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Branch and bound algorithms for single machine scheduling with batching to minimize the number of late jobs

Branch and bound algorithms for single machine scheduling with batching to minimize the number of late jobs
Branch and bound algorithms for single machine scheduling with batching to minimize the number of late jobs
This paper considers the problem of scheduling a single machine to minimize the number of late jobs in the presence of sequence-independent family set-up times. The jobs are partitioned into families, and a set-up time is required at the start of each batch, where a batch is a maximal set of jobs in the same family that are processed consecutively. We design branch and bound algorithms that have several alternative features. Lower bounds can be derived by relaxing either the set-up times or the due dates. A first branching scheme uses a forward branching rule with a depth-first search strategy. Dominance criteria, which determine the order of the early jobs within each family and the order of the batches containing early jobs, can be fully exploited in this scheme. A second scheme uses a ternary branching rule in which the next job is fixed to be early and starting a batch, to be early and not starting a batch, or to be late. The different features are compared on a large set of test problems, where the number of jobs ranges from 30 to 50 and the number of families ranges from 4 to 10.
scheduling, single machine, batches, families, set-up time, branch and bound
161-177
Crauwels, H.A.J.
e44cae47-7eab-4c94-8d48-f19a81981a16
Potts, C.N.
58c36fe5-3bcb-4320-a018-509844d4ccff
Van Oudheusden, D.
37dc52c1-d6a1-4689-8ea7-7aa9bb78d409
Van Wassenhove, L.N.
ee32c2b3-43ed-449b-917c-b81f9af226e3
Crauwels, H.A.J.
e44cae47-7eab-4c94-8d48-f19a81981a16
Potts, C.N.
58c36fe5-3bcb-4320-a018-509844d4ccff
Van Oudheusden, D.
37dc52c1-d6a1-4689-8ea7-7aa9bb78d409
Van Wassenhove, L.N.
ee32c2b3-43ed-449b-917c-b81f9af226e3

Crauwels, H.A.J., Potts, C.N., Van Oudheusden, D. and Van Wassenhove, L.N. (2005) Branch and bound algorithms for single machine scheduling with batching to minimize the number of late jobs. Journal of Scheduling, 8 (2), 161-177. (doi:10.1007/s10951-005-6365-4).

Record type: Article

Abstract

This paper considers the problem of scheduling a single machine to minimize the number of late jobs in the presence of sequence-independent family set-up times. The jobs are partitioned into families, and a set-up time is required at the start of each batch, where a batch is a maximal set of jobs in the same family that are processed consecutively. We design branch and bound algorithms that have several alternative features. Lower bounds can be derived by relaxing either the set-up times or the due dates. A first branching scheme uses a forward branching rule with a depth-first search strategy. Dominance criteria, which determine the order of the early jobs within each family and the order of the batches containing early jobs, can be fully exploited in this scheme. A second scheme uses a ternary branching rule in which the next job is fixed to be early and starting a batch, to be early and not starting a batch, or to be late. The different features are compared on a large set of test problems, where the number of jobs ranges from 30 to 50 and the number of families ranges from 4 to 10.

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More information

Published date: 2005
Keywords: scheduling, single machine, batches, families, set-up time, branch and bound
Organisations: Operational Research

Identifiers

Local EPrints ID: 29630
URI: https://eprints.soton.ac.uk/id/eprint/29630
PURE UUID: 8beb921c-f139-4a69-a192-950012cd4480

Catalogue record

Date deposited: 12 May 2006
Last modified: 17 Jul 2017 15:57

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