Near-optimal solutions and tight lower bounds for the parallel machines scheduling problem with learning effect

¹ Industrial Engineering Department, College of Engineering, King Saud University, 11421 Riyadh, Saudi Arabia
² Department of Computer Science and Information, College of Science, Majmaah University, 11952 Majmaah, Saudi Arabia
³ Department of Computer Science, Higher Institute of Computer Science and Mathematics of Monastir, Monastir University, 5000 Monastir, Tunisia

^* Corresponding author: m.jemmali@mu.edu.sa, mah_jem_2004@yahoo.fr

Received: 23 April 2019
Accepted: 27 January 2020

Abstract

In this paper, the parallel machines scheduling problem with Dejong’s learning effect is addressed. The considered problem has a practical interest since it models real-world situations. In addition, this problem is a challenging one because of its NP-Hardness. In this work, a set of heuristics are proposed. The developed heuristics are categorized into two types. The first category is based on the dispatching methods, with new enhancement variants. The second type is more sophisticated and requires solving NP-Hard problems. Furthermore, several lower bounds are developed in order to assess the performance of the proposed heuristics. These lower bounds are based on solving the problem of the determination of the minimum average load under taking into account some observations. Among these observations, the existence of a limit position that the jobs are not allowed to exceed in any optimal schedule. Finally, an extensive experimental study is conducted over benchmark test problems, with up to 1500 jobs and 5280 instances. The obtained results are outperforming those proposed in the literature.