Identical parallel-machine scheduling under availability constraints to minimize the sum of completion times

In this paper, we study the identical parallel machine scheduling problem with a planned maintenance period on each machine to minimize the sum of completion times. This paper is a first approach for this problem. We propose three exact methods to solve the problem at hand: mixed integer linear programming methods, a dynamic programming based method and a branch-and-bound method. Several constructive heuristics are proposed. A lower bound, dominance properties and two branching schemes for the branch-and-bound method are presented. Experimental results show that the methods can give satisfactory solutions.

[1]  Wayne E. Smith.  Various optimizers for single‐stage production , 1956 .

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

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

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

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

[6]  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..

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

[8]  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.

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

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

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

[12]  Chengbin Chu,et al.  Minimizing the weighted flow time on a single machine with the resumable availability constraint: worst case of the WSPT heuristic , 2008, Int. J. Comput. Integr. Manuf..

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

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

[15]  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 .

[16]  Edward G. Coffman,et al.  Scheduling independent tasks to reduce mean finishing time , 1974, CACM.

[17]  Wieslaw Kubiak,et al.  Two-machine flow shops with limited machine availability , 2002, Eur. J. Oper. Res..

[18]  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..

[19]  W. A. Horn.  Technical Note - Minimizing Average Flow Time with Parallel Machines , 1973, Oper. Res..

[20]  Günter Schmidt,et al.  Scheduling on semi-identical processors , 1984, Z. Oper. Research.

[21]  Rob T. B. Carney.  Some general observations and experiences in logistics , 1956 .

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