Parallel machine earliness/tardiness scheduling problem under the effects of position based learning and linear/nonlinear deterioration

This paper considers a parallel machine earliness/tardiness (ET) scheduling problem with different penalties under the effects of position based learning and linear and nonlinear deterioration. The problem has common due-date for all jobs, and effects of learning and deterioration are considered simultaneously. By the effects of learning we mean that the job processing time decreases along the sequence of partly similar jobs, and by the effects of deterioration we mean slowing performance or time increases along the sequence of jobs. This study shows that optimal solution for ET scheduling problem under effects of learning and deterioration is V-shape schedule under certain agreeable conditions. Furthermore, we design a mathematical model for the problem under study and algorithm and lower bound procedure to solve larger test problems. The algorithm can solve problems of 1000 jobs and four machines within 3s on average. The performance of the algorithm is evaluated using results of the mathematical model.

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

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

[3]  Gary D. Scudder,et al.  Sequencing with Earliness and Tardiness Penalties: A Review , 1990, Oper. Res..

[4]  Gur Mosheiov,et al.  Λ-Shaped Policies to Schedule Deteriorating Jobs , 1996 .

[5]  Anup K. Sen,et al.  Single machine weighted earliness-tardiness penalty problem with a common due date , 2001, Comput. Oper. Res..

[6]  Bahram Alidaee,et al.  Scheduling with time dependent processing times: Review and extensions , 1999, J. Oper. Res. Soc..

[7]  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..

[8]  Guoqing Wang,et al.  Parallel machine earliness and tardiness scheduling with proportional weights , 2003, Comput. Oper. Res..

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

[10]  T. C. Edwin Cheng,et al.  Due-date assignment and single machine scheduling with deteriorating jobs , 2004, J. Oper. Res. Soc..

[11]  Jatinder N. D. Gupta,et al.  Single facility scheduling with nonlinear processing times , 1988 .

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

[13]  Gur Mosheiov,et al.  V-Shaped Policies for Scheduling Deteriorating Jobs , 1991, Oper. Res..

[14]  T. C. Edwin Cheng,et al.  Minimizing total completion time in a two-machine flow shop with deteriorating jobs , 2006, Appl. Math. Comput..

[15]  B. Lin,et al.  Minimization of maximum lateness under linear deterioration , 2003 .

[16]  Sushil K. Gupta,et al.  Minimizing the makespan with late start penalties added to processing times in a single facility scheduling problem , 1990 .

[17]  Wen-Chiung Lee,et al.  Two-machine flowshop scheduling to minimize mean flow time under linear deterioration , 2006 .

[18]  Débora P. Ronconi,et al.  Minimizing earliness and tardiness penalties in a single-machine problem with a common due date , 2005, Eur. J. Oper. Res..

[19]  Frank Werner,et al.  Heuristic algorithms for unrelated parallel machine scheduling with a common due date, release dates, and linear earliness and tardiness penalties , 2001 .

[20]  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 .

[21]  Esther M. Arkin,et al.  Weighted-Tardiness Scheduling on Parallel Machines with Proportional Weights , 1991, Oper. Res..

[22]  Ji-Bo Wang,et al.  Flow shop scheduling with deteriorating jobs under dominating machines , 2006 .

[23]  Costas P. Pappis,et al.  Scheduling jobs with values exponentially deteriorating over time , 2002 .

[24]  Ji-Bo Wang,et al.  Flow shop scheduling problems with decreasing linear deterioration under dominant machines , 2007, Comput. Oper. Res..

[25]  Subhash C. Sarin,et al.  Work allocation to stations with varying learning slopes and without buffers , 2008, Eur. J. Oper. Res..

[26]  Marc E. Posner,et al.  Earliness-Tardiness Scheduling Problems, I: Weighted Deviation of Completion Times About a Common Due Date , 1991, Oper. Res..

[27]  Subhash C. Sarin,et al.  Optimal allocation of work in assembly lines for lots with homogenous learning , 2006, Eur. J. Oper. Res..

[28]  C. T. Ng,et al.  A note on a fully polynomial-time approximation scheme for parallel-machine scheduling with deteriorating jobs , 2007 .

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

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

[31]  Gur Mosheiov,et al.  Scheduling jobs under simple linear deterioration , 1994, Comput. Oper. Res..

[32]  Sid Browne,et al.  Scheduling Deteriorating Jobs on a Single Processor , 1990, Oper. Res..

[33]  T. C. Edwin Cheng,et al.  Single machine scheduling with step-deteriorating processing times , 2001, Eur. J. Oper. Res..

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

[35]  Zhiwei Zhu,et al.  Minimizing the sum of earliness/tardiness in multi-machine scheduling: a mixed integer programming approach , 2000 .

[36]  Dar-Li Yang,et al.  Some scheduling problems with deteriorating jobs and learning effects , 2010, Comput. Ind. Eng..

[37]  Bertrand M. T. Lin,et al.  A concise survey of scheduling with time-dependent processing times , 2004, Eur. J. Oper. Res..

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

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