Abstract
We investigate a competitive two-agent scheduling problem in the setting of proportionate flow shop, where the job processing times are machine-independent. The scheduling criterion of one agent is to minimize its total weighted late work, and the scheduling criterion of the other agent is to minimize its total weighted number of late jobs. The goal is to find the Pareto-optimal curve (i.e., the set of all Pareto-optimal points) and identify a corresponding Pareto-optimal schedule for each Pareto-optimal point. An exact pseudo-polynomial-time algorithm and an [Formula: see text]-approximate Pareto-optimal curve are designed to solve the problem, respectively.
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