4 research outputs found
Minimizing weighted mean absolute deviation of job completion times from their weighted mean
Cataloged from PDF version of article.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
FPTAS for half-products minimization with scheduling applications
Cataloged from PDF version of article.A special class of quadratic pseudo-boolean functions called “half-products” (HP) has recently been introduced. It has been
shown that HP minimization, while NP-hard, admits a fully polynomial time approximation scheme (FPTAS). In this note, we
provide a more efficient FPTAS. We further show how an FPTAS can also be derived for the general case where the HP function is
augmented by a problem-dependent constant and can justifiably be assumed to be nonnegative. This leads to an FPTAS for certain
partitioning type problems, including many from the field of scheduling.
c 2008 Elsevier B.V. All rights reserved