The authors regret that Lemma 4.2 in Shen, Dauzère-Pérès, & Neufeld (2018) is incomplete. While the lemma applies to cases I, II, III, as well as to the machine-independent setting in case IV, a sub-case of case IV must be considered. The length of a critical path in case IV will decrease if the moved operation [Formula presented]is assigned to a new machine for which [Formula presented]has a strictly smaller processing time than its current processing time. Let [Formula presented]be the processing time of operation [Formula presented]after it is moved on an eligible machine (resequencing or reassignment). Lemma 4.2 in Shen, Dauzère-Pérès, & Neufeld (2018) is extended below. Lemma 4.2 No immediate improvement in the makespan can be found by performing 1. Move type 1 for cases II and IV;2. Move type 2 for cases I and IV;3. Move types 3 and 4 for case IV if [Formula presented]holds. To investigate the impact of the “new” Lemma 4.2 on the algorithm performance, we first closely examined the critical path structures of all solutions. Case IV accounts for about 8.72% of all critical paths, which appears independent of solution qualities with 7.69% on average for initial solutions and 9.74% for final solutions. Moreover, only 0.07% of critical operations satisfy condition 3. This suggests that the additional moves allowed by the “new” Lemma 4.2 are rarely applied. Nevertheless, we adjusted our algorithm and reran the tests on all benchmark instances. No significant difference was found in the results. The authors would like to apologize for any inconvenience caused.
|Number of pages||1|
|Journal||European Journal of Operational Research|
|Publication status||Published - 16 Jan 2022|