Analysis of Scheduling Problem on Two Machines with Partial Precedence Order on the Set of Jobs

TL;DR

This paper studies an NP-hard scheduling problem on two machines with partial job precedence, proposing an approximation algorithm with a tight bound and identifying a polynomial case.

Contribution

It introduces a new approximation algorithm for the NP-hard problem and proves polynomial solvability under specific precedence conditions.

Findings

Proposed an approximation algorithm with a tight bound.

Proved polynomial solvability when each first machine job precedes two second machine jobs.

Addressed the complexity of scheduling with partial precedence constraints.

Abstract

In this paper, we consider an NP-hard problem of scheduling a set of jobs of equal processing time on two machines, given a partial precedence order on the set of jobs, with an objective to minimize the makespan. An approximation algorithm is proposed for this problem with a tight approximation bound. Polynomial solvability of the problem is proved in the case when each job on the first machine is in precedence relation with two jobs on the second machine.