Single machine scheduling with two competing agents and equal job processing times

•The paper studies two agent scheduling models with unit processing times.•We provide comprehensive complexity results for many min-max and min-sum type scheduling objectives.•We provide polynomial and pseudo-polynomial time algorithms for the problems under consideration. We study various two-agent...

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Bibliographic Details
Published in:European journal of operational research Vol. 244; no. 1; pp. 86 - 99
Main Authors: Oron, Daniel, Shabtay, Dvir, Steiner, George
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.07.2015
Elsevier Sequoia S.A
Subjects:
Agency theory
Algorithms
Completion time
Complexity
Computation
Equal processing times
Job shops
Mathematical analysis
Mathematical models
Mathematical problems
Operational research
Operations research
Optimization
Optimization algorithms
Polynomials
Production scheduling
Scheduling
Single machine scheduling
Studies
Two competing agents
Equal processing times
Two competing agents
Single machine scheduling
Complexity
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:•The paper studies two agent scheduling models with unit processing times.•We provide comprehensive complexity results for many min-max and min-sum type scheduling objectives.•We provide polynomial and pseudo-polynomial time algorithms for the problems under consideration. We study various two-agent scheduling problems on a single machine with equal job processing times. The equal processing time assumption enables us to design new polynomial-time or faster-than-known optimization algorithms for many problems. We prove, however, that there exists a subset of problems for which the computational complexity remains NP-hard. The set of hard problems includes different variations where the objective functions of the two agents are either minimizing the weighted sum of completion times or the weighted number of tardy jobs. For these problems, we present pseudo-polynomial time algorithms.
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2015.01.003