Two-machine shop scheduling with an uncapacitated interstage transporter

In this paper we study the two-machine flow shop and open shop problems to minimize the makespan with a single interstage transporter that may carry any number of jobs between the machines at a time. For each of these problems we present a best possible approximation algorithm within a class of schedules with at most two shipments. As a by-product of this research, for the problem of minimizing the makespan on parallel identical machines we analyze the ratio of the makespan for a non-preemptive schedule over the makespan of a preemptive schedule. Contributed by the Scheduling/Production Planning/Capacity Planning Department

[1]  Zhi-Long Chen,et al.  Machine scheduling with transportation considerations , 2001 .

[2]  Oded Berman,et al.  A 6/5-approximation algorithm for the two-machine routing open-shop problem on a two-node network , 2005, Eur. J. Oper. Res..

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

[4]  Sigrid Knust,et al.  Makespan minimization for flow-shop problems with transportation times and a single robot , 2001, Discret. Appl. Math..

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

[6]  Jean-Charles Billaut,et al.  Two-machine shop scheduling: Compromise between flexibility and makespan value , 2005, Eur. J. Oper. Res..

[7]  Wenci Yu,et al.  The two-machine flow shop problem with delays and the one-machine total tardiness problem , 1996 .

[8]  Hans Kellerer,et al.  Linear compound algorithms for the partitioning problem , 2000 .

[9]  Leslie A. Hall.  Approximability of flow shop scheduling , 1998, Math. Program..

[10]  Alessandro Agnetis,et al.  Tool handling and scheduling in a two-machine flexible manufacturing cell , 1996 .

[11]  Chelliah Sriskandarajah,et al.  Scheduling in Robotic Cells: Classification, Two and Three Machine Cells , 1997, Oper. Res..

[12]  Ronald L. Graham,et al.  Bounds on Multiprocessing Timing Anomalies , 1969, SIAM Journal of Applied Mathematics.

[13]  Alessandro Agnetis,et al.  Lot Scheduling in a Two-Machine Cell with Swapping Devices , 1996 .

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

[15]  Vitaly A. Strusevich,et al.  A Heuristic for the Two-machine Open-shop Scheduling Problem with Transportation Times , 1999, Discret. Appl. Math..

[16]  Oded Berman,et al.  A Simple Heuristic for m-Machine Flow-Shop and its Applications in Routing-Scheduling Problems , 1999, Oper. Res..

[17]  Toshihide Ibaraki,et al.  Automated Two-machine Flowshop Scheduling: A Solvable Case , 1991 .

[18]  D Rebaine,et al.  Two-machine open shop scheduling with special transportation times , 1999, J. Oper. Res. Soc..

[19]  Joseph Y.-T. Leung.  Open Shop Scheduling , 2004 .

[20]  Victor J. Rayward-Smith,et al.  Open shop scheduling with delays , 1992, RAIRO Theor. Informatics Appl..

[21]  Robert McNaughton,et al.  Scheduling with Deadlines and Loss Functions , 1959 .

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

[23]  Mauro Dell'Amico,et al.  Shop Problems With Two Machines and Time Lags , 1996, Oper. Res..

[24]  Wieslaw Kubiak,et al.  Sequencing of parts and robot moves in a robotic cell , 1989 .