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1 Erratum to: Math Meth Oper Res (2014) 79:293–326 DOI 10.1007/s00186-014-0464-y
In the proof of Theorem 1 in the appendix of the original article, the validity of the optimality conditions
for all \((\sigma _{i}^{\omega })^\mathrm{SGSM}\) and \(\rho _{ji}^\mathrm{SGSM}\) is proved by scaling the optimality conditions
which are, by assumption, valid for \(\sigma _{i}^\mathrm{GSM}\) and \(\rho _{ji}^\mathrm{GSM}\), by the factor
Equation (114) emerges from (89) this way, in general, only if
The definition of \(\rho _{ji}^{\mathrm{SGSM}}\), however, in the original proof is, up to the reversal of \(i\) and \(j\),
The theorem and the proof in the original article are therefore true, if \(\frac{\bar{\alpha }_{j}}{\alpha ^{*}_{j}\bar{n}}\) does not depend on the node \(j\). This holds, in particular, in the following cases:
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There is only one node; this is, e.g., the case in the example of Theorem 2 so that the asymmetry between the sets of optimal solutions of the SGSM and the GSM is retained.
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For each pair of nodes, the ratio between their demands is a constant independent of the scenario; this is, e.g., the case, if the demands for all nodes are identical in each demand scenario.
We conjecture that there are weaker assumptions for which Theorem 1 holds, but they require a modified proof. We apologize for our inadvertent omission.
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The online version of the original article can be found under doi:10.1007/s00186-014-0464-y.
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Rambau, J., Schade, K. Erratum to: The stochastic guaranteed service model with recourse for multi-echelon warehouse management. Math Meth Oper Res 80, 225–226 (2014). https://doi.org/10.1007/s00186-014-0476-7
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DOI: https://doi.org/10.1007/s00186-014-0476-7