Improved Approximation Schemes for Early Work Scheduling on Identical Parallel Machines with a Common Due Date

We study the early work scheduling problem on identical parallel machines in order to maximize total work, i.e., parts of non-preemptive jobs that are executed before a common due date. By preprocessing and constructing an auxiliary instance which has several good properties, for any desired accuracy $$\varepsilon $$ , we propose efficient polynomial time approximation scheme with running $$O\left( f(1/\varepsilon \right) n)$$ where n is number $$f(1/\varepsilon )$$ exponential $$1/\varepsilon fully \frac{1}{\varepsilon ^{2m+1}}+n\right) when fixed.