Due-window assignment and scheduling with general position-dependent processing times involving a deteriorating and compressible maintenance activity

In this paper, we consider common due-window assignment and scheduling problems with general position-dependent processing times involving deteriorating and compressible maintenance activity on a single machine. Two models associated with maintenance activity are examined in this article, in which the maintenance length is assumed to be either time-dependent and compressible or position-dependent and compressible. The objective is to find jointly the location and size of due-window, position of maintenance as well as resource amount allocated to it, and job sequence to minimise a total cost function based on earliness, tardiness, window location, window size and resource cost. We show that the problem considered in each of the two models’ setting can be optimally solved with polynomial time algorithm by reducing to assignment problem. Finally, two examples are provided to illustrate the solution procedures.

[1]  Fatemi Ghomi S.M.T.,et al.  Multi-objective production scheduling with controllable processing times and sequence-dependent setups for deteriorating items , 2012 .

[2]  T. C. Edwin Cheng,et al.  Single-machine scheduling with a common due window , 2001, Comput. Oper. Res..

[3]  Chengbin Chu,et al.  A survey of the state-of-the-art of common due date assignment and scheduling research , 2002, Eur. J. Oper. Res..

[4]  Frank Werner,et al.  Scheduling with common due date, earliness and tardiness penalties for multimachine problems: A survey , 2004, Math. Comput. Model..

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

[6]  T.C.E. Cheng,et al.  Common due-window assignment and scheduling of linear time-dependent deteriorating jobs and a deteriorating maintenance activity , 2012 .

[7]  T. C. Edwin Cheng,et al.  Single-machine common due window assignment and scheduling to minimize the total cost , 2013, Discret. Optim..

[8]  Dehua Xu,et al.  Scheduling jobs under increasing linear machine maintenance time , 2010, J. Sched..

[9]  Suh-Jenq Yang,et al.  Two due date assignment problems with position-dependent processing time on a single-machine , 2011, Comput. Ind. Eng..

[10]  Eugeniusz Nowicki,et al.  A survey of results for sequencing problems with controllable processing times , 1990, Discret. Appl. Math..

[11]  Suh-Jenq Yang,et al.  Multiple common due dates assignment and scheduling problems with resource allocation and general position-dependent deterioration effect , 2013 .

[12]  T.C.E. Cheng,et al.  Parallel-machine scheduling with controllable processing times and rate-modifying activities to minimise total cost involving total completion time and job compressions , 2014 .

[13]  Ceyda Oguz,et al.  Two‐machine flow shop scheduling with common due window to minimize weighted number of early and tardy jobs , 2009 .

[14]  Lin Chen,et al.  Approximation Algorithms for Scheduling with a Variable Machine Maintenance , 2010, AAIM.

[15]  T.C.E. Cheng,et al.  Survey of scheduling research involving due date determination decisions , 1989 .

[16]  T. C. Edwin Cheng,et al.  Single-machine due-window assignment and scheduling with resource allocation, aging effect, and a deteriorating rate-modifying activity , 2013, Comput. Ind. Eng..

[17]  Joanna Józefowska,et al.  Just-in-Time Scheduling : Models and Algorithms for Computer and Manufacturing Systems , 2007 .

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

[19]  Suh-Jenq Yang,et al.  Scheduling with Multiple Common Due Windows Assignment and General Position-Dependent and Resource-Dependent Processing Times , 2014 .

[20]  T.C.E. Cheng,et al.  Single-machine common due-date scheduling with batch delivery costs and resource-dependent processing times , 2013 .

[21]  S. S. Panwalkar,et al.  Determination of common due window location in a single machine scheduling problem , 1996 .

[22]  Ji-Bo Wang,et al.  Parallel machines scheduling with a deteriorating maintenance activity , 2011, J. Oper. Res. Soc..

[23]  Gur Mosheiov,et al.  Scheduling a maintenance activity and due-window assignment on a single machine , 2009, Comput. Oper. Res..

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

[25]  T. C. Edwin Cheng,et al.  Single-machine due-window assignment and scheduling with job-dependent aging effects and deteriorating maintenance , 2010, Comput. Oper. Res..

[26]  J. J. Kanet.  Minimizing the average deviation of job completion times about a common due date , 1981 .

[27]  T. C. Edwin Cheng,et al.  Two-stage flowshop earliness and tardiness machine scheduling involving a common due window , 2004 .

[28]  Raymond G. Vickson,et al.  Two Single Machine Sequencing Problems Involving Controllable Job Processing Times , 1980 .

[29]  Daniel Oron,et al.  Minimizing the number of tardy jobs on a proportionate flowshop with general position-dependent processing times , 2012, Comput. Oper. Res..

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

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

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

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

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

[35]  Vitaly A. Strusevich,et al.  Planning Machine Maintenance in Two-Machine Shop Scheduling , 2006, Oper. Res..

[36]  Jian-Jun Wang,et al.  Single-machine due date assignment problem with deteriorating jobs and resource-dependent processing times , 2013 .

[37]  S. M. Seyedhoseini,et al.  Multi-period lot sizing and job shop scheduling with compressible process times for multilevel product structures , 2013 .

[38]  T. C. Edwin Cheng,et al.  Minimizing Weighted Number of Early and Tardy Jobs with a Common Due Window Involving Location Penalty , 2001, Ann. Oper. Res..

[39]  Alexandre Dolgui,et al.  Scheduling with due date assignment under special conditions on job processing , 2012, J. Sched..

[40]  Gur Mosheiov,et al.  Scheduling a deteriorating maintenance activity on a single machine , 2010, J. Oper. Res. Soc..

[41]  Stanisław Gawiejnowicz,et al.  Basics of time-dependent scheduling , 2008 .

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

[43]  T.C.E. Cheng,et al.  Single-machine batch delivery scheduling with an assignable common due window , 2013 .

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

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

[46]  Chuanli Zhao,et al.  Single machine scheduling with general job-dependent aging effect and maintenance activities to minimize makespan , 2010 .

[47]  Ling Cheng,et al.  Note on "Single-machine due-window assignment and scheduling with resource allocation, aging effect, and a deteriorating rate-modifying activity" , 2014, Comput. Ind. Eng..

[48]  D. Yang,et al.  Scheduling problems with multiple due windows assignment and controllable processing times on a single machine , 2014 .

[49]  Surya D. Liman,et al.  Common due window size and location determination in a single machine scheduling problem , 1998, J. Oper. Res. Soc..

[50]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

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

[52]  Min Ji,et al.  Scheduling a variable maintenance and linear deteriorating jobs on a single machine , 2015, Inf. Process. Lett..

[53]  K. R. Baker,et al.  A bicriterion approach to time/cost trade-offs in sequencing , 1982 .

[54]  Gerhard J. Woeginger,et al.  A Review of Machine Scheduling: Complexity, Algorithms and Approximability , 1998 .

[55]  S. S. Panwalkar,et al.  Common Due Date Assignment to Minimize Total Penalty for the One Machine Scheduling Problem , 1982, Oper. Res..

[56]  R. G. Vickson,et al.  Choosing the Job Sequence and Processing Times to Minimize Total Processing Plus Flow Cost on a Single Machine , 1980, Oper. Res..

[57]  Christopher D. Geiger,et al.  A note on the optimal sequence position for a rate-modifying activity under simple linear deterioration , 2010, Eur. J. Oper. Res..

[58]  Ling-Huey Su,et al.  Scheduling parallel machines with resource-dependent processing times , 2009 .

[59]  H. Mokhtari,et al.  A multi-objective flow shop scheduling with resource-dependent processing times: trade-off between makespan and cost of resources , 2011 .