Work

Replication and sequencing of unreliable jobs on m parallel machines: New results

Year: 2025

Type: article

Abstract: This paper gives new results for the problem of sequencing m copies of n unreliable jobs (i.e., jobs that have a certain probability of being successfully carried out) on m parallel machines (one copy per machine). A job is carried out if at least one of its copies is successfully completed, in which case a certain revenue is earned. If the copy of a job fails, the corresponding machine is blocked and cannot perform the subsequently scheduled job copies. The problem is to sequence the n copies of each job on each of the m machines in order to maximize the expected revenue. For the case of m = 2 , Agnetis et al. (2022) proposed a metaheuristic approach and some upper bounding schemes. Here we address the general m -machine problem, giving a simple ( 1 − 1 / e ) -approximation algorithm, an even simpler algorithm, for which we show a tight logarithmic approximation guarantee, and an additional heuristic as well as an additional metaheuristic. We provide computational results, which, along with a new upper-bounding scheme, establish the effectiveness of our approaches in practice.

Source: Computers & Operations Research

DOI: 10.1016/j.cor.2025.107085

Authors: Alessandro Agnetis, Mario Benini, Paolo Detti, Ben Hermans, Marco Pranzo, Kevin Schewior

Institutions: University of Siena, KU Leuven, University of Southern Denmark, University of Cologne

Language: English

Topic: Scheduling and Optimization Algorithms

Subfield: Industrial and Manufacturing Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,570

Funders: Fonds Wetenschappelijk Onderzoek, Ministero dell’Istruzione, dell’Università e della Ricerca, Danmarks Frie Forskningsfond, Ministero dell'Istruzione e del Merito