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Fuzzy Constraints in JobShop Scheduling
 Journal of Intelligent Manufacturing
, 1995
"... : This paper proposes an extension of the constraintbased approach to jobshop scheduling, that accounts for the flexibility of temporal constraints and the uncertainty of operation durations. The set of solutions to a problem is viewed as a fuzzy set whose membership function reflects preference. ..."
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Cited by 53 (9 self)
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: This paper proposes an extension of the constraintbased approach to jobshop scheduling, that accounts for the flexibility of temporal constraints and the uncertainty of operation durations. The set of solutions to a problem is viewed as a fuzzy set whose membership function reflects preference. This membership function is obtained by an egalitarist aggregation of local constraintsatisfaction levels. Uncertainty is qualitatively described is terms of possibility distributions. The paper formulates a simple mathematical model of jobshop scheduling under preference and uncertainty, relating it to the formal framework of constraintsatisfaction problems in Artificial Intelligence. A combinatorial search method that solves the problem is outlined, including fuzzy extensions of wellknown lookahead schemes. 1. Introduction There are traditionally three kinds of approaches to jobshop scheduling problems: priority rules, combinatorial optimization and constraint analysis. The first kind ...
Satisfiability Tests and TimeBound Adjustments for Cumulative Scheduling Problems
, 1997
"... This paper presents a set of satisfiability tests and timebound adjustment algorithms that can be applied to cumulative scheduling problems. An instance of the Cumulative Scheduling Problem (CuSP) consists of (1) one resource with a given capacity and (2) a set of activities, each having a relea ..."
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Cited by 27 (3 self)
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This paper presents a set of satisfiability tests and timebound adjustment algorithms that can be applied to cumulative scheduling problems. An instance of the Cumulative Scheduling Problem (CuSP) consists of (1) one resource with a given capacity and (2) a set of activities, each having a release date, a deadline, a processing time and a resource capacity requirement. The problem is to decide whether there exists a start time assignment to all activities such that at no point in time the capacity of the resource is exceeded and all timing constraints are satisfied. The Cumulative Scheduling Problem can be seen as a relaxation of the decision variant of the ResourceConstrained Project Scheduling Problem. We present three necessary conditions for the existence of a feasible schedule. Two of them are obtained by polynomial relaxations of the CuSP. The third one is based on energetic reasoning. We show that the second condition is closely related to the subset bound, a well
Computing Improved Optimal Solutions to MaxMin Flexible Constraint Satisfaction Problems
 European Journal of Operational Research
, 1999
"... : The formal framework for decision making in a fuzzy environment is based on a general maxmin, bottlenecklike optimization problem, proposed by Zadeh. It is also the basis for extending the constraint satisfaction paradigm of Artificial Intelligence to accommodating flexible or prioritized constra ..."
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Cited by 12 (3 self)
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: The formal framework for decision making in a fuzzy environment is based on a general maxmin, bottlenecklike optimization problem, proposed by Zadeh. It is also the basis for extending the constraint satisfaction paradigm of Artificial Intelligence to accommodating flexible or prioritized constraints. This paper surveys refinements of the ordering of solutions supplied by the maxmin formulation, namely the discrimin partial ordering and the leximin complete preordering. A general algorithm is given which computes all maximal solutions in the sense of these relations. It also sheds light on the structure of the set of best solutions. Moreover, classes of problems for which there is a unique best discrimin and leximin solution are exhibited, namely, continuous problems with convex domains, and so called isotonic problems. Noticeable examples of such problems are fuzzy linear programming problems and fuzzy PERTlike scheduling problems. Introduction Flexible constraint satisfaction p...
Study on Adaptive Hybrid Genetic Algorithm and Its Applications to Engineering Design Problems
, 2005
"... ..."
Introducing Flexibility in Scheduling: the Preference Approach
"... . Although tools and methods are nowadays available to schedule operations into a workshop, this task is still often completed by hand. Because of ready dates and due dates, the strict satisfaction of constraints may be impossible and exibilities have to be considered. We present in this paper a ..."
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Cited by 2 (0 self)
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. Although tools and methods are nowadays available to schedule operations into a workshop, this task is still often completed by hand. Because of ready dates and due dates, the strict satisfaction of constraints may be impossible and exibilities have to be considered. We present in this paper a model which encompasses these exibilities. Up to now, exibilities are implicitely taken into account by the \human scheduler". Our modelization { derived from the Possibility Theory { allows for exible constraints on the decision variables. Typically, the time parameters (e.g. durations) will be determined by a set of possible values, ordered by preference. In other words, the exibility is catched by preferences on the set of values. The rst model we obtain is linked to bottleneck problem optimization and may lead to quite poor solutions. Therefore, some renements of the approach and of the solving procedure are presented. We also illustrate briey how this model may inclu...
Preemptive Scheduling of Identical Machines
, 2000
"... We study the scheduling situation where jobs, subject to duedates or deadlines, have to be preemptively scheduled on parallel identical machines. We rst provide a closed form expression for the optimum value of Lmax , the maximal lateness. We show that it can be computed in O(n log n), hence improv ..."
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Cited by 2 (1 self)
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We study the scheduling situation where jobs, subject to duedates or deadlines, have to be preemptively scheduled on parallel identical machines. We rst provide a closed form expression for the optimum value of Lmax , the maximal lateness. We show that it can be computed in O(n log n), hence improving the best known time complexity for P jpmtnjLmax . Second, we consider the case where jobs have identical processing times and we show that, for each xed number of machines, the minimum weighted number of late jobs can be computed in polynomial time by dynamic programming. The complexity status of the corresponding problem Pmjpmtn; p i = pj P w i U i was unknown before. Keywords: Parallel Machine Scheduling, Preemption, DueDates, Dynamic Programming, Equal Processing Times 1 Introduction We study the scheduling situation where n jobs J 1 ; ; J n with processing times p 1 ; ; p n have to be preemptively scheduled on m parallel identical machines. Preemption means that j...
Adjustments of Release and Due Dates for Cumulative Scheduling Problems
, 1997
"... This paper presents a set of satisfiability tests and timebound adjustments that can be applied to cumulative scheduling problems. We introduce the Cumulative Scheduling Problem (CuSP), an extension of the mmachine problem in which activities, having both release and due dates, can require more th ..."
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Cited by 2 (1 self)
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This paper presents a set of satisfiability tests and timebound adjustments that can be applied to cumulative scheduling problems. We introduce the Cumulative Scheduling Problem (CuSP), an extension of the mmachine problem in which activities, having both release and due dates, can require more than one unit of the resource. Given a CuSP instance, we present two necessary conditions for the existence of solutions. They are obtained by polynomial relaxations of the CuSP: the Fully Elastic relaxation and the Partially Elastic Relaxation. These necessary conditions are related to wellknown lower bounds of the mmachine problem. Moreover, we present two constraint propagation algorithms, based on the previously mentioned necessary conditions, to adjust release and due dates of activities. These algorithms extend the edgefinding techniques developed for the onemachine problem. Thanks to their "low " complexity, these algorithms have been incorporated in a branch and bound procedure to solve the ResourceConstrained Project Scheduling Problem. Computational results are reported.
Efficient Temporal Management through an Application Dependent Graph Decomposition
"... In the MARTHA project, a large number of robots in a harbour are given the global task of transporting standardized containers from one area to another (ships, trains, stocking areas). The global decisionmaking process consisting of allocating robots to those predefined tasks can be viewed as a sch ..."
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In the MARTHA project, a large number of robots in a harbour are given the global task of transporting standardized containers from one area to another (ships, trains, stocking areas). The global decisionmaking process consisting of allocating robots to those predefined tasks can be viewed as a scheduling and resource allocation problem, which is addressed here in a centralised way. Imprecision of temporal constraints (expected arrival and leaving times of ships and trains, durations of actions) make it meaningless to search for a strict optimal schedule. Our approach interleaves task allocation and execution,
TO BE PUBLISHED IN ANNALS OF OPERATIONS RESEARCH Satisfiability Tests and TimeBound Adjustments for Cumulative Scheduling Problems
"... This paper presents a set of satisfiability tests and timebound adjustment algorithms that can be applied to cumulative scheduling problems. An instance of the Cumulative Scheduling Problem (CuSP) consists of (1) one resource with a given capacity and (2) a set of activities, each having a release ..."
Abstract
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This paper presents a set of satisfiability tests and timebound adjustment algorithms that can be applied to cumulative scheduling problems. An instance of the Cumulative Scheduling Problem (CuSP) consists of (1) one resource with a given capacity and (2) a set of activities, each having a release date, a deadline, a processing time and a resource capacity requirement. The problem is to decide whether there exists a start time assignment to all activities such that at no point in time the capacity of the resource is exceeded and all timing constraints are satisfied. The Cumulative Scheduling Problem can be seen as a relaxation of the decision variant of the ResourceConstrained Project Scheduling Problem. We present three necessary conditions for the existence of a feasible schedule. Two of them are obtained by polynomial relaxations of the CuSP. The third one is based on energetic reasoning. We show that the second condition is closely related to the subset bound, a wellknown lower bound of the mMachine Problem. We also present three algorithms, based on the previously mentioned necessary conditions, to adjust release dates and deadlines of activities. These algorithms extend the timebound adjustment techniques developed for the OneMachine Problem. They have been incorporated in a branch and bound procedure to solve the ResourceConstrained Project Scheduling Problem. Computational results are reported.