Some single-machine scheduling problems with a truncation learning effect

  • Authors:

  • Chin-Chia Wu;Yunqiang Yin;Shuenn-Ren Cheng

  • Affiliations:

  • Department of Statistics, Feng Chia University, Taichung, Taiwan;College of Mathematics and Information Sciences, East China Institute of Technology, Fuzhou, Jiangxi 344000, China;Graduate Institute of Business Administration, Cheng Shiu University, Kaohsiung County, Taiwan

  • Venue:
  • Computers and Industrial Engineering
  • Year:
  • 2011

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Abstract

Scheduling with learning effects has received growing attention nowadays. A well-known learning model is called ''sum-of processing-times-based learning'' in which the actual processing time of a job is a non-increasing function of the jobs already processed. However, the actual processing time of a given job drops to zero precipitously when the normal job processing times are large. Motivated by this observation, we propose a truncation learning model where the actual job processing time is a function which depends not only on the processing times of the jobs already processed but also on a control parameter. The use of the truncated function is to model the phenomenon that the learning of a human activity is limited. Under the proposed learning model, we show that some single-machine scheduling problems can be solved in polynomial time. In addition, we further provide the worst-case error bounds for the problems to minimize the maximum lateness and total weighted completion time.