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NP-hardness of shop-scheduling problems with three jobs

Yu.N. Sotskov, N.V. Shakhlevich
1995 Discrete Applied Mathematics  
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

Matthias Mnich, René van Bevern
2018 Computers & Operations Research  
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?

Vadim G. Timkovsky
1998 Discrete Applied Mathematics  
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

Jacek Błażewicz, Piotr Formanowicz
2002 Reserche operationelle  
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

Gur Mosheiov
2002 Discrete Applied Mathematics  
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

Dae-Young Chung, Byung-Cheon Choi
2012 Journal of the Korean Operations Research and Management Science Society  
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]

Kameng Nip, Zhenbo Wang, Wenxun Xing
2015 Lecture Notes in Computer Science  
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  
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  
.) = 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

A. Soukhal, A. Oulamara, P. Martineau
2005 European Journal of Operational Research  
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  
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

Kameng Nip, Zhenbo Wang, Fabrice Nobibon Talla, R. Leus
2013 Social Science Research Network  
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

Kameng Nip, Zhenbo Wang, Fabrice Talla Nobibon, Roel Leus
2013 Journal of combinatorial optimization  
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

Thomas A. Roemer
2006 Journal of Scheduling  
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

J Hoogeveen
1996 European Journal of Operational Research  
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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