Minimising total flow-time on two parallel machines with planned downtimes and resumable jobs

This study considers the flow-time minimisation problem on two identical parallel machines, where the machines are subject to planned downtimes. Jobs that are interrupted due to machine downtimes may resume processing once the machine becomes available without incurring additional costs or setup times. We identify optimality properties, develop upper and lower bounding procedures, and present a branch and bound methodology based on the proposed properties and bounds. The computational efficiency is tested on problem instances with up to 35 jobs.

[1]  Michael Pinedo,et al.  Current trends in deterministic scheduling , 1997, Ann. Oper. Res..

[2]  Zhi-Long Chen,et al.  Scheduling jobs and maintenance activities on parallel machines , 2000 .

[3]  Chengbin Chu,et al.  Worst-case analysis of the WSPT and MWSPT rules for single machine scheduling with one planned setup period , 2008, Eur. J. Oper. Res..

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

[5]  Chung Yee Lee,et al.  Parallel-machine scheduling under potential disruption , 2007, Optim. Lett..

[6]  W. J. Chen,et al.  Minimizing total flow time in the single-machine scheduling problem with periodic maintenance , 2006, J. Oper. Res. Soc..

[7]  Chérif Sadfi,et al.  A dynamic programming algorithm for the single machine total completion time scheduling problem with availability constraints , 2001 .

[8]  Xiangtong Qi,et al.  Scheduling the maintenance on a single machine , 1999, J. Oper. Res. Soc..

[9]  Chung-Yee Lee,et al.  Single machine flow-time scheduling with scheduled maintenance , 1992, Acta Informatica.

[10]  J. S. Chen,et al.  Single-machine scheduling with flexible and periodic maintenance , 2006, J. Oper. Res. Soc..

[11]  Guoqing Wang,et al.  Preemptive Scheduling with Availability Constraints to Minimize Total Weighted Completion Times , 2005, Ann. Oper. Res..

[12]  Gur Mosheiov,et al.  Minimizing the sum of job completion times on capacitated parallel machines , 1994 .

[13]  Chung-Yee Lee,et al.  Machine scheduling with an availability constraint , 1996, J. Glob. Optim..

[14]  Jacek Blazewicz,et al.  An improved approximation algorithm for the single machine total completion time scheduling problem with availability constraints , 2005, Eur. J. Oper. Res..

[15]  Cherif Sadfi,et al.  Branch and bound and dynamic programming to minimize the total completion times on a single machine with availability constraints , 2005, 2005 IEEE International Conference on Systems, Man and Cybernetics.

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

[17]  Eric Sanlaville,et al.  Machine scheduling with availability constraints , 1998, Acta Informatica.

[18]  M. Azizoglu,et al.  Single machine scheduling with preventive maintenances , 2009 .

[19]  David S. Johnson,et al.  `` Strong '' NP-Completeness Results: Motivation, Examples, and Implications , 1978, JACM.

[20]  Chengbin Chu,et al.  Single-machine scheduling with an availability constraint to minimize the weighted sum of the completion times , 2008, Comput. Oper. Res..

[21]  Chung-Yee Lee,et al.  Capacitated Two-Parallel Machines Scheduling to Minimize Sum of Job Completion Times , 1993, Discret. Appl. Math..

[22]  Chung Yee Lee,et al.  Scheduling maintenance and semiresumable jobs on a single machine , 1999 .

[23]  Alexander H. G. Rinnooy Kan,et al.  Single machine flow-time scheduling with a single breakdown , 1989, Acta Informatica.

[24]  I. Kacem,et al.  Efficient branch-and-bound algorithm for minimizing the weighted sum of completion times on a single machine with one availability constraint , 2008 .

[25]  Günter Schmidt,et al.  Scheduling with limited machine availability , 2000, Eur. J. Oper. Res..