Annals of Operations Research

, Volume 92, Issue 0, pp 281–304 | Cite as

Shop‐scheduling problems with fixed and non‐fixedmachine orders of the jobs

  • N.V. Shakhlevich
  • N. Sotskov
  • F. Werner


The paper deals with the determination of an optimal schedule for the so‐calledmixed‐shopproblem when the makespan has to be minimized. In such a problem, some jobs havefixed machine orders (as in the job‐shop), while the operations of the otherjobs may be processed in arbitrary order (as in the open‐shop). We provebinary NP‐hardness of the preemptive problem with three machines and three jobs(two jobs have fixed machine orders and one may have an arbitrary machine order).We answer all other remaining open questions on the complexity status of mixed‐shopproblems with the makespan criterion by presenting different polynomial and pseudopolynomial algorithms.


Optimal Schedule Complexity Status Arbitrary Order Makespan Criterion Pseudopolynomial Algorithm 
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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • N.V. Shakhlevich
  • N. Sotskov
  • F. Werner

There are no affiliations available

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