entry Accepted: 01/11/2012
Entry Last Modified: 01/10/2012

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