Using integer programming to solve the machine scheduling problem with a flexible maintenance activity

Abstract This work addresses the single machine and parallel machine scheduling problems, where machine is flexibly maintained and mean flow time is used as a performance measure. Machine Mk should be stopped for maintenance for a constant time wk in the schedule. The maintenance period [uk , vk ] is assumed to be set in advance, and the maintenance time wk is assumed not to exceed the maintenance period (that is, wk ≤ vk – uk ). The time uk (vk ) is the earliest (latest) time at which the machine Mk starts (stops) its maintenance. Two cases, resumable and unresumable, are considered in the single machine and parallel machine problems, respectively. Moreover, four integer programming models are developed optimally to solve the problem.

[1]  Moshe Dror,et al.  Mathematical programming formulations for machine scheduling: A survey , 1991 .

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

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

[4]  Wieslaw Kubiak,et al.  Scheduling preemptable tasks on parallel processors with limited availability , 2000, Parallel Comput..

[5]  Upendra Dave,et al.  Heuristic Scheduling Systems , 1993 .

[6]  Günter Schmidt,et al.  Scheduling Independent Tasks with Deadlines on Semi-identical Processors , 1988 .

[7]  S. D. Wu,et al.  On Scheduling with Ready-Times, Due-Dates and Vacations , 1992 .

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

[9]  Maw-Sheng Chern,et al.  MINIMIZING THE MAKESPAN IN A SINGLE MACHINE SCHEDULING PROBLEM WITH A FLEXIBLE MAINTENANCE , 2002 .

[10]  Chao-Hsien Pan,et al.  A study of integer programming formulations for scheduling problems , 1997, Int. J. Syst. Sci..

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

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

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

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

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

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

[17]  Chung-Yee Lee,et al.  A note on "parallel machine scheduling with non-simultaneous machine available time" , 2000, Discret. Appl. Math..

[18]  Yong He,et al.  Optimal online algorithm for scheduling on two identical machines with machine availability constraints , 2002, Inf. Process. Lett..

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

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

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

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

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

[24]  A. Kan.  Machine Scheduling Problems: Classification, Complexity and Computations , 1976 .

[25]  Chung-Yee Lee,et al.  Parallel machines scheduling with nonsimultaneous machine available time , 1991, Discret. Appl. Math..