Abstract
We consider the cyclic job shop problem with no-wait constraints which consists in minimizing the cycle time. We assume that a single product is produced on a few machines. A job is processed by performing a given set of operations in a predetermined sequence. Each operation can be performed on exactly one machine. We consider the problem of minimization the cycle time with no-wait constraints between some pairs of sequential operations and investigate the complexity of the problem and some of its subproblems. In general, the problem is proved to be strongly NP-hard. In the case when the job is processed without downtime between operations, polynomial solvability is proved and the two algorithms are proposed. Also we develop an algorithm for the general case which is pseudopolynomial if the number of admissible downtime is fixed. The case of a single no-wait constraint is polynomially solvable. The problem with two no-wait constraints becomes NP-hard. We found effectively solvable cases and propose the corresponding algorithms.
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References
E. A. Bobrova, A. A. Romanova, V. V. Servakh, “The Complexity of the Cyclic Job Shop Problem with Identical Jobs,” Diskretn. Anal. Issled. Oper. 20 (4), 3–14 (2013).
A. A. Romanova and V. V. Servakh, “Optimization of Identical Jobs Production on the Base of Cyclic Schedules,” Diskretn. Anal. Issled. Oper. 15 (4), 47–60 (2008).
N. G. Hall, T. E. Lee, and M. E. Posner, “The Complexity of Cyclic Shop Scheduling Problems,” J. Scheduling 5 (4), 307–327 (2002).
C. Hanen, “Study of a NP-Hard Cyclic Scheduling Problem: the Recurrent Job-Shop,” European J. Oper. Res. 71, 82–101 (1994).
S. T. McCormick and U. S. Rao, “Some Complexity Results in Cyclic Scheduling,” Math. Comput. Modelling 20, 107–122 (1994).
M. Middendorf and V. Timkovsky, “On Scheduling Cycle Shops: Classification, Complexity, and Approximation,” J. Scheduling 5 (2), 135–169 (2002).
R. Roundy, “Cyclic Schedules for Job Shops with Identical Jobs,” Math. Oper. Res. 17 (4), 842–865 (1995).
K. A. Aldakhilallah and R. Ramesh, “Cyclic Scheduling Heuristics for a Reentrant Job Shop Manufacturing Environment,” Internat. J. Production Research 39, 2635–2675 (2001).
T. Boudoukh, M. Penn, and G. Weiss, “Scheduling Job Shops with Some Identical or Similar Jobs,” J. Scheduling 4, 177–199 (2001).
P. Brucker and T. Kampmeyer, “Tabu Search Algorithms for Cyclic Machine Scheduling Problems,” J. Scheduling 8, 303–322 (2005).
M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness (Freema, San Francisco, 1979; Mir, Moscow, 1982).
V. Kats and E. Levner, “Cyclic Scheduling in a Robotic Production Line,” J. Scheduling 5(1), 23–41 (2002).
V. S. Aizenshtat, “Multi-Operator Cyclic Processes,” Dokl. Nats. Akad. Nauk Belarus 7 (4), 224–227 (1963).
V. S. Tanaev, “A Scheduling Problemfora Flowshop Line with a Single Operator,” Inzh.-Fiz.Zh. 7 (3), 111–114 (1964).
Acknowledgment
The authors are grateful to the referee for the useful remarks.
Funding
The second author was supported by the Program No. I.5.1 of Fundamental Scientific Research of the Siberian Branch of the Russian Academy of Sciences (project no. 0314-2019-0019).
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Russian Text © The Author(s), 2019, published in Diskretnyi Analiz i Issledovanie Operatsii, 2019, Vol. 26, No. 4, pp. 56–73.
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Romanova, A.A., Servakh, V.V. Complexity of Cyclic Job Shop Scheduling Problems for Identical Jobs with No-Wait Constraints. J. Appl. Ind. Math. 13, 706–716 (2019). https://doi.org/10.1134/S1990478919040136
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DOI: https://doi.org/10.1134/S1990478919040136