An Optimal Online Algorithm for Scheduling on Two Parallel Machines with GoS Eligibility Constraints

We consider the online scheduling problem on two parallel machines with the Grade of Service (GoS) eligibility constraints. The jobs arrive over time, and the objective is to minimize the makespan. We develop a $$(1+\alpha )$$(1+α)-competitive optimal algorithm, where $$\alpha \approx 0.555$$α≈0.555 is a solution of $$\alpha ^3-2\alpha ^2-\alpha +1=0$$α3-2α2-α+1=0.