Single and Parallel Machine Scheduling with Variable Release Dates

TL;DR

This paper investigates a novel extension of the total weighted flowtime minimization problem by making job release dates decision variables constrained by a global deadline, demonstrating NP-completeness and evaluating solution methods.

Contribution

It introduces and analyzes the NP-completeness of a new scheduling problem with variable release dates constrained by a deadline, and empirically compares various solution approaches.

Findings

The problem is NP-complete even for a single machine.

Genetic algorithms, tree search, and constraint programming are evaluated.

The problem's complexity impacts the choice of solution methods.

Abstract

In this paper we study a simple extension of the total weighted flowtime minimization problem for single and identical parallel machines. While the standard problem simply defines a set of jobs with their processing times and weights and assumes that all jobs have release date 0 and have no deadline, we assume that the release date of each job is a decision variable that is only constrained by a single global latest arrival deadline. To our knowledge, this simple yet practically highly relevant extension has never been studied. Our main contribution is that we show the NP- completeness of the problem even for the single machine case and provide an exhaustive empirical study of different typical approaches including genetic algorithms, tree search, and constraint programming.