Two-machine open shop scheduling with an availability constraint

We study a two-machine open shop scheduling problem, in which one machine is not available for processing during a given time interval. The objective is to minimize the makespan. We show that the problem is NP-hard and present an approximation algorithm with a worst-case ratio of 43.

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

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

[3]  Eugene L. Lawler,et al.  Sequencing and scheduling: algorithms and complexity , 1989 .

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

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

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

[7]  Sartaj Sahni,et al.  Preemptive Scheduling of Independent Jobs with Release and Due Times on Open, Flow and Job Shops , 1981, Oper. Res..

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

[9]  George L. Nemhauser,et al.  Handbooks in operations research and management science , 1989 .

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

[11]  Teofilo F. Gonzalez,et al.  Open Shop Scheduling to Minimize Finish Time , 1976, JACM.

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

[13]  Lu Lu,et al.  An NP-Hard Open Shop Scheduling Problem with Polynomial Average Time Complexity , 1993, Math. Oper. Res..

[14]  Eugene L. Lawler,et al.  On Preemptive Scheduling of Unrelated Parallel Processors by Linear Programming , 1978, JACM.

[15]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[16]  Sartaj Sahni,et al.  Dual criteria preemptive open‐shop problems with minimum makespan , 1995 .