Single machine scheduling with exponential sum-of-logarithm-processing-times based learning effect |
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| Authors: | Ji-Bo Wang Linhui Sun Linyan Sun |
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| Institution: | 1. Operations Research and Cybernetics Institute, School of Science, Shenyang Institute of Aeronautical Engineering, Shenyang 110136, People’s Republic of China;2. Knowledge Management and Innovation Research Centre, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China;3. School of Business Administration, Xi’an University of Technology, Xi’an 710049, People’s Republic of China;4. The State Key Laboratory on Mechanic Manufacturing, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China;5. Management School, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China;6. The Key Laboratory of the Ministry of Education on Process Control and Efficiency, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China |
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| Abstract: | In this paper we consider the single machine scheduling problems with exponential sum-of-logarithm-processing-times based learning effect. By the exponential sum-of-logarithm-processing-times based learning effect, we mean that the processing time of a job is defined by an exponent function of the sum of the logarithm of the processing times of the jobs already processed. We consider the following objective functions: the makespan, the total completion time, the sum of the quadratic job completion times, the total weighted completion time and the maximum lateness. We show that the makespan minimization problem, the total completion time minimization problem and the sum of the quadratic job completion times minimization problem can be solved by the smallest (normal) processing time first (SPT) rule, respectively. We also show that the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time under certain conditions. |
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| Keywords: | Scheduling Single machine Learning effect |
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