Approximation Schemes for Minimizing the Maximum Lateness on a Single Machine with Release Times under Non-Availability or Deadline Constraints

TL;DR

This paper develops polynomial time approximation schemes for four single-machine scheduling problems aimed at minimizing maximum lateness under various constraints, including deadlines and non-availability periods.

Contribution

It introduces PTAS solutions for four complex scheduling problems with release times and specific constraints, expanding the scope of approximation algorithms in scheduling.

Findings

Existence of PTAS for all four problems.

Effective handling of non-availability constraints.

Improved scheduling strategies under multiple constraints.

Abstract

In this paper, we consider four single-machine scheduling problems with release times, with the aim of minimizing the maximum lateness. In the first problem we have a common deadline for all the jobs. The second problem looks for the Pareto frontier with respect to the two objective functions maximum lateness and makespan. The third problem is associated with a non-availability constraint. In the fourth one, the non-availibility interval is related to the operator who is organizing the execution of jobs on the machine (no job can start, and neither can complete during the operator non-availability period). For each of the four problems, we establish the existence of a polynomial time approximation scheme (PTAS).