Scheduling a single machine with parallel batching to minimize makespan and total rejection cost

Document Type

Article

Publication Date

5-11-2016

Abstract

We consider the problem of scheduling a set of n jobs on a single machine with parallel batching and with rejection being allowed. Two bi-criteria problems are considered: (a) minimize the makespan subject to the constraint that the total rejection cost does not exceed a given threshold, and (b) minimize the total rejection cost subject to the constraint that the makespan does not exceed a given threshold. For the case of a batching machine with infinite capacity (i.e., the batch size allowed on the machine is larger than or equal to the number of jobs), we assume that the jobs have release dates. We present an O(n2)-time 2-approximation algorithm for problem (a) and, in addition, we present dynamic programming algorithms and fully polynomial-time approximation schemes for both problems (a) and (b). For the case of a batching machine with finite capacity (i.e., the batch size allowed on the machine is less than the number of jobs), we assume that the jobs have identical release dates. We propose approximation algorithms for (a) and present dynamic programming algorithms and fully polynomial-time approximation schemes for both problems (a) and (b).

Identifier

84992299302 (Scopus)

Publication Title

Discrete Applied Mathematics

External Full Text Location

https://doi.org/10.1016/j.dam.2015.10.021

ISSN

0166218X

First Page

150

Last Page

163

Volume

204

Grant

TRADA-46-477

Fund Ref

National Natural Science Foundation of China

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