An FPTAS for scheduling a two‐machine flowshop with one unavailability interval

We study a deterministic two‐machine flowshop scheduling problem with an assumption that one of the two machines is not available in a specified time period. This period can be due to a breakdown, preventive maintenance, or processing unfinished jobs from a previous planning horizon. The problem is known to be NP‐hard. Pseudopolynomial dynamic programming algorithms and heuristics with worst case error bounds are given in the literature to solve the problem. They are different for the cases when the unavailability interval is for the first or second machine. The existence of a fully polynomial time approximation scheme (FPTAS) was formulated as an open conjecture in the literature. In this paper, we show that the two cases of the problem under study are equivalent to similar partition type problems. Then we derive a generic FPTAS for the latter problems with O(n5/ε4) time complexity. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

[1]  S. M. Johnson,et al.  Optimal two- and three-stage production schedules with setup times included , 1954 .

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

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

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

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

[6]  Zhen Liu,et al.  Preemptive Scheduling with Variable Profile, Precedence Constraints and Due Dates , 1995, Discret. Appl. Math..

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

[8]  Chung-Yee Lee,et al.  Minimizing the makespan in the two-machine flowshop scheduling problem with an availability constraint , 1997, Oper. Res. Lett..

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

[10]  Klaus H. Ecker,et al.  Scheduling Computer and Manufacturing Processes , 2001 .

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

[12]  Marie-Laure Espinouse,et al.  Minimizing the makespan in the two-machine no-wait flow-shop with limited machine availability , 1999 .

[13]  T. C. Edwin Cheng,et al.  Two-Machine Flowshop Scheduling with Consecutive Availability Constraints , 1999, Inf. Process. Lett..

[14]  Chung-Yee Lee.  Two-machine flowshop scheduling with availability constraints , 1999, Eur. J. Oper. Res..

[15]  T. C. Edwin Cheng,et al.  An improved heuristic for two-machine flowshop scheduling with an availability constraint , 2000, Oper. Res. Lett..

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

[17]  T. C. Edwin Cheng,et al.  Heuristics for two-machine no-wait flowshop scheduling with an availability constraint , 2001, Inf. Process. Lett..

[18]  Wieslaw Kubiak,et al.  Heuristic algorithms for the two-machine flowshop with limited machine availability ☆ , 2001 .

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

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

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