A note on machine scheduling with sum-of-logarithm-processing-time-based and position-based learning effects |
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| Authors: | Xingong Zhang Guangle Yan Wanzhen Huang Guochun Tang |
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| Affiliation: | 1. Depto de Ciencias de la Computación e Inteligencia Artificial, E.T.S. Ingeniería Informática y Telecomunicación, CITIC-UGR, Universidad de Granada, Granada, Spain;2. Depto. Lenguajes y Sistemas Informáticos, E.T.S. Ingeniería Informática y Telecomunicación, CITIC-UGR, Universidad de Granada, Granada, Spain;3. Interdisciplinary Computing and Complex BioSystems (ICOS) Research Group, School of Computing Science, Newcastle University, Newcastle upon Tyne, Tyne and Wear, United Kingdom;1. Department of Computer Science, University of Holguín, Holguín, Cuba;2. Department of Computer Science, Universidad Central de Las Villas, Villa Clara, Cuba;3. Department of Computer Science and Numerical Analysis, University of Córdoba, Córdoba, Spain;4. Department of Computer Science, King Abdulaziz University, Jeddah, Saudi Arabia;1. Department of Computer Science, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand;2. Department of Computer Science, Faculty of Art and Science, Sisaket Rajabhat University, Sisaket 33000, Thailand |
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| Abstract: | Recently, Biskup 2] classifies the learning effect models in scheduling environments into two types: position-based and sum-of-processing-time-based. In this paper, we study scheduling problem with sum-of-logarithm-processing-time-based and position-based learning effects. We show that the single machine scheduling problems to minimize the makespan and the total completion time can both be solved by the smallest (normal) processing time first (SPT) rule. We also show that the problems to minimize the maximum lateness, the total weighted completion times and the total tardiness have polynomial-time solutions under agreeable WSPT rule and agreeable EDD rule. In addition, we show that m-machine permutation flowshop problems are still polynomially solvable under the proposed learning model. |
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