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Scheduling with incompatible jobs
 DISCRETE APPLIED MATHEMATICS
, 1994
"... We consider scheduling problems in a multiprocessor system with incompatible jobs (two incompatible jobs cannot be processed by the same machine). We consider the problem to minimize the maximum job completion time. the makespan. This problem is NPcomplete. We present a number of polynomial time ap ..."
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Cited by 24 (2 self)
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We consider scheduling problems in a multiprocessor system with incompatible jobs (two incompatible jobs cannot be processed by the same machine). We consider the problem to minimize the maximum job completion time. the makespan. This problem is NPcomplete. We present a number of polynomial time approximation algorithms for this problem where the job incompatibilities possess a special structure. As the incompatibilities form a graph on the set ofjobs, our algorithms strongly rely on graph theoretic methods. We also solve an open problem by Birb et al. [l] on coloring precolored bipartite graphs.
Current trends in deterministic scheduling
 ANNALS OF OPERATIONS RESEARCH
, 1997
"... Scheduling is concerned with allocating limited resources to tasks to optimize certain objective functions. Due to the popularity of the Total Quality Management concept, ontime delivery of jobs has become one of the crucial factors for customer satisfaction. Scheduling plays an important role in ac ..."
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Cited by 19 (0 self)
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Scheduling is concerned with allocating limited resources to tasks to optimize certain objective functions. Due to the popularity of the Total Quality Management concept, ontime delivery of jobs has become one of the crucial factors for customer satisfaction. Scheduling plays an important role in achieving this goal. Recent developments in scheduling theory have focused on extending the models to include more practical constraints. Furthermore, due to the complexity studies conducted during the last two decades, it is now widely understood that most practical problems are NPhard. This is one of the reasons why local search methods have been studied so extensively during the last decade. In this paper, we review briefly some of the recent extensions of scheduling theory, the recent developments in local search techniques and the new developments of scheduling in practice. Particularly, we survey two recent extensions of theory: scheduling with a 1jobonrmachine pattern and machine scheduling with availability constraints. We also review several local search techniques, including simulated annealing, tabu search, genetic algorithms and constraint guided heuristic search. Finally, we study the robotic cell scheduling problem, the automated guided vehicles scheduling problem, and the hoist scheduling problem.
Scheduling of Jobs and Maintenance Activities on Parallel Machines
 35 th International Conference on Computers and Industrial Engineering
, 2000
"... Most machine scheduling models assume that the machines are available all the time. However, in many realistic situations, machines need to be maintained and hence may become unavailable during a certain period. In this paper, we study the problem of processing a set of jobs on parallel machines in ..."
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Cited by 9 (1 self)
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Most machine scheduling models assume that the machines are available all the time. However, in many realistic situations, machines need to be maintained and hence may become unavailable during a certain period. In this paper, we study the problem of processing a set of jobs on parallel machines in which each machine must be maintained once in the planning horizon. Our objective is to schedule jobs and maintenance activities so that total weighted completion time of jobs is minimized. Two cases are studied in this paper. In the first case, there is a sufficient amount of resource and hence different machines can be maintained simultaneously if necessary. In the second case, only one machine can be maintained at any given time. In this paper, we first show that, even when all the jobs have the same weight, both cases of the problem are NPhard. We then propose branch and bound algorithms based on the column generation approach for solving both cases of the problem. The algorithms are ca...
Approximation Algorithms for Scheduling with Reservations
"... Abstract. We study the problem of scheduling n independent jobs on a system of m identical parallel machines in the presence of reservations. This constraint is practically important; for various reasons, some machines are not available during specified time intervals. The objective is to minimize t ..."
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Cited by 8 (4 self)
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Abstract. We study the problem of scheduling n independent jobs on a system of m identical parallel machines in the presence of reservations. This constraint is practically important; for various reasons, some machines are not available during specified time intervals. The objective is to minimize the makespan. This problem is inapproximable in the general case unless P = NP which motivates the study of suitable restrictions. We use an approach based on algorithms for multiple subset sum problems; our technique yields a polynomial time approximation scheme (PTAS) which is best possible in the sense that the problem does not admit an FPTAS unless P = NP. The PTAS presented here is the first one for the problem under consideration; so far, not even for special cases approximation schemes have been proposed. We also derive a low cost algorithm with a constant approximation ratio and discuss additional FPTASes for special cases and complexity results. 1
Faster Approximation Algorithms for Scheduling with Fixed Jobs
"... We study the problem of scheduling jobs on identical parallel machines without preemption. In the considered setting, some of the jobs are already assigned machines and starting times, for example due to external constraints not explicitly modelled. The objective is to assign the rest of the jobs in ..."
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Cited by 3 (1 self)
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We study the problem of scheduling jobs on identical parallel machines without preemption. In the considered setting, some of the jobs are already assigned machines and starting times, for example due to external constraints not explicitly modelled. The objective is to assign the rest of the jobs in order to minimize the makespan. It is known that this problem cannot be approximated better than within a factor of 3/2 unless P = NP. An algorithm that achieves 3/2 + ɛ for any ɛ> 0 was presented by Diedrich and Jansen [DJ09], but its running time is doubly exponential in 1/ɛ. We present an improved algorithm with approximation ratio 3/2 and polynomial running time. We also give matching results for the related problem of scheduling with reservations. The new algorithm is both faster and conceptually simpler than the previously known algorithms. 1
Parallel machines scheduling with machine shutdowns
 Computers and Mathematics with Applications
, 1998
"... Abstractwe study the nonpreemptive parallel machines scheduling problem where some of the machines are planned to be shutdown. We apply LPT algorithm to the problem and analyze its performance. Our analysis shows that the makespan of the LPT schedule is bounded by twice the optimum makespan if no m ..."
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Cited by 3 (0 self)
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Abstractwe study the nonpreemptive parallel machines scheduling problem where some of the machines are planned to be shutdown. We apply LPT algorithm to the problem and analyze its performance. Our analysis shows that the makespan of the LPT schedule is bounded by twice the optimum makespan if no more than half of the machines are allowed to be shutdown simultaneously. We also show that this bound ls tight by constructing a worstcase example. @ 1998 Elsevier Science Ltd. All rights reserved. KeywordsParallel algorithm
Mapping and Load Balancing on Distributed Memory Systems
 In.: Proc. of the Eight Symposium on Microcomputer and Microprocessor Applications
, 1994
"... Two kinds of tools are necessary to optimise the use of available resources by the execution of parallel programs on distributed memory systems: mapping and load balancing tools. A mapping tool is well suited for programs whose behaviour is predictable while for many "real applications", it needs to ..."
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Cited by 2 (0 self)
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Two kinds of tools are necessary to optimise the use of available resources by the execution of parallel programs on distributed memory systems: mapping and load balancing tools. A mapping tool is well suited for programs whose behaviour is predictable while for many "real applications", it needs to be complemented by a dynamic load balancing tool. Both tools are currently investigated to be included in the programming environment designed by the SEPP COPERNICUS project. I.
The worstcase analysis of the MULTIFIT algorithm for scheduling nonsimultaneous parallel machines. Discrete Applied Mathematics
, 1999
"... In this paper we consider the nonsimultaneous multiprocessor scheduling problem, or NMSP for short. The NMSP is a makespan minimization scheduling problem which involves the nonpreemptive assignment of independent jobs on m parallel machines with di erent starting times. It is well known that the lo ..."
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Cited by 2 (0 self)
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In this paper we consider the nonsimultaneous multiprocessor scheduling problem, or NMSP for short. The NMSP is a makespan minimization scheduling problem which involves the nonpreemptive assignment of independent jobs on m parallel machines with di erent starting times. It is well known that the longest processing time (LPT) algorithm and the modi ed LPT(MLPT) algorithm yield schedules with makespans bounded by 3 1 − and 4=3 times the optimum makespan, 2 2m respectively. In this paper, we show that the best known worstcase performance bound, 4=3 of the MLPT, is tight by constructing a worstcase example. Then, we employ the binpacking heuristic algorithm called the MULTIFIT to solve the NMSP and show that the makespan of the schedule generated by the MULTIFIT algorithm is bounded by 9=7 +2 −k times the optimum makespan, where k is the selected number of the major iterations in the MULTIFIT. This worstcase bound of the MULTIFIT algorithm is, so far, the best bound for the NMSP and
ANDES: Evaluating Mapping Strategies with Synthetic Programs
 Euromicro J. of Systems Architecture
, 1997
"... This paper presents the ANDES performance evaluation tool. ANDES is based on the synthetic execution of parallel programs and it is used for the evaluation of mapping strategies. The Meganode, a distributed memory parallel computer, is considered as our target architecture. ANDES takes into account ..."
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Cited by 1 (1 self)
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This paper presents the ANDES performance evaluation tool. ANDES is based on the synthetic execution of parallel programs and it is used for the evaluation of mapping strategies. The Meganode, a distributed memory parallel computer, is considered as our target architecture. ANDES takes into account a benchmark of quantitative models of parallel algorithms and a set of mapping strategies (greedy and iterative algorithms are used). We show how this tool allows an extensive comparison of mapping strategies by using the benchmark, the mapping strategies and different cost functions. 1 Introduction Distributed memory multiprocessors (DMM) are the current trend of highperformance parallel computers. They represent a good balance between cost and performance, mainly because of the connection of several commercial, general and relatively cheap microprocessors. A distributed memory multiprocessor is a computer composed of autonomous processors connected by a high speed communication network....
Machine Scheduling with Availability Constraints
, 1999
"... In most scheduling literature the continuous availability of machines is assumed. However, in real world applications, this may not be the case. The machine may not be available during certain time periods due to deterministic or stochastic reasons. In this paper, the machine scheduling with availab ..."
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Cited by 1 (0 self)
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In most scheduling literature the continuous availability of machines is assumed. However, in real world applications, this may not be the case. The machine may not be available during certain time periods due to deterministic or stochastic reasons. In this paper, the machine scheduling with availability constraints for both deterministic and stochastic cases will be analyzed. The existing literature will be reviewed.