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We consider a competitive two-agent scheduling problem on multiple identical machines with release dates and preemption. In the scheduling model, there are two agents a and b each having their own job sets a={J1a,…,Jnaa} and b={J1b,…,Jnbb}, respectively. Each job Jj∈a∪b has a release date ri and the n=na+nb jobs need to be preemptively scheduled on m identical machines. For m=2, we show that the trade-off curve of all the Pareto optimal points can be characterized in polynomial time. When m is input, we show that P|rj,pmtn|Lmaxa:Lmaxb≤Q can be solved in strongly polynomial time.

A Competitive Two-Agent Scheduling Problem on Parallel Machines with Release Dates and Preemption