Single-machine scheduling problems with both deteriorating jobs and learning effects

Abstract In this paper we consider the single-machine scheduling problems with job-position-based and sum-of-processing-times based processing times. The real processing time of a job is a function of its position and the total processing time of the jobs that are in front of it in the sequence. The objective is to minimize the makespan, and to minimize the mean finish time. We prove that some special cases are polynomially solvable under some restrictions of the parameters. In addition, for some another special cases of minimization of the mean finish time and the makespan, we show that an optimal schedule is V-shaped with respect to job normal processing times. Then, we propose a heuristic based on the V-shaped property, and show through a computational experiment that it performs efficiently.

[1]  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..

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

[3]  Ji-Bo Wang,et al.  A due-date assignment problem with learning effect and deteriorating jobs , 2010 .

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

[5]  Lixin Tang,et al.  Two-machine flowshop scheduling problems involving a batching machine with transportation or deterioration consideration , 2009 .

[6]  John J. Kanet,et al.  Minimizing Variation of Flow Time in Single Machine Systems , 1981 .

[7]  Gur Mosheiov,et al.  A note on scheduling deteriorating jobs , 2005, Math. Comput. Model..

[8]  Lixin Tang,et al.  Two-Agent Scheduling with Linear Deteriorating Jobs on a Single Machine , 2008, COCOON.

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

[10]  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..

[11]  Wen-Chiung Lee,et al.  A Note on Deteriorating Jobs and Learning in Single-Machine Scheduling Problems , 2004 .

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

[13]  G. Wang,et al.  Single-machine scheduling with past-sequence-dependent setup times and effects of deterioration and learning , 2009 .

[14]  Wen-Chiung Lee,et al.  A note on single-machine group scheduling problems with position-based learning effect , 2009 .

[15]  Ji-Bo Wang,et al.  Two-machine flow shop problem with effects of deterioration and learning , 2009, Comput. Ind. Eng..

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

[17]  Wen-Chiung Lee,et al.  Multi-machine scheduling with deteriorating jobs and scheduled maintenance , 2008 .

[18]  Ji-Bo Wang,et al.  Learning effect and deteriorating jobs in the single machine scheduling problems , 2009 .

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

[20]  Gur Mosheiov,et al.  A due-window assignment problem with position-dependent processing times , 2008, J. Oper. Res. Soc..

[21]  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 .

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

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

[24]  T. C. Edwin Cheng,et al.  Scheduling Problems with the Effects of deterioration and Learning , 2007, Asia Pac. J. Oper. Res..

[25]  Yu-Hsiang Chung,et al.  Minimizing the total completion time in permutation flow shop with machine-dependent job deterioration rates , 2009, Comput. Oper. Res..

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

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

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

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

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