An algorithm for solving the job-shop problem
Management Science
Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
Closure properties of constraints
Journal of the ACM (JACM)
Open Shop Scheduling to Minimize Finish Time
Journal of the ACM (JACM)
Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Handbook of Scheduling: Algorithms, Models, and Performance Analysis
Handbook of Scheduling: Algorithms, Models, and Performance Analysis
Minimizing Makespan in No-Wait Job Shops
Mathematics of Operations Research
A Note on Open Shop Preemptive Schedules
IEEE Transactions on Computers
The edge chromatic number of a directed-mixed multigraph
Journal of Graph Theory
Complete Complexity Classification of Short Shop Scheduling
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
The mixed shop scheduling problem
Discrete Applied Mathematics
Properties of optimal schedules in preemptive shop scheduling
Discrete Applied Mathematics
Three, four, five, six, or the complexity of scheduling with communication delays
Operations Research Letters
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We present a comprehensive complexity analysis of classical shop scheduling problems subject to various combinations of constraints imposed on the processing times of operations, the maximum number of operations per job, the upper bound on schedule length, and the problem type (taking values "open shop," "job shop," "mixed shop"). It is shown that in the infinite class of such problems there exists a finite basis system that allows one to easily determine the complexity of any problem in the class. The basis system consists of ten problems, five of which are polynomially solvable, and the other five are NP-complete. (The complexity status of two basis problems was known before, while the status of the other eight is determined in this paper.) Thereby the dichotomy property of that parameterized class of problems is established. Since one of the parameters is the bound on schedule length (and the other two numerical parameters are tightly related to it), our research continues the research line on complexity analysis of short shop scheduling problems initiated for the open shop and job shop problems in the paper by Williamson et al. (Oper. Res. 45(2):288---294, 1997). We improve on some results of that paper.