NDLI: A Complete 4-parametric complexity classification of short shop scheduling problems

Content Provider	Springer Nature Link
Author	Kov, Alexander Sevastyav, Sergey Sviridenko, Maxim
Copyright Year	2011
Abstract	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.
Starting Page	427
Ending Page	446
Page Count	20
File Format	PDF
ISSN	10946136
Journal	Journal of Scheduling
Volume Number	15
Issue Number	4
e-ISSN	10991425
Language	English
Publisher	Springer US
Publisher Date	2011-07-22
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Shop scheduling Makespan minimization Complexity classification Production/Logistics/Supply Chain Calculus of Variations and Optimal Control; Optimization Artificial Intelligence (incl. Robotics) Operations Research/Decision Theory Optimization
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Management Science and Operations Research Engineering Software

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