Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Nondominated Schedules for a Job-Shop with Two Competing Users
Computational & Mathematical Organization Theory
A Multiple-Criterion Model for Machine Scheduling
Journal of Scheduling
Scheduling Problems with Two Competing Agents
Operations Research
Multi-agent scheduling on a single machine to minimize total weighted number of tardy jobs
Theoretical Computer Science
Two-Agent Scheduling with Linear Deteriorating Jobs on a Single Machine
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Approximation algorithms for multi-agent scheduling to minimize total weighted completion time
Information Processing Letters
A Lagrangian approach to single-machine scheduling problems with two competing agents
Journal of Scheduling
A tabu method for a two-agent single-machine scheduling with deterioration jobs
Computers and Operations Research
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This paper considers the single-machine scheduling problems in which two distinct agents are concerned. Each agent has a set of jobs with different release times, and both of them expect to complete their respective jobs as early as possible. We take the makespan of each agent as its own criterion and take the linear combination of the two makespans as our objective function. In this paper, both off-line and online models are considered. When preemption is allowed, we present an exact algorithm for the off-line model and an optimal algorithm for the on-line model. When preemption is not allowed we point out that the problem is NP-hard for the off-line model and give a (2+1/θ)-competitive algorithm for the on-line model. We also prove that a lower bound of the competitive ratio for the later model is 1 + θ/(1 + θ), where θ is a given factor not less than 1.