A 3-approximation list scheduling algorithm for a single-machine scheduling problem with a non-renewable resource and total weighted completion time criterion

TL;DR

This paper introduces a 3-approximation list scheduling algorithm for a complex single-machine scheduling problem involving non-renewable resources and weighted completion times, providing a near-optimal solution with proven tight bounds.

Contribution

The paper presents the first 3-approximation algorithm for the NP-hard single-machine scheduling problem with non-renewable resources and weighted completion time.

Findings

The proposed algorithm achieves a 3-approximation ratio.

The approximation ratio of 3 is proven to be tight.

The problem is NP-hard, justifying the need for approximation algorithms.

Abstract

This paper studies a single-machine scheduling problem with a non-renewable resource (NR-SSP) and total weighted completion time criterion. The non-renewable resource is consumed when the machine starts processing a job. We consider the case where each job's weight in the objective function is proportional to its resource consumption amount. The problem is known to be NP-hard in this case. We propose a 3-approximation list scheduling algorithm for this problem. Besides, we show that the approximation ratio 3 is tight for the algorithm.