Worst-case and numerical analysis of heuristic algorithms for flowshop scheduling problems with a time-dependent learning effect

In this paper, we investigate a time-dependent learning effect in a flowshop scheduling problem. We assume that the time-dependent learning effect of a job was a function of the total normal processing time of jobs scheduled before the job. The following objective functions are explored: the makespan, the total flowtime, the sum of weighted completion times, the sum of the kth power of completion times, and the maximum lateness. Some heuristic algorithms with worst-case analysis for the objective functions are given. Moreover, a polynomial algorithm is proposed for the special case with identical processing time on each machine and that with an increasing series of dominating machines, respectively. Finally, the computational results to evaluate the performance of the heuristics are provided.

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

[2]  A. Nouweland,et al.  Flow-shops with a dominant machine , 1992 .

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

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

[5]  Czeslaw Smutnicki,et al.  Some results of the worst-case analysis for flow shop scheduling , 1998, Eur. J. Oper. Res..

[6]  T. C. Edwin Cheng,et al.  Single-machine scheduling with sum-of-logarithm-processing-times-based learning considerations , 2009, Inf. Sci..

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

[8]  George J. Kyparisis,et al.  Algorithms with performance guarantees for flow shops with regular objective functions , 2005 .

[9]  Dehua Xu,et al.  Notes on "some single-machine scheduling problems with general position-dependent and time-dependent learning effects" , 2011, Inf. Sci..

[10]  Adam Janiak,et al.  The learning effect: Getting to the core of the problem , 2007, Inf. Process. Lett..

[11]  Adam Janiak,et al.  A note on a makespan minimization problem with a multi-ability learning effect , 2010 .

[12]  Ji-Bo Wang,et al.  Flow shop scheduling jobs with position-dependent processing times , 2005 .

[13]  Dar-Li Yang,et al.  Minimizing the makespan in a single machine scheduling problem with a time-based learning effect , 2006, Inf. Process. Lett..

[14]  T. C. Edwin Cheng,et al.  A two-agent single-machine scheduling problem with truncated sum-of-processing-times-based learning considerations , 2011, Comput. Ind. Eng..

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

[16]  Teofilo F. Gonzalez,et al.  Flowshop and Jobshop Schedules: Complexity and Approximation , 1978, Oper. Res..

[17]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

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

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

[20]  Adam Janiak,et al.  Solution algorithms for the makespan minimization problem with the general learning model , 2009, Comput. Ind. Eng..

[21]  Wen-Chiung Lee,et al.  Scheduling problems with general effects of deterioration and learning , 2011, Inf. Sci..

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

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

[24]  S. M. Johnson,et al.  Optimal two- and three-stage production schedules with setup times included , 1954 .

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

[26]  Dar-Li Yang,et al.  Note on "Single-machine and flowshop scheduling with a general learning effect model" and "Some single-machine and m-machine flowshop scheduling problems with learning considerations" , 2010, Inf. Sci..

[27]  D. Yang,et al.  A two-machine flowshop sequencing problem with limited waiting time constraints , 1995 .

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

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

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

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

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

[33]  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..

[34]  Chin-Chia Wu,et al.  Minimizing the makespan on a single machine with learning and unequal release times , 2010, Comput. Ind. Eng..

[35]  Wen-Chiung Lee,et al.  Some single-machine and m-machine flowshop scheduling problems with learning considerations , 2009, Inf. Sci..

[36]  Gur Mosheiov,et al.  Note on scheduling with general learning curves to minimize the number of tardy jobs , 2005, J. Oper. Res. Soc..

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

[38]  Adam Janiak,et al.  Complexity results for single-machine scheduling with positional learning effects , 2008, J. Oper. Res. Soc..

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

[40]  Dehua Xu,et al.  Some scheduling problems with general position-dependent and time-dependent learning effects , 2009, Inf. Sci..

[41]  Wen-Chiung Lee,et al.  A single-machine learning effect scheduling problem with release times , 2010 .

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

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

[44]  R. M. Wyskida,et al.  Cost Estimator's Reference Manual , 1987 .

[45]  Adam Janiak,et al.  Experience-Based Approach to Scheduling Problems With the Learning Effect , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.