Optimizing parallel batch scheduling on uniform machines: a focus on equal job durations with varied release dates and sizes

School of Computer Science and Technology, Shandong Technology and Business University, Yantai 264005, P.R. China

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 11 January 2024
Accepted: 2 March 2026

Abstract

In this paper, we explore a parallel batch scheduling problem, focusing on scenarios where jobs, equal in duration, differ in release dates and sizes, and are processed on uniform machines with varied batch capacities. The objective function to be minimized is makespan, i.e., the maximum completion time of all the jobs. We present two exact algorithms tailored for a scenario characterized by jobs whose sizes are sequentially divisible. Addressing the general context where this divisibility does not hold, we introduce a 2-approximation algorithm which is considered the best achievable in some sense, since improving the approximation ratio superior to 2 is improbable without resolving the P versus NP problem.