A simple proof of the Moore-Hodgson Algorithm for minimizing the number of late jobs

TL;DR

This paper provides a concise and novel proof of the Moore-Hodgson Algorithm, which optimally schedules jobs on a single machine to minimize late jobs, a classic problem in scheduling theory.

Contribution

It introduces a new, shorter proof of the Moore-Hodgson Algorithm's correctness, enhancing understanding of this well-known scheduling method.

Findings

The proof confirms the correctness of the Moore-Hodgson Algorithm.

The approach simplifies existing proofs, making the algorithm's validity more accessible.

The algorithm effectively minimizes late jobs in single-machine scheduling problems.

Abstract

The Moore-Hodgson Algorithm minimizes the number of late jobs on a single machine. That is, it finds an optimal schedule for the classical problem $1~|\;|~\sum{U_j}$. Several proofs of the correctness of this algorithm have been published. We present a new short proof.