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

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.

[1]  Chang-Shing Lee,et al.  A genetic fuzzy agent using ontology model for meeting scheduling system , 2006, Inf. Sci..

[2]  Shijie Sun,et al.  A note on flow shop scheduling problems with a learning effect on no-idle dominant machines , 2007, Appl. Math. Comput..

[3]  Gur Mosheiov,et al.  Scheduling with general job-dependent learning curves , 2003, Eur. J. Oper. Res..

[4]  Tamer Eren,et al.  Minimizing total tardiness in a scheduling problem with a learning effect , 2007 .

[5]  Reza Tavakkoli-Moghaddam,et al.  A hybrid multi-objective immune algorithm for a flow shop scheduling problem with bi-objectives: Weighted mean completion time and weighted mean tardiness , 2007, Inf. Sci..

[6]  Zhiyong Xu,et al.  Some results of the worst-case analysis for flow shop scheduling with a learning effect , 2008, Annals of Operations Research.

[7]  Ji-Bo Wang,et al.  Single-machine scheduling problems with the effects of learning and deterioration , 2007 .

[8]  Louis E. Yelle.  THE LEARNING CURVE: HISTORICAL REVIEW AND COMPREHENSIVE SURVEY , 1979 .

[9]  Ertan Güner,et al.  A bicriteria flowshop scheduling with a learning effect , 2008 .

[10]  Chin-Chia Wu,et al.  A bi-criteria two-machine flowshop scheduling problem with a learning effect , 2006, J. Oper. Res. Soc..

[11]  Michael Pinedo,et al.  Scheduling: Theory, Algorithms, and Systems , 1994 .

[12]  Dirk Biskup,et al.  A state-of-the-art review on scheduling with learning effects , 2008, Eur. J. Oper. Res..

[13]  T. P. Wright,et al.  Factors affecting the cost of airplanes , 1936 .

[14]  B. Williams,et al.  Operations management. , 2001, Optometry.

[15]  Adam Janiak,et al.  A new approach to the learning effect: Beyond the learning curve restrictions , 2008, Comput. Oper. Res..

[16]  Christos Koulamas,et al.  Single-machine and two-machine flowshop scheduling with general learning functions , 2007, Eur. J. Oper. Res..

[17]  Wen-Chiung Lee,et al.  A bi-criterion single-machine scheduling problem with learning considerations , 2004, Acta Informatica.

[18]  Barry Render,et al.  Operations Management , 2019, CCSP (ISC)2 Certified Cloud Security Professional Official Study Guide, 2nd Edition.

[19]  Dirk Biskup,et al.  Single-machine scheduling with learning considerations , 1999, Eur. J. Oper. Res..

[20]  Ruey-Shun Chen,et al.  A study on the critical success factors for corporations embarking on knowledge community-based e-learning , 2007, Inf. Sci..

[21]  J.-B. Wang,et al.  Flow-shop scheduling with a learning effect , 2005, J. Oper. Res. Soc..

[22]  Ammar Oulamara,et al.  Permutation flowshop scheduling problems with time lags to minimize the weighted sum of machine completion times , 2008 .

[23]  J.-B. Wang.  Single machine scheduling with a time-dependent learning effect and deteriorating jobs , 2009, J. Oper. Res. Soc..

[24]  B. Lina,et al.  Development of new features of ant colony optimization for flowshop scheduling $ , 2008 .

[25]  Gur Mosheiov,et al.  Scheduling problems with a learning effect , 2001, Eur. J. Oper. Res..

[26]  Dar-Li Yang,et al.  Single-machine group scheduling with a time-dependent learning effect , 2006, Comput. Oper. Res..

[27]  Guoqing Wang,et al.  Single Machine Scheduling with Learning Effect Considerations , 2000, Ann. Oper. Res..

[28]  Wayne E. Smith.  Various optimizers for single‐stage production , 1956 .

[29]  Bernard W. Taylor,et al.  Operations management : multimedia version , 2000 .