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NP-hardness of shop-scheduling problems with three jobs
1995
Discrete Applied Mathematics
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The main result of this paper is an NP-hardness proof for scheduling 3 jobs on 3 machines, whether preemptions of operations are allowed or forbidden. ...
The purpose of this paper is to improve the results obtained in [14-161 on the study of the complexity of shop-scheduling problems with fixed number of jobs when n < m. ...
Acknowledgement The authors gratefully acknowledge the anonymous referees for their helpful comments and corrections of the first, second, and third versions of the paper. ...
doi:10.1016/0166-218x(95)80004-n
fatcat:sncphigzhbaqhozbdfajmfdf3m
Parameterized complexity of machine scheduling: 15 open problems
2018
Computers & Operations Research
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2018 pre-print arXiv:1709.01670v2 fatcat:tfqv6zdwxjdndoltzudrqxxdwaOther Versions
Machine scheduling problems are a long-time key domain of algorithms and complexity research. A novel approach to machine scheduling problems are fixed-parameter algorithms. ...
To stimulate this thriving research direction, we propose 15 open questions in this area whose resolution we expect to lead to the discovery of new approaches and techniques both in scheduling and parameterized ...
Woeginger for pointing out Open Problem 11. ...
doi:10.1016/j.cor.2018.07.020
fatcat:srss3krmhnd6jj5on4asgxp4em
Is a unit-time job shop not easier than identical parallel machines?
1998
Discrete Applied Mathematics
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Employing this general reduction we prove the NP-hardness of unit-time job-shop scheduling problems which had unknown complexity status before. ...
That is any scheduling problem for m identical parallel machines to minimize a criterion of the class reduces to a scheduling problem for an m-machine unit-time job shop to minimize the same criterion. ...
The reductions listed below prove the NP-hardness or strong NP-hardness of unit-time job-shop scheduling problems listed in the third column. ...
doi:10.1016/s0166-218x(98)00032-8
fatcat:zzdndmyqbbgabni67l7kw2vq4q
Scheduling jobs in open shops with limited machine availability
2002
Reserche operationelle
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In this paper, open shop scheduling problems with limited machine availability are studied. ...
In the paper, results are given for the scheduling problems associated with the three types of jobs. For preemptable jobs polynomial-time algorithms based on the two-phase method are proposed. ...
In [12] it has been shown that scheduling resumable jobs in a two-machine flow shop system with one period of non-availability is an NP-hard problem. ...
doi:10.1051/ro:2002008
fatcat:6xagidiqsnanjgh6dbjabpisxq
Complexity analysis of job-shop scheduling with deteriorating jobs
2002
Discrete Applied Mathematics
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This paper addresses job-shop scheduling problems with deteriorating jobs, i.e. jobs whose processing times are an increasing function of their starting time. ...
Finally, we prove NP-hardness of the job-shop problem even for two machines. ? ...
This paper was supported in part by the Recanati Fund of The School of Business Administration, The Hebrew University, Jerusalem, Israel. ...
doi:10.1016/s0166-218x(00)00385-1
fatcat:xfrbwwyaw5f5fck3sx5hg2pepa
Just-in-time Scheduling with Multiple Competing Agents
다수의 경쟁이 존재하는 환경에서 적시 스케줄링에 관한 연구
2012
Journal of the Korean Operations Research and Management Science Society
다수의 경쟁이 존재하는 환경에서 적시 스케줄링에 관한 연구
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We consider a multi-agent scheduling problem such that each agent tries to maximize the weighted number of just-in-time jobs. ...
We show that when the number of agents is fixed, the single machine case with the first objective is NP-hard in the ordinary sense, and present the polynomial-time algorithm for the two-machine flow shop ...
Further-
more, they showed that the problem with identi-
cal weights is strongly NP-hard if the number
of machines is three or more. ...
doi:10.7737/jkorms.2012.37.1.019
fatcat:5nw64mxlwbdzpftn2tfx57l3hi
Combinations of Some Shop Scheduling Problems and the Shortest Path Problem: Complexity and Approximation Algorithms
[chapter]
2015
Lecture Notes in Computer Science
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We study several combinatorial optimization problems which combine the classic shop scheduling problems (open shop scheduling or job shop scheduling) and the shortest path problem. ...
We show that these problems are NP-hard even if the number of machines is two, and they cannot be approximated within a factor of less than 2 if the number of machines is an input unless P = NP. ...
This work also inspired the study of the combination of different combinatorial optimization problems. Flow shop, open shop and job shop are three basic models of multi-stage scheduling problems. ...
doi:10.1007/978-3-319-21398-9_8
fatcat:p7wtku6f25goblc64vt7eumwfm
Page 5837 of Mathematical Reviews Vol. , Issue 2004g
[page]
2004
Mathematical Reviews
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Summary: “The single-machine family scheduling problem of min- imizing the number of late jobs has been known to be NP-hard, but whether it is NP-hard in the strong sense is cited as an open problem in ...
One consequence of these results is that the recognition version of the two machine job shop makespan problem with at most five operations per job is unary NP-complete. ...
Page 461 of The Journal of the Operational Research Society Vol. 57, Issue 4
[page]
2006
The Journal of the Operational Research Society
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.) = dk — 1t3.k)- Then the problem is to find a schedule mx which minimizes $°7_ ,|D3.¢; subject to C>.2¢))= Crmax- We note that the problem is NP-hard since the proof of NP- hardness of the two-machine ...
Since permutation flow-shop problems are considered in_ this
paper, a schedule is identified as a permutation z= (n(1),
nd T Fujie—A class of three-machine flow-shop problems 461
m2), ...,2(n)) of N. ...
Complexity of flow shop scheduling problems with transportation constraints
2005
European Journal of Operational Research
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For the makespan objective function, we prove that this problem is strongly NP-hard when the capacity of a truck is limited to two or three parts with an unlimited buffer at the output of the each machine ...
This paper investigates two-machine flow shop scheduling problems taking transportation into account. ...
This work has led to the study of the complexity of flow shop scheduling problems in which the capacity of the truck is limited to two or three jobs. ...
doi:10.1016/j.ejor.2003.03.002
fatcat:5xyegnyjvngbjnq63ap4l2v474
Page 7231 of Mathematical Reviews Vol. , Issue 97K
[page]
1997
Mathematical Reviews
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Part I deals with the two-machine flow shop problem F2D with delays and Part II consists of three papers published elsewhere, and deals with the problem of minimizing total tardiness on a single machine ...
The general F2D problem is NP-hard as proved by Vaessens and Dell Amico. In Chapters 2 and 3 of the present book, two more restricted cases are proved to be NP-hard. ...
A Combination of Flow Shop Scheduling and the Shortest Path Problem
2013
Social Science Research Network
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We argue that this problem is NP-hard even if the number of machines is two, and is NP-hard in the strong sense for the general case. ...
The objective of the obtained problem is to select a subset of jobs that constitutes a feasible solution to the shortest path problem, and to execute the selected jobs on the flow shop machines to minimize ...
Flow shop scheduling is one of the three basic models of multi-stage scheduling (the others are open shop scheduling and job shop scheduling). ...
doi:10.2139/ssrn.2381955
fatcat:zwxwge2vizfjheu2kuqk2jlh6e
A combination of flow shop scheduling and the shortest path problem
2013
Journal of combinatorial optimization
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We argue that this problem is NP-hard even if the number of machines is two, and is NP-hard in the strong sense for the general case. ...
The objective of the obtained problem is to select a subset of jobs that constitutes a feasible solution to the shortest path problem, and to execute the selected jobs on the flow shop machines to minimize ...
Flow shop scheduling is one of the three basic models of multi-stage scheduling (the others are open shop scheduling and job shop scheduling). ...
doi:10.1007/s10878-013-9670-4
fatcat:jowszqshyrhuxohkc6ga4eym7i
A note on the complexity of the concurrent open shop problem
2006
Journal of Scheduling
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The concurrent open shop problem is a relaxation of the well known open job shop problem, where the components of a job can be processed in parallel by dedicated, component specific machines. ...
In particular, Leung et al. (2005) show, contrary to the assertion in Wagneur and Sriskandarajah (1993) , that the problem of minimizing the average job completion time is not necessarily strongly NP-hard ...
Conclusion This paper established that minimizing average completion time in the concurrent job shop with two machines (i.e. PD2 C j ) is strongly NP-hard. ...
doi:10.1007/s10951-006-7042-y
fatcat:4ljxjs7fqjblpm442i2rfnpa6i
Preemptive scheduling in a two-stage multiprocessor flow shop is NP-hard
1996
European Journal of Operational Research
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We show that preemptive scheduling in a two-stage flow shop with at least two identical parallel machines in one of the stages so as to minimize makespan is NP-hard in the strong sense. 1991 Mathematics ...
A simi-1ar1y efficient aJgorithm is unlikely to exist for the simplest common generalization of these pr0blems. ...
In this note. we will show that preemptive scheduling in a two-stage flow shop with at least two identical parallel machines in one of the stages so as to minimize makespan is NP-hard in the strong sense ...
doi:10.1016/0377-2217(94)00235-5
fatcat:2dpe64hanjgavaofqasiwjjamy
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