Approximating Scheduling Machines with Capacity Constraints

TL;DR

This paper introduces a 3-approximation algorithm for the Scheduling Machines with Capacity Constraints problem, extending the Iterative Rounding Method to handle capacity limits, which is a novel application in this context.

Contribution

It is the first to apply the Iterative Rounding Method to scheduling problems with capacity constraints, providing a new approximation approach.

Findings

Developed a 3-approximation algorithm for the problem.

Extended the Iterative Rounding Method to capacity-constrained scheduling.

First application of this method to such scheduling problems.

Abstract

In the Scheduling Machines with Capacity Constraints problem, we are given k identical machines, each of which can process at most m_i jobs. M jobs are also given, where job j has a non-negative processing time length t_j >= 0. The task is to find a schedule such that the makespan is minimized and the capacity constraints are met. In this paper, we present a 3-approximation algorithm using an extension of Iterative Rounding Method introduced by Jain. To the best of the authors' knowledge, this is the first attempt to apply Iterative Rounding Method to scheduling problem with capacity constraints.