# Erratum to: A survey on offline scheduling with rejection

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## Erratum to: J Sched (2013) 16:3–28 DOI 10.1007/s10951-012-0303-z

- 1.
The result appearing in Theorem 8 (page 10) was presented earlier (in a slightly different form) by Koulamas (2011). We overlooked this result, and want to give him the proper credit for it.

- 2.
On page 4, we include the following statement: “if \(F_{1}\) is indeed the dominant criterion then using the lexicographical approach will yield a non-balanced solution for which \(A=\emptyset \) and \(\overline{A}=J\).” However, this is not always the case. Consider, for example, an instance of the \(1|rej|\epsilon (F_{1},RC)\) problem with \(F_{1}\in \{T_{\max },\varSigma T_{j},\varSigma U_{j}\}\), where it is possible to schedule the entire set of jobs (\(J\)) such that all jobs are non-tardy, i.e., such that \(T_{\max }=0\). For such an instance, using the lexicographical approach with \(F_{1}\) being the dominant criterion will yield a solution in which \(A=J\) and \(\overline{A}=\emptyset \), thereby contradicting our statement.

- 3.
The value of the positional penalty for \(\delta _{1}\sum \sum \left| W_{i}-W_{j}\right| +\delta _{2}\sum W_{j}\) in Table 4 (page 14) should be replaced by \(\xi _{j}(k)=\delta _{1}(j-1)(k-j+1)+\delta _{2}(j-1)\).

- 4.
On page 16, we mention that Steiner and Zhang (2011) present a pseudo-polynomial time optimization algorithm to solve the \(1|rej|\sum _{J_{j}\in A}T_{j}+RC\) problem in \(O(n^{4}(\sum _{j=1}^{n}p_{j} )^{3})\) time, which further implies that this algorithm can serve as an \(O(n^{7})\) time algorithm to solve the special case of equal processing times. However, we failed to observe that Steiner and Zhang provided a faster \(O(n^{2})\) time optimization algorithm to solve this special case.

## Notes

### Acknowledgments

The authors want to thank Prof. Christos Koulamas for pointing out the above errors.

## References

- Koulamas, C. (2011). A unified solution approach for the due date assignment problem with tardy jobs.
*International Journal of Production Economics*,*132*, 292–295.CrossRefGoogle Scholar - Steiner, G., & Zhang, R. (2011). Revised delivery-time quotation in scheduling with tardiness penalties.
*Operations Research*,*59*, 1504–1511.CrossRefGoogle Scholar