Single machine scheduling with general time-dependent deterioration, position-dependent learning and past-sequence-dependent setup times

The paper deals with single machine scheduling problems with setup time considerations where the actual processing time of a job is not only a non-decreasing function of the total normal processing times of the jobs already processed, but also a non-increasing function of the job’s position in the sequence. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are past-sequence-dependent (p-s-d). We consider the following objective functions: the makespan, the total completion time, the sum of the δth (δ ≥ 0) power of job completion times, the total weighted completion time and the maximum lateness. We show that the makespan minimization problem, the total completion time minimization problem and the sum of the δ th (δ ≥ 0) power of job completion times minimization problem can be solved by the smallest (normal) processing time first (SPT) rule, respectively. We also show that the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time under certain conditions.

[1]  Adam Janiak,et al.  Scheduling Problems with Learning and Ageing Effects: A Survey , 2011 .

[2]  Ji-Bo Wang,et al.  Worst-case behavior of simple sequencing rules in flow shop scheduling with general position-dependent learning effects , 2011, Ann. Oper. Res..

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

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

[5]  Wen-Chiung Lee,et al.  Single-machine scheduling with general sum-of-processing-time-based and position-based learning effects , 2011 .

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

[7]  T.C.E. Cheng,et al.  Scheduling problems with deteriorating jobs and learning effects including proportional setup times , 2010, Comput. Ind. Eng..

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

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

[10]  Li Sun,et al.  Single-machine scheduling problems with deteriorating jobs and learning effects , 2009, Comput. Ind. Eng..

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

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

[13]  Li-Yan Wang,et al.  Single-machine scheduling with a time-dependent deterioration , 2009 .

[14]  Ji-Bo Wang,et al.  Scheduling jobs with truncated exponential learning functions , 2013, Optim. Lett..

[15]  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.

[16]  Lixin Tang,et al.  Single Machine Scheduling with Deteriorating Jobs , 2008, 2008 4th International Conference on Wireless Communications, Networking and Mobile Computing.

[17]  Dar-Li Yang,et al.  Single machine scheduling with past-sequence-dependent setup times and learning effects , 2007, Inf. Process. Lett..

[18]  Suh-Jenq Yang,et al.  Single-machine scheduling with past-sequence-dependent delivery times and learning effect , 2011 .

[19]  Jatinder N. D. Gupta,et al.  A review of scheduling research involving setup considerations , 1999 .

[20]  Chin-Chia Wu,et al.  Single-machine and two-machine flowshop scheduling problems with truncated position-based learning functions , 2013, J. Oper. Res. Soc..

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

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

[23]  Feng Chu,et al.  Single machine scheduling with past-sequence-dependent delivery times and learning effect , 2013, 2013 10th IEEE INTERNATIONAL CONFERENCE ON NETWORKING, SENSING AND CONTROL (ICNSC).

[24]  T.C.E. Cheng,et al.  Single-machine scheduling with deteriorating jobs and past-sequence-dependent setup times , 2011 .

[25]  Ji-Bo Wang,et al.  Single-machine scheduling with past-sequence-dependent setup times and time-dependent learning effect , 2008, Comput. Ind. Eng..

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

[27]  J.-B. Wang,et al.  Worst-case analysis for flow shop scheduling problems with an exponential learning effect , 2012, J. Oper. Res. Soc..

[28]  Wen-Chiung Lee,et al.  A note on single-machine scheduling with general learning effect and past-sequence-dependent setup time , 2011, Comput. Math. Appl..

[29]  Dan Wang,et al.  Minimizing makespan in a two-machine flow shop with effects of deterioration and learning , 2011, Optimization Letters.

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

[31]  Christos Koulamas,et al.  Single-machine scheduling problems with past-sequence-dependent setup times , 2008, Eur. J. Oper. Res..

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

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

[34]  Ming Liu,et al.  Parallel-machine scheduling with past-sequence-dependent delivery times and learning effect , 2013 .

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

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

[37]  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..

[38]  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..

[39]  Ji-Bo Wang,et al.  Single machine total completion time minimization scheduling with a time-dependent learning effect and deteriorating jobs , 2012, Int. J. Syst. Sci..

[40]  Ji-Bo Wang,et al.  A revision of some single-machine and m-machine flowshop scheduling problems with learning considerations , 2012, Inf. Sci..

[41]  Chou-Jung Hsu,et al.  Unrelated parallel machine scheduling with past-sequence-dependent setup time and learning effects , 2011 .

[42]  Wen-Chiung Lee,et al.  Scheduling with general position-based learning curves , 2011, Inf. Sci..

[43]  MengChu Zhou,et al.  Single-Machine Scheduling With Job-Position-Dependent Learning and Time-Dependent Deterioration , 2012, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

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

[45]  Li-Yan Wang,et al.  A note on single-machine total completion time problem with general deteriorating function , 2009 .

[46]  Dar-Li Yang,et al.  Single-machine scheduling problems with past-sequence-dependent delivery times and position-dependent processing times , 2012, J. Oper. Res. Soc..

[47]  Radoslaw Rudek,et al.  Computational complexity and solution algorithms for flowshop scheduling problems with the learning effect , 2011, Comput. Ind. Eng..

[48]  Wen-Chiung Lee,et al.  A note on single-machine makespan problem with general deteriorating function , 2009 .

[49]  Ji-Bo Wang,et al.  Single machine scheduling with time-dependent deterioration and exponential learning effect , 2010, Comput. Ind. Eng..

[50]  Chin-Chia Wu,et al.  Some single-machine scheduling problems with a truncation learning effect , 2011, Comput. Ind. Eng..

[51]  Wen-Chiung Lee,et al.  Single-machine group-scheduling problems with deteriorating setup times and job-processing times , 2008 .

[52]  Chin-Chia Wu,et al.  A Truncated Sum of Processing‐Times–Based Learning Model for a Two‐Machine Flowshop Scheduling Problem , 2014 .

[53]  Chin-Chia Wu,et al.  Some polynomial solvable single-machine scheduling problems with a truncation sum-of-processing-times based learning effect , 2012 .

[54]  Ping Ji,et al.  Parallel machines scheduling with deteriorating and learning effects , 2012, Optimization Letters.

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