The Complexity of Mean Flow Time Scheduling Problems with Release Times

TL;DR

This paper investigates the computational complexity of scheduling jobs with release times to minimize average flow time, providing polynomial solutions for equal processing times and proving NP-hardness for the general case.

Contribution

It introduces a polynomial-time algorithm for equal processing times and establishes NP-hardness for arbitrary processing times in flow time scheduling.

Findings

Polynomial-time algorithm for equal processing times

NP-hardness for arbitrary processing times

Applicability to open-shop problems with release times

Abstract

We study the problem of preemptive scheduling n jobs with given release times on m identical parallel machines. The objective is to minimize the average flow time. We show that when all jobs have equal processing times then the problem can be solved in polynomial time using linear programming. Our algorithm can also be applied to the open-shop problem with release times and unit processing times. For the general case (when processing times are arbitrary), we show that the problem is unary NP-hard.