Journal of Scheduling

, Volume 18, Issue 3, pp 329–329

Erratum to: A survey on offline scheduling with rejection

• Dvir Shabtay
• Nufar Gaspar
• Moshe Kaspi
Erratum

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

Below, we list four oversights that were found in our paper.
1. 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. 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. 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. 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

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