Exact and heuristic algorithms for parallel-machine scheduling with DeJong's learning effect

We consider a parallel-machine scheduling problem with a learning effect and the makespan objective. The impact of the learning effect on job processing times is modelled by the general DeJong's learning curve. For this NP-hard problem we propose two exact algorithms: a sequential branch-and-bound algorithm and a parallel branch-and-bound algorithm. We also present the results of experimental evaluation of these algorithms on a computational cluster. Finally, we use the exact algorithms to estimate the performance of two greedy heuristic scheduling algorithms for the problem.

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

[3]  Dar-Li Yang,et al.  Erratum to: "Machine scheduling with a general learning effect" [Math. Comput. Modelling 51(1-2) (2010) 84-90] , 2010, Math. Comput. Model..

[4]  E. L. Lawler,et al.  Branch-and-Bound Methods: A Survey , 1966, Oper. Res..

[5]  茨木 俊秀,et al.  Enumerative approaches to combinatorial optimization , 1987 .

[6]  Abraham Seidmann,et al.  The Effects of Imposed Learning Curves on Performance Improvements , 1988 .

[7]  Ertan Güner,et al.  Minimizing the earliness/tardiness costs on parallel machine with learning effects and deteriorating jobs: a mixed nonlinear integer programming approach , 2008 .

[8]  Joseph Y.-T. Leung,et al.  Handbook of Scheduling: Algorithms, Models, and Performance Analysis , 2004 .

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

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

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

[12]  Dvir Shabtay,et al.  A survey of scheduling with controllable processing times , 2007, Discret. Appl. Math..

[13]  Maciej Drozdowski,et al.  Scheduling for Parallel Processing , 2009, Computer Communications and Networks.

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

[15]  Wen-Chiung Lee,et al.  Single-machine and flowshop scheduling with a general learning effect model , 2009, Comput. Ind. Eng..

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

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

[18]  T. C. Edwin Cheng,et al.  Some scheduling problems with deteriorating jobs and learning effects , 2008, Comput. Ind. Eng..

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

[20]  Xiaochun Jiang,et al.  Taxonomy for integrating scheduling theory and human factors: Review and research opportunities , 2009 .

[21]  Jack Dongarra,et al.  MPI: The Complete Reference , 1996 .

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

[23]  Tamer Eren,et al.  A bicriteria parallel machine scheduling with a learning effect , 2009 .

[24]  Tamer Eren,et al.  A note on minimizing maximum lateness in an m-machine scheduling problem with a learning effect , 2009, Appl. Math. Comput..

[25]  Gur Mosheiov,et al.  Minimizing total absolute deviation of job completion times: extensions to position-dependent processing times and parallel identical machines , 2008, J. Oper. Res. Soc..

[26]  L. B.S. Raccoon A learning curve primer for software engineers , 1996, SOEN.

[27]  Greg Burns,et al.  LAM: An Open Cluster Environment for MPI , 2002 .

[28]  Tamer Eren,et al.  A bicriteria parallel machine scheduling with a learning effect of setup and removal times , 2009 .

[29]  E. Talbi Parallel combinatorial optimization , 2006 .

[30]  Wen-Chiung Lee,et al.  Erratum to 'Some single-machine and m-machine flowshop scheduling problems with learning considerations' [Inform. Sci. 179(2009) 3885-3892] , 2010, Inf. Sci..

[31]  Stanislaw Gawiejnowicz,et al.  Time-Dependent Scheduling , 2008, Monographs in Theoretical Computer Science. An EATCS Series.

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

[33]  Bernard Gendron,et al.  Parallel Branch-and-Branch Algorithms: Survey and Synthesis , 1994, Oper. Res..

[34]  Ronald L. Graham,et al.  Bounds on Multiprocessing Timing Anomalies , 1969, SIAM Journal of Applied Mathematics.

[35]  Ji-Bo Wang Erratum to: A note on flow shop scheduling problems with a learning effect on no-idle dominant machines [Appl. Math. Computation 184 (2007) 945-949] , 2008, Appl. Math. Comput..

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

[37]  V. Reddy Dondeti,et al.  Impact of learning and fatigue factors on single machine scheduling with penalties for tardy jobs , 1998, Eur. J. Oper. Res..

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

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

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

[41]  Teodor Gabriel Crainic,et al.  Parallel Branch‐and‐Bound Algorithms , 2006 .

[42]  Stanislaw Gawiejnowicz,et al.  A Note on Scheduling on a Single Processor with Speed Dependent on a Number of Executed Jobs , 1996, Inf. Process. Lett..

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

[44]  William L. Maxwell,et al.  Theory of scheduling , 1967 .

[45]  Ertan Güner,et al.  Parallel machine earliness/tardiness scheduling problem under the effects of position based learning and linear/nonlinear deterioration , 2009, Comput. Oper. Res..

[46]  Wen-Chiung Lee,et al.  A note on the total completion time problem in a permutation flowshop with a learning effect , 2009, Eur. J. Oper. Res..

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