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Preemptive Scheduling with Variable Profile, Precedence Constraints and Due Dates
 Discrete Applied Mathematics
, 1993
"... This paper is concerned with the problem of scheduling preemptive tasks subject to precedence constraints in order to minimize the maximum lateness and the makespan. The number of available parallel processors is allowed to vary in time. It is shown that when an Earliest Due Date first algorithm pro ..."
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Cited by 9 (2 self)
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This paper is concerned with the problem of scheduling preemptive tasks subject to precedence constraints in order to minimize the maximum lateness and the makespan. The number of available parallel processors is allowed to vary in time. It is shown that when an Earliest Due Date first algorithm provides an optimal nonpreemptive schedule for unitexecution time (UET) tasks, then the preemptive priority scheduling algorithm, referred to as Smallest Laxity First, provides an optimal preemptive schedule for realexecutiontime (RET) tasks. When the objective is to minimize the makespan, we get the same kind of result between Highest Level First schedules solving nonpreemptive tasks with UET and the Longest Remaining Path first schedule for the corresponding preemptive scheduling problem with RET tasks. These results are applied to four specific profile scheduling problems and new optimality results are obtained. Keywords: Preemptive Scheduling, List Schedule, Priority Schedule, Variable P...
Stochastic Scheduling with Variable Profile and Precedence Constraints
 STOCHASTIC SCHEDULING WITH VARIABLE PROFILE 187
, 1991
"... In this paper, we consider the stochastic profile scheduling problem of a partially ordered set of tasks on uniform processors. The set of available processors varies in time. The running times of the tasks are independent random variables with exponential distributions. We obtain a sufficient condi ..."
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Cited by 5 (3 self)
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In this paper, we consider the stochastic profile scheduling problem of a partially ordered set of tasks on uniform processors. The set of available processors varies in time. The running times of the tasks are independent random variables with exponential distributions. We obtain a sufficient condition under which a list policy stochastically minimizes the makespan within the class of preemptive policies. This result allows us to obtain a simple optimal policy when the partial order is an interval order, or an inforest, or an outforest. Keywords: Stochastic Scheduling, Profile Scheduling, Makespan, Precedence Constraint, Interval Order, InForest, OutForest, Uniform Processors, Stochastic Ordering. 1 Introduction Consider the following scheduling problem. We are given a set of tasks to be run in a system consisting of uniform processors (i.e., processors having different speeds). The executions of these tasks must satisfy some precedence constraints which are described by a dire...
Scheduling Interval Orders with Release Dates and Deadlines
, 1996
"... We study the problem of scheduling unitlength tasks with release dates and deadlines subject to precedence constraints and unit communication delays. Two polynomialtime algorithms are defined: one constructs schedules for graphs with uniform release dates, the other for graphs with arbitrary relea ..."
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Cited by 3 (2 self)
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We study the problem of scheduling unitlength tasks with release dates and deadlines subject to precedence constraints and unit communication delays. Two polynomialtime algorithms are defined: one constructs schedules for graphs with uniform release dates, the other for graphs with arbitrary release dates. They have a special structure: unlike most scheduling algorithms, they do not consider individual tasks, but pairs of tasks. It is proved that the algorithms find minimumlateness schedules for interval orders on an arbitrary number of processors. 1 Introduction Finding a shortest schedule for a precedence graph is a very difficult problem: deciding whether a schedule for a set of tasks of length at most D exists on an arbitrary number of processors is an NPcomplete problem, even without precedence constraints. The problem remains NPcomplete if all task lengths are equal and the number of processors is arbitrary [11]. Only for special classes of precedence relations there are po...
Profile Scheduling by List Algorithms
, 1994
"... The notion of profile scheduling was first introduced by Ullman in 1975 in the complexity analysis of deterministic scheduling algorithms. In such a model, the number of processors available to a set of tasks may vary in time. Since the last decade, this model has been used to deal with systems subj ..."
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Cited by 2 (1 self)
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The notion of profile scheduling was first introduced by Ullman in 1975 in the complexity analysis of deterministic scheduling algorithms. In such a model, the number of processors available to a set of tasks may vary in time. Since the last decade, this model has been used to deal with systems subject to processor failures, multiprogrammed systems, or dynamically reconfigured systems. The aim of this paper is to overview optimal polynomial solutions for scheduling a set of partially ordered tasks in these systems. Particular attentions are given to a class of algorithms referred to as list scheduling algorithms. The objective of the scheduling problem is to minimize either the maximum lateness or the makespan. Results on preemptive and nonpreemptive deterministic scheduling, and on preemptive stochastic scheduling, are presented.
Scheduling jobs on open shops with limited machine availability
 RAIRO Oper. Res
, 1997
"... Abstract. In this paper, open shop scheduling problems with limited machine availability are studied. Such a limited availability of machines may appear in many reallife situations, e.g. as preventive maintenance activities. Three types of jobs are distinguished: nonpreemptable, resumable and preem ..."
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Cited by 1 (0 self)
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Abstract. In this paper, open shop scheduling problems with limited machine availability are studied. Such a limited availability of machines may appear in many reallife situations, e.g. as preventive maintenance activities. Three types of jobs are distinguished: nonpreemptable, resumable and preemptable. An operation of a resumable job if not completed before a nonavailability period of a machine may be suspended and continued without additional cost when the machine becomes available. In the paper, results are given for the scheduling problems associated with the three types of jobs. For preemptable jobs polynomialtime algorithms based on the twophase method are proposed.
Makespan Minimization of Task Graphs with Random Task Running Times
 In Interconnection Networks and Mapping and Scheduling Parallel Computations, D. F. Hsu et al. (Eds.), AMS, DIMACS series
, 1994
"... . The problem of scheduling a set of tasks on two parallel and identical processors is considered. The executions of tasks are constrained by precedence relations. The running times of the tasks are independent random variables with a common exponential distribution. The goal of scheduling is to min ..."
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. The problem of scheduling a set of tasks on two parallel and identical processors is considered. The executions of tasks are constrained by precedence relations. The running times of the tasks are independent random variables with a common exponential distribution. The goal of scheduling is to minimize the makespan, i.e. the maximum task completion time. A simple optimal preemptive policy is proven to stochastically minimize the makespan when the precedence graph belongs to a class of forestcut graphs. 1. Introduction Parallel programs are usually represented by task graphs which are directed acyclic graphs where vertices represent tasks and arcs represent precedence relations between tasks. The executions of these tasks have to satisfy these precedence constraints in such a way that a task can start execution only when all its predecessor tasks have completed execution. For any given task graph, the scheduling problem consists in assigning tasks to a set of processors in such a wa...
Scheduling with Limited Processor Availability
"... In scheduling theory the basic model assumes that all machines are continuously available for processing throughout the planning horizon. This assumption might be justified in some cases but it does not apply if certain maintenance requirements, breakdowns or other constraints that cause the machine ..."
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In scheduling theory the basic model assumes that all machines are continuously available for processing throughout the planning horizon. This assumption might be justified in some cases but it does not apply if certain maintenance requirements, breakdowns or other constraints that cause the machines not to be available for processing have to be considered. In this chapter we discuss results related to deterministic scheduling problems where machines are not continuously available for processing. Examples of such constraints can be found in many areas. Limited availabilities of machines may result from preschedules which exist mainly because most of the real world resources planning problems are dynamic. A natural approach to cope with a dynamic environment is to trigger a new planning horizon when the changes in the data justify it. However, due to many necessities, as process preparation for instance, it is mandatory to take results of earlier plans as fixed which obviously limits availability of resources for any subsequent plan. Consider e.g. ERP (Enterprise Resource Planning) production planning systems