An asymptotic PTAS for batch scheduling with nonidentical job sizes to minimize makespan

Abstract

Motivated by the existence of an APTAS (Asymptotic PTAS) for bin packing problem, we consider the batch scheduling problem with nonidentical job sizes to minimize makespan. For the proportional special version, i.e., there exists a fixed number α such that p j =α s j for every 1≤j≤n, we first present a lower bound of 3/2 for the approximation ratio and then design an APTAS.