Online scheduling with known arrival times
Online scheduling with known arrival times
We consider an online scheduling environment where decisions are made without knowledge of the data of jobs that may arrive later. However, additional jobs can only arrive at known future times. This environment interpolates between the classical offline and online scheduling environments, and approaches the classical online environment when there are many equally spaced potential job arrival times.
The objective is to minimize the sum of weighted completion times, a widely used measure of work-in-process inventory cost and customer service. For a nonpreemptive single machine environment, we show that a lower bound on the competitive ratio of any online algorithm is the solution of a mathematical program. This lower bound is between $(1+SQRT(5))/2 and 2, with the exact value depending on the potential job arrival times. We also provide a "best possible" online scheduling algorithm, and show that its competitive ratio matches this lower bound.
We analyze two practically motivated special cases where the potential job arrival times have a special structure. When there are many equally spaced potential job arrival times, the competitive ratio of our online algorithm approaches the best possible competitive ratio of 2 for the classical online problem.
competitive analysis, machine scheduling, online algorithm, total weighted completion time
92-102
Hall, Nicholas G.
150c925d-8d57-40f8-9bfe-01ccb34cebc6
Posner, Marc E.
61d2f06b-65e2-48a3-bd3d-be8f47dcd481
Potts, Chris N.
58c36fe5-3bcb-4320-a018-509844d4ccff
February 2009
Hall, Nicholas G.
150c925d-8d57-40f8-9bfe-01ccb34cebc6
Posner, Marc E.
61d2f06b-65e2-48a3-bd3d-be8f47dcd481
Potts, Chris N.
58c36fe5-3bcb-4320-a018-509844d4ccff
Hall, Nicholas G., Posner, Marc E. and Potts, Chris N.
(2009)
Online scheduling with known arrival times.
Mathematics of Operations Research, 34 (1), .
(doi:10.1287/moor.1080.0346).
Abstract
We consider an online scheduling environment where decisions are made without knowledge of the data of jobs that may arrive later. However, additional jobs can only arrive at known future times. This environment interpolates between the classical offline and online scheduling environments, and approaches the classical online environment when there are many equally spaced potential job arrival times.
The objective is to minimize the sum of weighted completion times, a widely used measure of work-in-process inventory cost and customer service. For a nonpreemptive single machine environment, we show that a lower bound on the competitive ratio of any online algorithm is the solution of a mathematical program. This lower bound is between $(1+SQRT(5))/2 and 2, with the exact value depending on the potential job arrival times. We also provide a "best possible" online scheduling algorithm, and show that its competitive ratio matches this lower bound.
We analyze two practically motivated special cases where the potential job arrival times have a special structure. When there are many equally spaced potential job arrival times, the competitive ratio of our online algorithm approaches the best possible competitive ratio of 2 for the classical online problem.
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Published date: February 2009
Keywords:
competitive analysis, machine scheduling, online algorithm, total weighted completion time
Organisations:
Operational Research
Identifiers
Local EPrints ID: 149833
URI: http://eprints.soton.ac.uk/id/eprint/149833
ISSN: 0364-765X
PURE UUID: f1b114fa-7822-4eb2-95f9-424bf948c738
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Date deposited: 04 May 2010 09:14
Last modified: 14 Mar 2024 01:11
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Author:
Nicholas G. Hall
Author:
Marc E. Posner
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