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

Abstract

We study the early work scheduling problem on identical parallel machines in order to maximize the total early work, i.e., the 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 an efficient polynomial time approximation scheme with running time $$O\left( f(1/\varepsilon \right) n)$$ , where n is the number of jobs and $$f(1/\varepsilon )$$ is exponential in $$1/\varepsilon $$ , and a fully polynomial time approximation scheme with running time $$O\left( \frac{1}{\varepsilon ^{2m+1}}+n\right) $$ when the number of machines is fixed.