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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 52 (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 ...
A Flow Shop with Compatibility Constraints in a Steelmaking Plant
 IN ZWEBEN AND FOX (EDS) INTELLIGENT SCHEDULING
, 1994
"... We present a scheduling methodology for applications where the generation of schedules is constrained by antagonistic and vague knowledge. Besides temporal and capacity constraints, compatibility constraints between consecutive jobs are managed. We model the vague constraints and uncertain data b ..."
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Cited by 14 (11 self)
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We present a scheduling methodology for applications where the generation of schedules is constrained by antagonistic and vague knowledge. Besides temporal and capacity constraints, compatibility constraints between consecutive jobs are managed. We model the vague constraints and uncertain data by fuzzy set theory. The importance of single jobs and and the difficulty to schedule them is defined on the different constraints and is used to control the generation of schedules. A preliminary schedule is generated by considering the important jobs and those that are difficult to schedule first. Easy or not so important jobs are scheduled later. Finally, the achieved schedule is "repaired" until a schedule is found that achieves a given level of satisfaction. Since the goodness of solutions is rated by fuzzy sets, robust schedules achieve better evaluations than weak schedules. However, if no robust solution is found constraints will be relaxed. This methodology is appropriate for applications in process engineering where uncertain knowledge is dominant. We explain the methodology with a case study from a steelmaking plant for highgrade steel.
Fuzzy Set Theory Applications in Production Management Research: A Literature Survey
 Journal of Intelligent Manufacturing
, 1998
"... Fuzzy set theory has been used to model systems that are hard to define precisely. As a methodology, fuzzy set theory incorporates imprecision and subjectivity into the model formulation and solution process. Fuzzy set theory represents an attractive tool to aid research in production management whe ..."
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Cited by 11 (0 self)
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Fuzzy set theory has been used to model systems that are hard to define precisely. As a methodology, fuzzy set theory incorporates imprecision and subjectivity into the model formulation and solution process. Fuzzy set theory represents an attractive tool to aid research in production management when the dynamics of the production environment limit the specification of model objectives, constraints and the precise measurement of model parameters. This paper provides a survey of the application of fuzzy set theory in production management research. The literature review that we compiled consists of 73 journal articles and nine books. A classification scheme for fuzzy applications in production management research is defined. We also identify selected bibliographies on fuzzy sets and applications. Keywords: Production Management, Fuzzy Set Theory, Fuzzy Mathematics. 1 Introduction Fuzzy set theory has been studied extensively over the past 30 years. Most of the early interest i...
On the sure criticality of tasks in activity networks with imprecise durations
 IEEE Transactions on Systsems, Man, and Cybernetics PartB 2002
"... Abstract—The notion of the necessary criticality (both with respect to path and to activity) of a network with imprecisely defined (by means of intervals or fuzzy intervals) activity duration times is introduced and analyzed. It is shown, in the interval case, that both the problem of asserting whet ..."
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Cited by 5 (4 self)
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Abstract—The notion of the necessary criticality (both with respect to path and to activity) of a network with imprecisely defined (by means of intervals or fuzzy intervals) activity duration times is introduced and analyzed. It is shown, in the interval case, that both the problem of asserting whether a given path is necessarily critical and the problem of determining an arbitrary necessarily critical path (more exactly, a subnetwork covering all the necessarily critical paths) are easy. The corresponding solution algorithms are proposed. However, the problem of evaluating whether a given activity is necessarily critical does not seem to be such. Certain conditions are formulated which in some situations (but not in all possible) allow evaluating the necessary criticality of activities. The results obtained for networks with interval activity duration times are generalized to the case of networks with fuzzy activity duration times. Two effective algorithms of calculating the degree of necessary criticality of a fixed path, as well as an algorithm of determining the paths that are necessarily critical to the maximum degree, are proposed. Index Terms—Fuzzy CPM, possibility and necessity, project management and scheduling. I.
Research Issues and Challenges in Fuzzy Scheduling
, 1994
"... Scheduling is an activity fraught with fuzziness. The prevalence of Murphy 's Law in real life situations, noise infected measurements, vague objectives of different importance, where compromises between antagonistic optimization criteria are generally allowed, and the difficulty of estimating proce ..."
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Cited by 1 (0 self)
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Scheduling is an activity fraught with fuzziness. The prevalence of Murphy 's Law in real life situations, noise infected measurements, vague objectives of different importance, where compromises between antagonistic optimization criteria are generally allowed, and the difficulty of estimating process times all contribute to make the construction of predictive schedules a complex task. Both authors have gained indepth practical experience in the field of fuzzy scheduling. Application domains of implemented systems ranged from production scheduling of mechanical and hydraulic presses [18, 19] to finegrained scheduling of highgrade steel production [25]. In addition to fundamental and advanced theoretic research on fuzzy scheduling, Slany's Ph.D. thesis [25] also contains an annotated bibliography 1 with more than 400 references on fuzzy scheduling. The present paper takes a step back from actual implementations to introduce the main aspects of fuzzy scheduling to a broader audience...
A Fuzzy Scheduling Problem with Dynamic Job Priorities and an Extension to Multiple Criteria Abstract
"... In real world scheduling problems, priorities of jobs may change over time. A less important job today may be of high importance tomorrow and vice versa. Another important aspect of decision making in manufacturing environments is often the impreciseness of the problem definition, comprising both th ..."
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Cited by 1 (1 self)
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In real world scheduling problems, priorities of jobs may change over time. A less important job today may be of high importance tomorrow and vice versa. Another important aspect of decision making in manufacturing environments is often the impreciseness of the problem definition, comprising both the available data and the knowledge about the preference structure of the decision maker. The paper presents a study of neighbourhood search heuristics for fuzzy scheduling. We especially address the problem of changing job priorities over time as studied at the Sherwood Press Corporation, a Nottingham based printing company. It can be shown, that the use of multiple criteria within the search process may improve the effectiveness of local search operators.
Fuzzy critical path method in intervalvalued activity networks
 Int. J. Pure Appl. Sci. Technol
"... Abstract: Critical Path method (CPM) is widely used in project scheduling and controlling. In conventional project scheduling problem, the crisp numbers are used for the activity times. But in reality, in an imprecise and uncertain environment, it is an unrealistic assumption. To represent the uncer ..."
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Cited by 1 (0 self)
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Abstract: Critical Path method (CPM) is widely used in project scheduling and controlling. In conventional project scheduling problem, the crisp numbers are used for the activity times. But in reality, in an imprecise and uncertain environment, it is an unrealistic assumption. To represent the uncertainty involved we have considered the intervalvalued numbers to represent the activity times. In this paper, we compute project characteristics such as earliest times, latest times and float times in terms of intervals. In this method, we introduce a new approach to find latest times by removing negative intervals times which can be generated by other methods. Also a new fuzzy critical path method based on the fuzzy theory is developed to solve the project scheduling problem under the fuzzy environment. Through a numerical example, calculation steps in this method and the results are presented.
A New Approach to find Total Float time and Critical Path in a fuzzy Project Network
"... The purpose of the critical path method (CPM) is to identify the critical activities in the critical path of an activity network. In the real world for many projects we have to use human judgment for estimating the duration of activities. However, the unknowns or vagueness about the time duration fo ..."
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The purpose of the critical path method (CPM) is to identify the critical activities in the critical path of an activity network. In the real world for many projects we have to use human judgment for estimating the duration of activities. However, the unknowns or vagueness about the time duration for activities in network planning, has led to the development of fuzzy CPM. A way to deal with this imprecise data is to employ the concept of fuzziness, where the vague activity times can be represented by fuzzy sets. In this paper a new method based on fuzzy theory is developed to solve the project scheduling problem under fuzzy environment. Assuming that the duration of activities are triangular fuzzy numbers, in this method we compute total float time of each activity and fuzzy critical path without computing forward and backward pass calculations. Through a numerical example, calculation steps in this method and the results are illustrated. Compare with other fuzzy critical method the proposed method is simple, fast and effective to find total float time of each activity and fuzzy critical path in a fuzzy project network.
unknown title
"... Fuzziness is not a priori an obvious concept and demands some explanation. “Fuzziness ” is what Black (NF 1937) calls “vagueness ” † when he distinguishes it from “generality ” and from “ambiguity. ” Generalizing refers to the application of a symbol to a multiplicity of objects in the field ..."
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Fuzziness is not a priori an obvious concept and demands some explanation. “Fuzziness ” is what Black (NF 1937) calls “vagueness ” † when he distinguishes it from “generality ” and from “ambiguity. ” Generalizing refers to the application of a symbol to a multiplicity of objects in the field