# MPI-I-97-1-005

## Bicriteria job sequencing with release dates

### Wang, Yaoguang

**MPI-I-97-1-005**. February** **1997, 18 pages. | Status:** **available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:

We consider the single machine job sequencing problem

with release dates. The main purpose of this paper

is to investigate efficient and effective

approximation algorithms with a bicriteria performance

guarantee. That is, for some $(\rho_1, \rho_2)$, they

find schedules simultaneously within a factor of $\rho_1$ of

the minimum total weighted completion times and

within a factor of $\rho_2$ of the minimum makespan.

The main results of the paper are summarized as follows.

First, we present a new $O(n\log n)$ algorithm with the performance

guarantee $\left(1+\frac{1}{\beta}, 1+\beta\right)$ for any

$\beta \in [0,1]$. For the problem with integer processing times

and release dates, the algorithm has the bicriteria performance guarantee

$\left(2-\frac{1}{p_{max}}, 2-\frac{1}{p_{max}}\right)$,

where $p_{max}$ is the maximum processing time.

Next, we study an elegant approximation algorithm

introduced recently by Goemans. We show that

its randomized version has expected bicriteria performance

guarantee $(1.7735, 1.51)$ and the derandomized

version has the guarantee $(1.7735, 2-\frac{1}{p_{max}})$.

To establish the performance guarantee, we also use two

LP relaxations and some randomization techniques

as Goemans does, but take a different approach

in the analysis, based on a decomposition theorem. Finally, we

present a family of bad instances showing that

it is impossible to achieve $\rho_1\leq 1.5$ with this LP lower

bound.

Acknowledgement:** **

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**URL to this document: **http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1997-1-005

**BibTeX**
`@TECHREPORT{``Wang1997``,`

` AUTHOR = {Wang, Yaoguang},`

` TITLE = {Bicriteria job sequencing with release dates},`

` TYPE = {Research Report},`

` INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},`

` ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},`

` NUMBER = {MPI-I-97-1-005},`

` MONTH = {February},`

` YEAR = {1997},`

` ISSN = {0946-011X},`

`}`