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.