Some scheduling problems with general position-dependent and time-dependent learning effects

In scheduling problems with learning effects, most of the research is based on specific learning functions. In this paper, we develop a general model with learning effects where the actual processing time of a job is not only a function of the total normal processing times of the jobs already processed, but also a function of the job's scheduled position. In particular, it is shown that some single machine scheduling problems and m-machine permutation flowshop problems are still polynomially solvable under the proposed model. These results are significant extensions of some of the existing results on learning effects in the literature.

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

[2]  Wen-Chiung Lee,et al.  A two-machine flowshop maximum tardiness scheduling problem with a learning effect , 2006 .

[3]  Dar-Li Yang,et al.  Minimizing the total completion time in a single-machine scheduling problem with a time-dependent learning effect , 2006, Eur. J. Oper. Res..

[4]  Xingong Zhang,et al.  Machine scheduling problems with a general learning effect , 2010, Math. Comput. Model..

[5]  W. Townsend.  The Single Machine Problem with Quadratic Penalty Function of Completion Times: A Branch-and-Bound Solution , 1978 .

[6]  Dirk Simons,et al.  Common due date scheduling with autonomous and induced learning , 2004, Eur. J. Oper. Res..

[7]  Wen-Chiung Lee,et al.  Heuristic algorithms for solving the maximum lateness scheduling problem with learning considerations , 2007, Comput. Ind. Eng..

[8]  Gur Mosheiov,et al.  Parallel machine scheduling with a learning effect , 2001, J. Oper. Res. Soc..

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

[10]  T. C. Edwin Cheng,et al.  Single-machine scheduling with deteriorating jobs and learning effects to minimize the makespan , 2007, Eur. J. Oper. Res..

[11]  Adedeji Badiru,et al.  Computational survey of univariate and multivariate learning curve models , 1992 .

[12]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

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

[14]  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..

[15]  T. C. Edwin Cheng,et al.  Some scheduling problems with sum-of-processing-times-based and job-position-based learning effects , 2008, Inf. Sci..

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

[17]  Dehua Xu,et al.  Parallel machine scheduling with almost periodic maintenance and non-preemptive jobs to minimize makespan , 2008, Comput. Oper. Res..

[18]  Dehua Xu,et al.  Makespan Minimization for Two Parallel Machines Scheduling with a Periodic Availability Constraint: The Preemptive Offline Version , 2009, 2010 Third International Joint Conference on Computational Science and Optimization.

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

[20]  Dehua Xu,et al.  A note on "scheduling of nonresumable jobs and flexible maintenance activities on a single machine to minimize makespan" , 2009, Eur. J. Oper. Res..

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

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

[23]  Wen-Chiung Lee,et al.  Single-machine scheduling problems with a learning effect , 2008 .

[24]  Kwang-Hyun Cho,et al.  Real-time preemptive scheduling of sporadic tasks based on supervisory control of discrete event systems , 2008, Inf. Sci..

[25]  J.-B. Wang,et al.  A note on scheduling problems with learning effect and deteriorating jobs , 2006, Int. J. Syst. Sci..

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

[27]  Adam Janiak,et al.  Scheduling jobs with position-dependent processing times , 2004, J. Oper. Res. Soc..

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

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

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

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

[32]  Maurice Bonney,et al.  The economic manufacture/order quantity (EMQ/EOQ) and the learning curve: Past, present, and future , 1999 .

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

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

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

[36]  Bertrand M. T. Lin.  Complexity results for single-machine scheduling with positional learning effects , 2007, J. Oper. Res. Soc..

[37]  Dehua Xu,et al.  Scheduling jobs under increasing linear machine maintenance time , 2010, J. Sched..

[38]  Dar-Li Yang,et al.  Single-machine scheduling problems with the time-dependent learning effect , 2007, Comput. Math. Appl..

[39]  Chin-Chia Wu,et al.  Minimizing total completion time in a two-machine flowshop with a learning effect , 2004 .