A note on the optimal sequence position for a rate-modifying activity under simple linear deterioration

This paper addresses the integration of two emerging classes of scheduling problems which, for the most part, have evolved independently. These problem classes are (i) scheduling problems with time-dependent processing times and (ii) scheduling problems with rate-modifying activities (RMAs). The integration of these two concepts is motivated by human operators who experience fatigue while carrying out tasks and take rest breaks for recovery, but is also applicable to machines that experience performance degradation over time and require maintenance in order to sustain acceptable production rates. We explore a sequence-independent, single processor makespan problem with position-dependent processing times and prove that under certain conditions, the optimal policy is to schedule the RMA in the middle of the task sequence.

[1]  Chung-Yee Lee,et al.  Single-machine scheduling with maintenance and repair rate-modifying activities , 2001, Eur. J. Oper. Res..

[2]  T.C.E. Cheng,et al.  Single machine scheduling with a restricted rate‐modifying activity , 2005 .

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

[4]  Valery S. Gordon,et al.  A note: Common due date assignment for a single machine scheduling with the rate-modifying activity , 2009, Comput. Oper. Res..

[5]  Daniel Oron,et al.  Due-date assignment and maintenance activity scheduling problem , 2006, Math. Comput. Model..

[6]  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..

[7]  T. C. Edwin Cheng,et al.  Parallel-batch scheduling of deteriorating jobs with release dates to minimize the makespan , 2011, Eur. J. Oper. Res..

[8]  Chris N. Potts,et al.  Single machine scheduling models with deterioration and learning: handling precedence constraints via priority generation , 2008, J. Sched..

[9]  Bahram Alidaee,et al.  Scheduling on a Single Processor with Variable Speed , 1996, Inf. Process. Lett..

[10]  Suh-Jenq Yang,et al.  Minimizing the makespan on single-machine scheduling with aging effect and variable maintenance activities , 2010 .

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

[12]  Shijie Sun,et al.  Scheduling linear deteriorating jobs with rejection on a single machine , 2009, Eur. J. Oper. Res..

[13]  S. Eilon.  ON A MECHANISTIC APPROACH TO FATIGUE AND REST PERIODS , 1964 .

[14]  C.-Y. Lee,et al.  Machine scheduling with a rate-modifying activity , 2001, Eur. J. Oper. Res..

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

[16]  Gur Mosheiov,et al.  New Results On Sequencing With Rate Modification , 2003 .

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

[18]  Ravi S. Adapathya,et al.  Strategic Behavior, Workload, and Performance in Task Scheduling , 1991 .