Makespan optimization in a single-machine scheduling problem with dynamic job ready times—Complexity and algorithms

An industrial problem encountered in steel mills is considered in the paper. The problem is formulated as a single-processor scheduling problem with a dynamic model of the task release date. In this model, a task is released for processing when its preprocessing is in the final state. The instantane...

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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 182; pp. 162 - 168
Main Authors: Gorczyca, Mateusz, Janiak, Adam, Janiak, Wladyslaw, Dymański, Marcin
Format: Journal Article
Language:English
Published: Elsevier B.V 19.02.2015
Subjects:
Algorithms
Computational complexity
Iron and steel plants
Mathematical models
Metaheuristics
Preprocessing
Reduction
Resource allocation
Scheduling
Simulated annealing
Steel mills
Tasks
Scheduling
Metaheuristics
Computational complexity
Resource allocation
ISSN:0166-218X, 1872-6771
Online Access:Get full text
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Summary:An industrial problem encountered in steel mills is considered in the paper. The problem is formulated as a single-processor scheduling problem with a dynamic model of the task release date. In this model, a task is released for processing when its preprocessing is in the final state. The instantaneous rate of the change of the preprocessing state (from the initial to the final one) depends on the amount of resource allotted to the task. The resource available for task preprocessing is renewable and upper bounded. The problem consists in establishing the task sequence and the resource allocation that minimize the makespan. This problem has already been considered in the literature, but its complexity has not been formally proved. The proof of NP-hardness by polynomial reduction from the partition problem is presented in this paper. Two metaheuristics (simulated annealing and tabu search) are proposed to solve the problem. Both are tested, and the results are analyzed.
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ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2013.10.003