A Statistical Comparison of Metaheuristics for Unrelated Parallel Machine Scheduling Problems with Setup Times

Abstract

Manufacturing scheduling aims to optimize one or more performance measures by allocating a set of resources to a set of jobs or tasks over a given period of time. It is an area that considers a very important decision-making process for manufacturing and production systems. In this paper, the unrelated parallel machine scheduling problem with machine-dependent and job-sequence-dependent setup times is addressed. This problem involves the scheduling of tasks on unrelated machines with setup times in order to minimize the makespan. The genetic algorithm is used to solve small and large instances of this problem when processing and setup times are balanced (Balanced problems), when processing times are dominant (Dominant P problems), and when setup times are dominant (Dominant S problems). For small instances, most of the values achieved the optimal makespan value, and, when compared to the metaheuristic ant colony optimization (ACOII) algorithm referred to in the literature, it was found that there were no significant differences between the two methods. However, in terms of large instances, there were significant differences between the optimal makespan obtained by the two methods, revealing overall better performance by the genetic algorithm for Dominant S and Dominant P problems.

Developing New Bounds for the Performance Guarantee of the Jump Neighborhood for Scheduling Jobs on Uniformly Related Machines

“…Using Equation (10) and Lemma 3, we have η(x) ≤ C(x), and ∑ j∈J w j p j ≤ s m η(x * ), respectively. Therefore,…”

“…Equation (10) makes it evident that η(x * ) ≤ C(x * ). Further, considering the nonnegativity of the term multiplying η(x * ), we have:…”

“…Therefore, the development and analysis of approximate solution methods become imperative. In recent studies, scheduling problems in parallel machine environments have been investigated across various industries, including semiconductor manufacturing [2,3], metalworking [4], textile manufacturing [5], automotive manufacturing [6,7], chemical processes [8], offshore oil and gas extraction [9], as well as manufacturing scheduling for contingent new requirements [10][11][12][13][14][15]. Additionally, scheduling challenges within service-related sectors have been studied, encompassing healthcare [7,16,17], audit [18], transport and cross-docking [19,20], hospital waste collection [21], emergency response for forest fire extinguishing [22], and drone scheduling problems [23], among others.…”