Some scheduling problems with sum-of-processing-times-based and job-position-based learning effects

Authors:
T.C. Edwin Cheng;Chin-Chia Wu;Wen-Chiung Lee
Affiliations:
Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;Department of Statistics, Feng Chia University, Taichung, Taiwan;Department of Statistics, Feng Chia University, Taichung, Taiwan
Venue:
Information Sciences: an International Journal
Year:
2008

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Abstract

In this paper we introduce a new scheduling model with learning effects in which the actual processing time of a job is a function of the total normal processing times of the jobs already processed and of the job's scheduled position. We show that the single-machine problems to minimize makespan and total completion time are polynomially solvable. In addition, we show that the problems to minimize total weighted completion time and maximum lateness are polynomially solvable under certain agreeable conditions. Finally, we present polynomial-time optimal solutions for some special cases of the m-machine flowshop problems to minimize makespan and total completion time.