Abstract
We consider the scheduling problems arising when two agents, each with a family of jobs, compete to perform their respective jobs on a single machine. A setup time is needed for a job if it is the first job to be processed on the machine or its processing on the machine follows a job that belongs to another family. Each agent wants to minimize a certain cost function, which depends on the completion times of its jobs only. The aim is to find a schedule for all the jobs of the two agents that minimizes the objective of one agent while keeping the objective of the other agent being bounded by a fixed value $$Q$$Q. Polynomial-time and pseudo-polynomial-time algorithms are designed to solve the problem involving various combinations of regular scheduling objective functions.
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