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Article Dans Une Revue Journal of Global Optimization Année : 2011

On Two-Stage Robust LP with RHS Uncertainty: Complexity Results and Applications

Michel Minoux
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Résumé

We investigate here the class—denoted R-LP-RHSU—of two-stage robust linear programming problems with right-hand-side uncertainty. Such problems arise in many applications e.g: robust PERT scheduling (with uncertain task durations); robust maximum flow (with uncertain arc capacities); robust network capacity expansion problems; robust inventory management; some robust production planning problems in the context of power production/distribution systems. It is shown that such problems can be formulated as large scale linear programs with associated nonconvex separation subproblem. A formal proof of strong NP-hardness for the general case is then provided, and polynomially solvable subclasses are exhibited. Differences with other previously described robust LP problems (featuring row-wise uncertainty instead of column wise uncertainty) are highlighted.

Dates et versions

hal-01170463 , version 1 (01-07-2015)

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Michel Minoux. On Two-Stage Robust LP with RHS Uncertainty: Complexity Results and Applications. Journal of Global Optimization, 2011, 49 (3), pp.521-537. ⟨10.1007/s10898-010-9645-2⟩. ⟨hal-01170463⟩
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