Scheduling deteriorating Jobs on a Single Machine with Release times and rejection

This paper considers scheduling deteriorating jobs on a single machine with release times and rejection. Deteriorating job means that its actual processing time is a increasing function on its execution starting time. In this situation, jobs can be rejected by paying penalties. Each job is associated with a release time. The objective is to minimize the makespan plus the total penalty incurred by rejecting jobs. We present two dynamic programming algorithms and then design an FPTAS for the considered problem.

[1]  Steven S. Seiden.  Preemptive multiprocessor scheduling with rejection , 2001, Theor. Comput. Sci..

[2]  Jinjiang Yuan,et al.  Single machine scheduling with release dates and rejection , 2009, Eur. J. Oper. Res..

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

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

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

[6]  Leen Stougie,et al.  Multiprocessor scheduling with rejection , 1996, SODA '96.

[7]  Michael Pinedo,et al.  Planning and Scheduling in Manufacturing and Services , 2008 .

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

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

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

[11]  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..

[12]  Gerhard J. Woeginger,et al.  When does a dynamic programming formulation guarantee the existence of an FPTAS? , 1999, SODA '99.

[13]  Sudipta Sengupta,et al.  Algorithms and Approximation Schemes for Minimum Lateness/Tardiness Scheduling with Rejection , 2003, WADS.

[14]  Alexander V. Kononov,et al.  Complexity and approximability of scheduling resumable proportionally deteriorating jobs , 2010, Eur. J. Oper. Res..

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

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

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