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Complexity of shop-scheduling problems with fixed number of jobs: a survey

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Abstract

The paper surveys the complexity results for job shop, flow shop, open shop and mixed shop scheduling problems when the number n of jobs is fixed while the number r of operations per job is not restricted. In such cases, the asymptotical complexity of scheduling algorithms depends on the number m of machines for a flow shop and an open shop problem, and on the numbers m and r for a job shop problem. It is shown that almost all shop-scheduling problems with two jobs can be solved in polynomial time for any regular criterion, while those with three jobs are NP-hard. The only exceptions are the two-job, m-machine mixed shop problem without operation preemptions (which is NP-hard for any non-trivial regular criterion) and the n-job, m-machine open shop problem with allowed operation preemptions (which is polynomially solvable for minimizing makespan).

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Correspondence to Peter Brucker.

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Brucker, P., Sotskov, Y.N. & Werner, F. Complexity of shop-scheduling problems with fixed number of jobs: a survey. Math Meth Oper Res 65, 461–481 (2007). https://doi.org/10.1007/s00186-006-0127-8

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  • DOI: https://doi.org/10.1007/s00186-006-0127-8

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