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

Peter Brucker (), Yu Sotskov and Frank Werner

Mathematical Methods of Operations Research, 2007, vol. 65, issue 3, 481 pages

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). Copyright Springer-Verlag 2007

Date: 2007
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DOI: 10.1007/s00186-006-0127-8

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