Minimizing weighted mean absolute deviation of job completion times from their weighted mean
Author
Erel, E.
Ghosh, J. B.
Date
2011Source Title
Applied Mathematics and Computation
Print ISSN
0096-3003
Publisher
Elsevier
Volume
217
Issue
22
Pages
9340 - 9350
Language
English
Type
ArticleItem Usage Stats
134
views
views
113
downloads
downloads
Abstract
We address a single-machine scheduling problem where the objective is to minimize the weighted mean absolute deviation of job completion times from their weighted mean. This problem and its precursors aim to achieve the maximum admissible level of service equity. It has been shown earlier that the unweighted version of this problem is NP-hard in the ordinary sense. For that version, a pseudo-polynomial time dynamic program and a 2-approximate algorithm are available. However, not much (except for an important solution property) exists for the weighted version. In this paper, we establish the relationship between the optimal solution to the weighted problem and a related one in which the deviations are measured from the weighted median (rather than the mean) of the job completion times; this generalizes the 2-approximation result mentioned above. We proceed to give a pseudo-polynomial time dynamic program, establishing the ordinary NP-hardness of the problem in general. We then present a fully-polynomial time approximation scheme as well. Finally, we report the findings from a limited computational study on the heuristic solution of the general problem. Our results specialize easily to the unweighted case; they also lead to an approximation of the set of schedules that are efficient with respect to both the weighted mean absolute deviation and the weighted mean completion time. © 2011 Elsevier Inc. All rights reserved.
Keywords
Approximation schemeDynamic program
Scheduling
Approximation scheme
Computational studies
Dynamic program
Heuristic solutions
Job completion
Level of service
NP-hard
NP-hardness
Optimal solutions
Single-machine scheduling
Solution property
Time dynamic
Weighted mean
Weighted median
Polynomial approximation