Single‐machine and two‐machine flowshop scheduling problems with truncated position‐based learning functions

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.