Some polynomial solvable single-machine scheduling problems with a truncation sum-of-processing-times-based learning effect

Recently, scheduling with learning effects has received growing attention. A well-known learning model is called 'sum-of processing-times-based learning' where 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, this paper develops a truncated learning model in which the actual job processing time not only depends on the processing times of the jobs already processed but also depends on a control parameter. The use of the truncated function is to model the phenomenon that the learning of a human activity is limited. In this paper, some single-machine scheduling problems can be solved in polynomial time. Besides, the error bounds are also provided for the problems to minimise the maximum lateness and the total weighted completion time. [Received 20 September 2010; Revised 11 November 2010, 22 January 2011; Accepted 5 February 2011]