A note on machine scheduling with sum-of-logarithm-processing-time-based and position-based learning effects

Authors:
Xingong Zhang;Guangle Yan;Wanzhen Huang;Guochun Tang
Affiliations:
College of Mathematics Science, Chongqing Normal University, China;Business School, University of Shanghai for Science and Technology, China;Department of Mathematical Sciences, Lakehead University, Canada;Institute of Management Engineering, Shanghai Second Polytechnic University, China
Venue:
Information Sciences: an International Journal
Year:
2012

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Abstract

Recently, Biskup [2] classifies the learning effect models in scheduling environments into two types: position-based and sum-of-processing-time-based. In this paper, we study scheduling problem with sum-of-logarithm-processing-time-based and position-based learning effects. We show that the single machine scheduling problems to minimize the makespan and the total completion time can both be solved by the smallest (normal) processing time first (SPT) rule. We also show that the problems to minimize the maximum lateness, the total weighted completion times and the total tardiness have polynomial-time solutions under agreeable WSPT rule and agreeable EDD rule. In addition, we show that m-machine permutation flowshop problems are still polynomially solvable under the proposed learning model.