Single-machine and two-machine flowshop scheduling problems with truncated position-based learning functions |
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Authors: | C-C Wu Y Yin S-R Cheng |
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Institution: | 1.Feng Chia University,Taichung,Taiwan;2.East China Institute of Technology,Jiangxi,China;3.Cheng Shiu University,Kaohsiung County,Taiwan |
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Abstract: | Scheduling with learning effects has received growing attention nowadays. A well-known learning model is called ‘position-based learning’ in which the actual processing time of a job is a non-increasing function of its position to be processed. However, the actual processing time of a given job drops to zero precipitously as the number of jobs increases. Motivated by this observation, we propose two truncated learning models in single-machine scheduling problems and two-machine flowshop scheduling problems with ordered job processing times, respectively, where the actual processing time of a job is a function of its position and a control parameter. Under the proposed learning models, we show that some scheduling problems can be solved in polynomial time. In addition, we further analyse the worst-case error bounds for the problems to minimize the total weighted completion time, discounted total weighted completion time and maximum lateness. |
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