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Operations Research
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Mathematics of Operations Research
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SIAM Journal on Optimization
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INFORMS Journal on Computing
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Robust linear optimization under general norms
Operations Research Letters
A scenario-based approach for robust linear optimization
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
Efficient robust linear optimization for large repositioning problems
INOC'11 Proceedings of the 5th international conference on Network optimization
Information Sciences: an International Journal
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Transportation Science
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Management Science
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Maritime repositioning of empty containers under uncertain port disruptions
Computers and Industrial Engineering
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We develop a robust optimization framework for dynamic empty repositioning problems modeled using time-space networks. In such problems, uncertainty arises primarily from forecasts of future supplies and demands for assets at different time epochs. The proposed approach models such uncertainty using intervals about nominal forecast values and a limit on the systemwide scaled deviation from the nominal forecast values. A robust repositioning plan is defined as one in which the typical flow balance constraints and flow bounds are satisfied for the nominal forecast values, and the plan is recoverable under a limited set of recovery actions. A plan is recoverable when feasibility can be reestablished for any outcome in a defined uncertainty set. We develop necessary and sufficient conditions for flows to be robust under this definition for three types of allowable recovery actions. When recovery actions allow only flow changes on inventory arcs, we show that the resulting problem is polynomially solvable. When recovery actions allow limited reactive repositioning flows, we develop feasibility conditions that are independent of the size of the uncertainty set. A computational study establishes the practical viability of the proposed framework.