Improved Bicriteria Existence Theorems for Scheduling

TL;DR

This paper presents improved theoretical bounds on the simultaneous optimization of makespan and average completion time in scheduling, using an advanced linear programming approach.

Contribution

It introduces stronger bounds for schedule existence that optimize both criteria simultaneously, generalizing previous results with a novel linear programming method.

Findings

Existence of schedules with makespan at most (1+rho) times the minimum.

Average completion time at most (1-e)^rho times the minimum.

Proof employs an infinite-dimensional linear program.

Abstract

Two common objectives for evaluating a schedule are the makespan, or schedule length, and the average completion time. This short note gives improved bounds on the existence of schedules that simultaneously optimize both criteria. In particular, for any rho> 0, there exists a schedule of makespan at most 1+rho times the minimum, with average completion time at most (1-e)^rho times the minimum. The proof uses an infininite-dimensional linear program to generalize and strengthen a previous analysis by Cliff Stein and Joel Wein (1997).