Non-Preemptive Scheduling on Machines with Setup Times

TL;DR

This paper presents an approximation algorithm for non-preemptive scheduling of jobs with setup times on identical machines, achieving a near 1.5 approximation ratio for minimizing makespan.

Contribution

It introduces a polynomial-time approximation algorithm for scheduling with setup times, improving the approximation ratio close to 3/2.

Findings

Approximation factor arbitrarily close to 1.5

Polynomial-time algorithm for scheduling with setup times

Effective handling of multiple job types on identical machines

Abstract

Consider the problem in which n jobs that are classified into k types are to be scheduled on m identical machines without preemption. A machine requires a proper setup taking s time units before processing jobs of a given type. The objective is to minimize the makespan of the resulting schedule. We design and analyze an approximation algorithm that runs in time polynomial in n, m and k and computes a solution with an approximation factor that can be made arbitrarily close to 3/2.