Reply to Second Revision
نویسنده
چکیده
We address the problem of scheduling a single batching machine to minimize the maximum lateness with a constraint restricting the batch size. A solution for this NP-hard problem is defined by a selection of jobs for each batch and an ordering of those batches. As an alternative, we choose to represent a solution as a sequence of jobs. This approach is justified by our development of a dynamic program to find a schedule that minimizes the maximum lateness while preserving the underlying job order. Given this solution representation, we are able to define and evaluate various job-insert and jobswap neighborhood searches. Furthermore we introduce a new neighborhood, named split-merge, that allows multiple job inserts in a single move. The split-merge neighborhood is of exponential size, but can be searched in polynomial time by dynamic programming. Computational results with an iterated descent algorithm that employs the split-merge neighborhood show that it compares favorably with corresponding iterated descent algorithms based on the job-insert and job-swap neighborhoods. Dear Associate Editor, On behalf of my co-authors, I am submitting the revised material considering all of the comments made by the reviewers. We are including a pdf file that responds to all points raised, “Reply2Reviewers.pdf”, as well as the revised manuscript. As indicated in the original cover letter this paper has not been submitted for publication nor has it been published in whole or in part elsewhere. I attest to the fact that all authors listed on the title page have read the manuscript, attest to the validity and legitimacy of the data and its interpretation, and agree to its submission to this journal (Computers & Operations Research). In this paper we propose an exponential neighborhood for the batching machine problem of minimizing the maximum lateness with restricted batch size that can be searched in polynomial time using dynamic programming.
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