On 2-stage robust LP with RHS uncertainty: complexity results and applications

Michel Minoux ()

Journal of Global Optimization, 2011, vol. 49, issue 3, 537 pages

Abstract: 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. Copyright Springer Science+Business Media, LLC. 2011

Keywords: Robust linear programming; Right-hand side uncertainty; Complexity of robust linear programming; Robust network optimization; Robust production planning; Robust PERT scheduling; Robust inventory management (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (12)

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DOI: 10.1007/s10898-010-9645-2

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