Efficient algorithms for scheduling semiconductor burn-in operations
Operations Research
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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
Scheduling Algorithms
Competitive Two-Agent Scheduling and Its Applications
Operations Research
On the complexity of bi-criteria scheduling on a single batch processing machine
Journal of Scheduling
Minimizing total completion time on a batch processing machine with job families
Operations Research Letters
Unbounded parallel-batching scheduling with two competitive agents
Journal of Scheduling
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We consider a scheduling problem in which two agents, each with a set of non-preemptive jobs, compete to perform their jobs on a common bounded parallel-batching machine. Each of the agents wants to minimize an objective function that depends on the completion times of its own jobs. The goal is to schedule the jobs such that the overall schedule performs well with respect to the objective functions of both agents. We focus on minimizing the makespan or the total completion time of one agent, subject to an upper bound on the makespan of the other agent. We distinguish two categories of batch processing according to the compatibility of the agents. In the case where the agents are incompatible, their jobs cannot be processed in the same batch, whereas all the jobs can be processed in the same batch when the agents are compatible. We show that the makespan problem can be solved in polynomial time for the incompatible case and is NP-hard in the ordinary sense for the compatible case. Furthermore, we show that the latter admits a fully polynomial-time approximation scheme. We prove that the total completion time problem is NP-hard and is polynomially solvable for the incompatible case with a fixed number of job types.