Complexity analysis and approximation algorithms for the single-machine scheduling problem with workload-dependent maintenance activities

This paper considers the single-machine scheduling problem with workload-dependent maintenance activities of variable length. The time needed to perform a maintenance activity is a function of the total processing time of the jobs that are processed between the starting time of this activity and the...

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Bibliographic Details
Published in:Journal of scheduling Vol. 28; no. 4; pp. 391 - 406
Main Authors: Liu, Peihai, Gu, Manzhan, Lu, Xiwen
Format: Journal Article
Language:English
Published: New York Springer US 01.08.2025
Springer Nature B.V
Subjects:
Algorithms
Approximation
Artificial Intelligence
Business and Management
Calculus of Variations and Optimal Control; Optimization
Completion time
Complexity
Decision making
Maintenance
Operations Research/Decision Theory
Optimization
Preventive maintenance
Scheduling
Supply Chain Management
Workload
Workloads
Single-machine scheduling
Approximation algorithms
Computational complexity
Maintenance activities
ISSN:1094-6136, 1099-1425
Online Access:Get full text
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Summary:This paper considers the single-machine scheduling problem with workload-dependent maintenance activities of variable length. The time needed to perform a maintenance activity is a function of the total processing time of the jobs that are processed between the starting time of this activity and the end of the last previous activity. In the case where the function is concave, we study the computational complexity of the three problems with the goal of minimizing the makespan, the total completion time, and the total weighted completion time, respectively. In addition, we propose a 2-approximation algorithm for the first problem and a 2.5-approximation algorithm for the second problem.
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ISSN:1094-6136
1099-1425
DOI:10.1007/s10951-025-00842-3