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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    OR spectrum 19 (1997), S. 23-29 
    ISSN: 1436-6304
    Keywords: Job shop scheduling ; dispatching rules ; coordination ; look ahead information ; simulation ; Werkstattsteuerung ; Steuerungsregeln ; Koordination ; Vorausschauende Informationen ; Simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In diesem Beitrag wird ein neuartiger Ansatz zur Koordination dezentraler Werkstattsteuerungsregeln vorgestellt und mit Hilfe einer Simulationsstudie analysiert. Die Koordination basiert auf vorausschauenden Informationen und enthält einen Auftragsnachfrage-/-angebotsmechanismus. Die Simulations-experimente zeigen, daß durch den Einsatz des Koordinationsmechanismus die Leistung herkömmlicher Steuerungsregeln signifikant verbessert wird.
    Notes: Abstract In this paper a new coordination approach for decentralized job shop scheduling rules is presented and analyzed in a simulation study. The coordination is based on look ahead information and contains a mechanism for demanding and supplying jobs. The simulation experiments show that the performance of conventional scheduling rules is significantly improved using the coordination mechanism.
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    OR spectrum 19 (1997), S. 23-29 
    ISSN: 1436-6304
    Keywords: Key words: Job shop scheduling ; dispatching rules ; coordination ; look ahead information ; simulation ; Schlüsselwörter: Werkstattsteuerung ; Steuerungsregeln ; Koordination ; Vorausschauende Informationen ; Simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung. In diesem Beitrag wird ein neu-artiger Ansatz zur Koordination dezentraler Werkstattsteuerungsregeln vorgestellt und mit Hilfe einer Simulationsstudie analysiert. Die Koordination basiert auf vorausschauenden Informationen und enthält einen Auftragsnachfrage-/-angebotsmechanismus. Die Simulations- experimente zeigen, daß durch den Einsatz des Koordinationsmechanismus die Leistung herkömmlicher Steuerungsregeln signifikant verbessert wird.
    Notes: Abstract. In this paper a new coordination approach for decentralized job shop scheduling rules is presented and analyzed in a simulation study. The coordination is based on look ahead information and contains a mechanism for demanding and supplying jobs. The simulation experiments show that the performance of conventional scheduling rules is significantly improved using the coordination mechanism.
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  • 3
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    Electronic Resource
    Springer
    Mathematical programming 42 (1988), S. 53-68 
    ISSN: 1436-4646
    Keywords: Design of experiments ; normal random variates ; pseudorandom ; simulation ; statistical inference
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract More and more problems are being tackled by simulation as large computing costs per hour approach those of mathematicians' time. Abuses of simulation arise from ignorance or careless use of little understood procedures, and some of the fundamental tools of the subject are much less well understood than commonly supposed. This is illustrated here by the saga of pseudorandom number generators, normal variate generators and the analysis of queueing system simulations. On the positive side, genuinely new uses of simulation are appearing, particularly in statistical inference. These are exemplified by recursive algorithms for simulating complex systems and simulation-based likelihood inference for point processes.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of intelligent manufacturing 3 (1992), S. 43-57 
    ISSN: 1572-8145
    Keywords: Machine learning ; simulation ; flexible manufacturing systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract This paper describes a synergistic approach that is applicable to a wide variety of system control problems. The approach utilizes a machine learning technique, goal-directed conceptual aggregation (GDCA), to facilitate dynamic decision-making. The application domain employed is Flexible Manufacturing System (FMS) scheduling and control. Simulation is used for the dual purpose of providing a realistic depiction of FMSs, and serves as an engine for demonstrating the viability of a synergistic system involving incremental learning. The paper briefly describes prior approaches to FMS scheduling and control, and machine learning. It outlines the GDCA approach, provides a generalized architecture for dynamic control problems, and describes the implementation of the system as applied to FMS scheduling and control. The paper concludes with a discussion of the general applicability of this approach.
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  • 5
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    Journal of intelligent manufacturing 3 (1992), S. 193-204 
    ISSN: 1572-8145
    Keywords: Neural networks ; simulation ; continuous improvement systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The use of a neural network embedded in a larger general-purpose simulation system (GPSS) simulation used to model continuous improvement systems (CIS) policies in a factory setting is described. The neural network is used to accelerate the identification of an effective CIS policy by providing a more realistic simulation framework. The interface between general simulation theory and neural network simulation is examined. Neural networks, when embedded in larger general-purpose simulations, are found to offer the potential for improving on the capabilities of those simulations, in particular manufacturing simulations for continuous improvement of production processes.
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  • 6
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    Journal of intelligent manufacturing 3 (1992), S. 263-276 
    ISSN: 1572-8145
    Keywords: parallel distributed ; processing ; simulation ; object-oriented programming systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The field of neural networks is being investigated by many researchers in order to provide solutions to difficult problems in the area of manufacturing systems. Computer simulation of neural networks is an important part of this investigation. This paper applies concepts from an important trend in software engineering research, namely object-oriented programming, to model neural networks. The design and implementation of a software object library is crucial to obtaining the full benefits of object-oriented programming. In this paper we discuss the design and implementation of a foundation library of software objects for the purpose of simulating and validating different network architectures and learning rules. The library contains objects that implement various types of nodes and learning rules. We discuss the results of our experiments to illustrate the benefits of using an object-oriented approach to modeling neural networks.
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  • 7
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    Journal of intelligent manufacturing 9 (1998), S. 225-234 
    ISSN: 1572-8145
    Keywords: Expert system ; advisory system ; machining ; simulation ; intelligent machining
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A unique advisory system is developed for machining processes. It is unique in using analytical and simulation models for the induction of rules, rules which must otherwise be generated from experiments. These rules are combined with heuristic rules for inferring optimal machining parameters. The utility and accuracy of the process models are illustrated and the architecture of the advisory system is described. Also described are its capability to incorporate other application programs through functions, regardless of the programming language, and to address constraints in decision making. Face milling is described as a specific application.
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  • 8
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    Journal of intelligent manufacturing 9 (1998), S. 361-367 
    ISSN: 1572-8145
    Keywords: Adaptive genetic algorithms ; flow-shop ; dynamic population size ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract This paper describes the characteristics of two hybrid genetic algorithms (GAs) for generating allocation and sequencing of production lots in a flow-shop environment based on a non-linear, multi-criteria objective function. Both GAs are used as search techniques: in the first model the task of the GA is to allocate and sequence the jobs; in the second model, the GA is combined with a dispatching rule (Earliest Due Date, EDD) thus limiting its task only on the allocation of the jobs. Both GAs are characterized by a dynamic population size with dynamic birth rate, as well as by multiple-operator reproduction criteria and by adaptive crossover and mutation rates. A discrete-event simulation model has been used in order to evaluate the performances of the tentative schedules. The proposed algorithms have been subsequently compared with a classical branch and bound method.
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  • 9
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    Journal of intelligent manufacturing 1 (1990), S. 117-123 
    ISSN: 1572-8145
    Keywords: Production scheduling ; artificial intelligence ; export systems ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Scheduling is a complex problem which occurs often in a manufacturing environment. There are many possible variations within the context of a scheduling problem, enough to overwhelm anyone but an expert. A production manager, faced with the task of job scheduling for a particular process, might well benefit from the advice of a scheduling expert. Even though the scheduling literature is full of optimizing rules for a variety of manufacturing environments few, if any, of these rules have been used in practice. The bewildering variety of theoretical results, the lack of a mechanism to match theoretical results to practical problems and the difficulty in establishing the practical efficacy of the theoretical results are among the reasons for this gap between scheduling theory and practice. This paper describes a scheduling expert system framework which addresses these problems and helps bridge this gap. The solution techniques available in SCHEDEX produce a specific schedule for the problem according to a procedure which has been mathematically proven to provide a satisfactory and often optimal solution, given the criteria for the problem. A simulation model also tests for the effectiveness of a selected technique with respect to the chosen performance measure(s).
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  • 10
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    Journal of intelligent manufacturing 10 (1999), S. 323-329 
    ISSN: 1572-8145
    Keywords: Computer-aided design ; rapid prototyping ; modeling ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The direct slicing of CAD models created in CADDS V to generate geometric data for rapid prototyping using fused feposition modeling technique (FDM) is presented in this paper. The report file from an explicit model is accessed for obtaining model data. Algorithms have been developed for determining the volumes of model material as well as support materials. New algorithms have been developed for filling the sheet solid. A simulation module has been developed to verify whether the filling is correctly done. Example of a model is manufactured using this approach is also presented in this paper.
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  • 11
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    Journal of intelligent manufacturing 10 (1999), S. 405-421 
    ISSN: 1572-8145
    Keywords: Flexible manufacturing systems control ; intelligent manufacturing ; neural networks ; simulation ; material handling systems ; automated guided vehicles
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract This paper presents a framework of intelligent manufacturing scheduling and control with specific applications to operations of rail-guided vehicle systems (RGVS). A RGVS control architecture is discussed with a focus on a simulated experiment in operations of the load/unload area of a real industrial flexible manufacturing system (FMS). In the operation stage of a material handling system (MHS), all shop floor data are subject to change as time goes. These data can be collected using a data acquisition device and stored in a dynamic database. The RGVS simulator used in this experimental study is designed to incorporate some possible situations representing existing material handling scenarios in order to evaluate alternative control policies. At the development stage of the controller, all possible combinations of most commonly encountered scenarios such as RGV failures, production schedule changes, machine breakdowns, and rush orders are to be simulated and corresponding results collected. The data are then structured into training data pairs to properly train an artificial neural network. The neural network, trained by using input/output data sets obtained from a number of simulation runs, will then provide control strategy recommendations. At the application stage, whenever an abnormal scenario occurs, a pre-processor will be activated to pre-screen and prepare an input vector for the trained neural network. If such an abnormal scenario falls outside the existing domain of data sets employed to train the neural network, as judged by the MHS supervisory controller, an off-line training module will be activated to eventually update the neural network. The recommended control strategies will be transmitted to the MHS control for real-time execution. If there is no further abnormal event detected, the dynamic data base (DDB) module simply continues to monitor the MHS activities. The proposed MHS control system combines the features of example based neural network technology and simulation modeling for true intelligent, on-line, pseudo real-time control. Not only will the system assure that feasible material handling control actions be taken, but also it will implement better control decisions through continuous learning from experiences captured as the operation time of the MHS accumulates.
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  • 12
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    Journal of intelligent manufacturing 10 (1999), S. 449-462 
    ISSN: 1572-8145
    Keywords: Control chart ; pattern recognition ; neural network ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Abnormal patterns on manufacturing process control charts can reveal potential quality problems due to assignable causes at an early stage, helping to prevent defects and improve quality performance. In recent years, neural networks have been applied to the pattern recognition task for control charts. The emphasis has been on pattern detection and identification rather than more detailed pattern parameter information, such as shift magnitude, trend slope, etc., which is vital for effective assignable cause analysis. Moreover, the identification of concurrent patterns (where two or more patterns exist together) which are commonly encountered in practical manufacturing processes has not been reported. This paper proposes a neural network-based approach to recognize typical abnormal patterns and in addition to accurately identify key parameters of the specific patterns involved. Both single and concurrent patterns can be characterized using this approach. A sequential pattern analysis (SPA) design was adopted to tackle complexity and prevent interference between pattern categories. The performance of the model has been evaluated using a simulation approach, and numerical and graphical results are presented which demonstrate that the approach performs effectively in control chart pattern recognition and accurately identifies the key parameters of the recognized pattern(s) in both single and concurrent pattern circumstances.
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  • 13
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    Journal of intelligent manufacturing 4 (1993), S. 151-161 
    ISSN: 1572-8145
    Keywords: artificial memory ; simulation ; data analysis ; job-shop scheduling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper is devoted to the development of a knowledge-based system (KBS) called ‘Artificial Memory’, The goal of this KBS is to ‘solve’ multicriteria job-shop scheduling problems. Since job-shop scheduling problems are NP-hard, it is extremely difficult to obtain optimal solutions for industrial problems. Thus, a host of heuristic algorithms, most of which are based on priority rules, have been proposed in the literature. The efficiency of these algorithms strongly depends on the criteria to be optimized as well as the values of the parameters associated with the particular instance of the scheduling problem. The basic hypothesis of the artificial memory approach is a continuity assumption: we assume that identical decisions applied to similar instances lead to similar values of the criteria. This assumption is fundamental to validate this knowledge-based system. For each criterion, the artificial memory contains a synthesis of the performances of different algorithms upon sets of ‘similar’ instances. These performances are acquired using simulation. When the artificial memory is employed, the characteristic values of a new instance are computed and examined by the artificial memory system. The performances of the different algorithms for the considered criterion are estimated for the new instance and an appropriate algorithm is chosen accordingly. In order to build this KBS and to estimate the performances of algorithms upon a new instance, we use a mathematical approach. Some difficulties arose in the development of this KBS and had to be overcome: the corresponding proposed solutions are developed. The paper also presents a number of numerical experimental applications.
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  • 14
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    Journal of intelligent manufacturing 7 (1996), S. 243-250 
    ISSN: 1572-8145
    Keywords: Job-shop scheduling ; real-time dispatching ; simulation ; neural networks
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: To schedule a job shop, the first task is to select an appropriate scheduling algorithm or rule. Because of the complexity of scheduling problems, no general algorithm sufficient for solving all scheduling problems has yet been developed. Most job-shop scheduling systems offer alternative algorithms for different situations, and experienced human schedulers are needed to select the best dispatching rule in these systems. This paper proposes a new algorithm for job-shop scheduling problems. This algorithm consists of three stages. First, computer simulation techniques are used to evaluate the efficiency of heuristic rules in different scheduling situations. Second, the simulation results are used to train a neural network in order to capture the knowledge which can be used to select the most efficient heuristic rule for each scheduling situation. Finally, the trained neural network is used as a dispatching rule selector in the real-time scheduling process. Research results have shown great potential in using a neural network to replace human schedulers in selecting an appropriate approach for real-time scheduling. This research is part of an ongoing project of developing a real-time planning and scheduling system.
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  • 15
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    Journal of intelligent manufacturing 8 (1997), S. 3-14 
    ISSN: 1572-8145
    Keywords: Production system analysis ; object-oriented approach ; production control ; simulation ; Petri networks
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Tool specification for production system control requires the identification of the main characteristics of the production system. The production systems are varied, and the production control tools (such as scheduling algorithms and resource assignment rules) are often dedicated to only one class of these systems. Tool assessment for production system control requires modelling of the production system. We propose a new approach to production systems, to identify the nature and the complexity of the system according to the classification of Conway et al., and to specify a dynamic model that will allow us to simulate production control decisions. This paper presents this object-oriented approach, which identifies the resources and the organization features of the studied system. It then, proposes some predetermined classes of objects, which enable us to classify the system components and to use pre-existing dynamic models. These dynamic models are based on timed and coloured Petri nets. The overall architecture of our methodology follows three steps: top-down analysis of resources and bottom-up recognition of predetermined objects, instantiation and integration of objects, and implementation of objects. An example illustrates its use in the textile industry.
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  • 16
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    Journal of intelligent manufacturing 8 (1997), S. 405-413 
    ISSN: 1572-8145
    Keywords: Manufacturing systems ; decision making systems ; simulation ; discrete and continuous optimization ; discrete ψ-transform method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Algorithms for discrete and continuous optimization are a very important part of decision making systems in manufacturing. Most planning, scheduling and layout problems require these algorithms. In practice, research into efficient algorithms meets two principal obstacles. The first one is linked to the fact that quite often the criteria cannot be expressed in an analytic form, so it is not possible to use existing theoretical resolution methods. The second is due to the fact that most of the problems for which the criteria can be represented in analytic form are NP-hard problems. This situation can be simplified using simulation. But the use of simulation and optimization methods together often gives a local optimum. The proposed method in this paper is based on the use of a discrete modification of ψ-transforms jointly with some heuristics for local optimization. The originality of this approach is in the possibility to avoid a local optimum, while using models of simulation for the computation of values of the criteria. An example of the utilization of the method is given: it concerns the optimization of the launching of the parts in production in systems of the job-shop type. The proposed method is compared with a heuristic known to be very good in the same number of simulations. The results of five tests with different model sizes show the efficiency of the proposed method.
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  • 17
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    Journal of intelligent manufacturing 1 (1990), S. 77-91 
    ISSN: 1572-8145
    Keywords: Production scheduling ; expert system ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A complete knowledge based procedure for the design and manufacture of a round hole broach tool is described. The knowledge based design system (KBDS) produces a tool specification from user inputs describing the task to be performed. These design results are then used by the knowledge base to generate a geometric CAD/CAM representation, which can be utilized directly to display a drawing of the tool or to generate a CNC program for producing it. The process of formulating a knowledge-based design system demonstrates: the integration of expertise from experts, handbooks and theory; the awareness of restrictions on the scope of design that can be handled by a given system: the use of failure handling mechanisms to detect design failures and either adjust the emerging design or indicate infeasibility.
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  • 18
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    Journal of intelligent manufacturing 6 (1995), S. 175-190 
    ISSN: 1572-8145
    Keywords: Concurrent engineering ; cell design ; cell control ; simulation ; knowledge-based expert system ; neural networks
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract One of the major thrusts of ‘agile/lean/responsive’ manufacturing strategies of the twentyfirst century is to introduce advanced information technology into manufacturing. This paper presents a framework for robust manufacturing system design with the integration of simulation, neural networks and knowledge-based expert system tools. An operation/ cost-driven cell design methodology was applied to concurrently consider cell physical design and the complexity of cell control functions. Simulation was exercised to estimate performance measures based on input parameters and given cell configurations. A rulebased expert system was employed to store the acquired expert knowledge regarding the relation between cell control complexities, cost of cell controls, performance measures and cell configuration. Neural networks were applied to predict the cell design configuration and corresponding complexities of cell control functions. Training of neural networks was performed with both forward and backward methods by using the same pair of data sets. Hence, trained neural networks will be able to predict either input or output parameters. This innovative new design methodology was illustrated via a successful implementation exercise resulting in actually acquiring an automated cell at industrial settings. The experience learned from this exercise indicates that the proposed design methodology works well as an effective decision support system for cell designers and the management in determining appropriate cell configuration and cell control functions at the design stage.
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  • 19
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    Journal of intelligent manufacturing 8 (1997), S. 125-136 
    ISSN: 1572-8145
    Keywords: Artificial intelligence ; simulation ; database management system ; object oriented paradigm ; simulation program generation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Although many studies have illustrated AI-based simulation, the concept of combining databases with AI and simulation is relatively new. Complementing AI and simulation with databases aids in the development of a completely integrated simulation environment that spans the whole simulation life cycle. This study illustrates the design of a simulation program generator, the intelligent simulation code generator (ISCG), which uses a database management system as the user-oriented interface, an object-oriented system to develop the knowledge base and simulation environment, and a target simulation language as the simulation software. The ISCG offers data independence, system independence, simulation-specific transparency, and target language neutrality. Furthermore, the ISCG offers system design flexibility.
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  • 20
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    Order 12 (1995), S. 213-220 
    ISSN: 1572-9273
    Keywords: 06A10 ; 68C25 ; Parallel computation ; m-machine problem ; tree
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetP={v 1,...,v n } be a set ofn jobs to be executed on a set ofm identical machines. In many instances of scheduling problems, if a jobv i has to be executed before the jobv j and both jobs are to be executed on different machines, some sort of information exchange has to take place between the machines executing them. The time it takes for this exchange of information is called a communication delay. In this paper we give anO(n) algorithm to find an optimal scheduling with communication delays when the number of machines is not limited and the precedence constraints on the jobs form a tree.
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  • 21
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    Order 12 (1995), S. 327-349 
    ISSN: 1572-9273
    Keywords: 06A07 ; 06A10 ; Partially ordered set ; linear extension ; balancing pairs ; cross-product conjecture ; Ahlswede-Daykin inequality ; sorting
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In a finite partially ordered set, Prob (x〉y) denotes the proportion of linear extensions in which elementx appears above elementy. In 1969, S. S. Kislitsyn conjectured that in every finite poset which is not a chain, there exists a pair (x,y) for which 1/3⩽Prob(x〉y)⩽2/3. In 1984, J. Kahn and M. Saks showed that there exists a pair (x,y) with 3/11〈Prob(x〉y)〈8/11, but the full 1/3–2/3 conjecture remains open and has been listed among ORDER's featured unsolved problems for more than 10 years. In this paper, we show that there exists a pair (x,y) for which (5−√5)/10⩽Prob(x〉y)⩽(5+√5)/10. The proof depends on an application of the Ahlswede-Daykin inequality to prove a special case of a conjecture which we call the Cross Product Conjecture. Our proof also requires the full force of the Kahn-Saks approach — in particular, it requires the Alexandrov-Fenchel inequalities for mixed volumes. We extend our result on balancing pairs to a class of countably infinite partially ordered sets where the 1/3–2/3 conjecture isfalse, and our bound is best possible. Finally, we obtain improved bounds for the time required to sort using comparisons in the presence of partial information.
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  • 22
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    Order 13 (1996), S. 101-117 
    ISSN: 1572-9273
    Keywords: 06A10 ; (Partially) ordered set ; maximal chain ; maximal antichain ; cutset ; fibre
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract There is a product of two linear orders of size $$2^{\aleph _0 } $$ with the property that every subset or complement thereof contains a maximal chain. Furthermore, for regular ℵα, there is a product of two linear orders of size ℵα+2 that when colored with fewer than ℵα colors always has a monochromatic maximal chain. As a corollary, for every uncountable strong limit cardinal κ, there is an ordered set of cardinality κ that must be colored with at least κ colors before no monochromatic maximal chains are present. Duals of these results show that at least as much is true for maximal antichains.
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  • 23
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    Order 2 (1985), S. 193-198 
    ISSN: 1572-9273
    Keywords: 06A10 ; 06D99 ; 52A25 ; Finite distributive lattices ; finite posets ; valuations ; convex polytopes ; extreme points
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let L be a finite distributive lattice and V(L) the real vector space of all valuations on L. We verify the conjecture of Geissinger that the extreme points of the convex polytope M(L)={v ∈ L : 0 ≤ v ≤ 1} are precisely the 0–1 valuations.
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  • 24
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    Order 2 (1985), S. 257-264 
    ISSN: 1572-9273
    Keywords: 06A10 ; 68E05 ; Sorting ; merging ; linear extension
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a finite poset P and x, yεP let pr(x〉y) be the fraction of linear extensions which put x above y. N. Linial has shown that for posets of width 2 there is always a pair x, y with 1/3 ⩽ pr(x〉y)⩽2/3. The disjoint union C 1∪C 2 of a 1-element chain with a 2-element chain shows that the bound 1/3 cannot be further increased. In this paper the extreme case is characterized: If P is a poset of width 2 then the bound 1/3 is exact iff P is an ordinal sum of C 1∪C 2's and C 1's.
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  • 25
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    Order 3 (1986), S. 283-286 
    ISSN: 1572-9273
    Keywords: 06A10 ; 06A12 ; 06B99 ; Partially ordered set ; semilattice ; lattice ; cofinality
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    Topics: Mathematics
    Notes: Abstract A partial ordering on a set P can be weakened to an upper or lower semilattice ordering, respectively a lattice ordering, if and only if P is filtered in the appropriate direction(s).
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    Order 3 (1987), S. 355-357 
    ISSN: 1572-9273
    Keywords: 05App ; 06A10 ; Factor poset ; antichain ; depth
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    Topics: Mathematics
    Notes: Abstract Denote g(m, n) the minimum of min A, where A is a subset of {1, 2, ..., m} of size n and there do not exist two distinct x and y in A such that x divides y. We use a method of poset to prove that g(m, n)=2 i for positive integer i≤log3 m and 1+s(m, i−1)〈n≤1+s(m, i), where s(m, i) is the number of odd integers x such that m/3 i 〈x≤m.
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    Order 4 (1987), S. 127-142 
    ISSN: 1572-9273
    Keywords: 06A10 ; 68-XX ; Poset ; closures ; Hasse diagram
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    Topics: Mathematics
    Notes: Abstract The combinatorial properties of the poset of closures are studied, especially the degrees in the Hasse diagram.
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    Order 3 (1986), S. 1-2 
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    Keywords: 06A10 ; Jump number
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    Topics: Mathematics
    Notes: Abstract The following result is proved in this note: For any positive integers w and t, if an ordered set P has jump number at least (t+1) w−1, then either the width of P is more than w, or P has a tower, i.e., a linear sum of pairs of noncomparable elements, of height more than t.
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    Order 4 (1987), S. 155-164 
    ISSN: 1572-9273
    Keywords: 05C55 ; 06A10 ; 62J ; Regressions ; Ramsey theory
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    Topics: Mathematics
    Notes: Abstract A regressive function (also called a regression or contractive mapping) on a partial order P is a function σ mapping P to itself such that σ(x)≤x. A monotone k-chain for σ is a k-chain on which σ is order-preserving; i.e., a chain x 1〈...〈xksuch that σ(x 1)≤...≤σ(xk). Let P nbe the poset of integer intervals {i, i+1, ..., m} contained in {1, 2, ..., n}, ordered by inclusion. Let f(k) be the least value of n such that every regression on P nhas a monotone k+1-chain, let t(x,j) be defined by t(x, 0)=1 and t(x,j)=x t(x,j−1). Then f(k) exists for all k (originally proved by D. White), and t(2,k) 〈 f(K) 〈t(е + εk, k) , where εk → 0 as k→∞. Alternatively, the largest k such that every regression on P nis guaranteed to have a monotone k-chain lies between lg*(n) and lg*(n)−2, inclusive, where lg*(n) is the number of appliations of logarithm base 2 required to reduce n to a negative number. Analogous results hold for choice functions, which are regressions in which every element is mapped to a minimal element.
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    Order 4 (1987), S. 269-272 
    ISSN: 1572-9273
    Keywords: 06A10 ; 05A15 ; Interval order ; enumeration
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    Topics: Mathematics
    Notes: Abstract An algorithm is obtained for enumerating the interval orders of a given cardinality.
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    Order 3 (1987), S. 345-353 
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    Keywords: 06A10 ; 06A23 ; Order-dimension ; Ferrers relation ; partition lattice ; linear lattice
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    Topics: Mathematics
    Notes: Abstract The aim of this paper is to study the order-dimension of partition lattices and linear lattices. Our investigations were motivated by a question due to Bill Sands: For a lattice L, does dim L=n always imply |L|≥2 n ? We will answer this question in the negative since both classes of lattices mentioned above form counterexamples. In the case of the partition lattices, we will determine the dimension up to an absolute constant. For the linear lattice over GF(2), L n , we determine the dimension up to a factor C/n for an absolute constant C.
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    Order 3 (1987), S. 369-382 
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    Keywords: 06A10 ; Partial order ; tree ; chain decomposition ; width
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    Topics: Mathematics
    Notes: Abstract We establish some inequalities connecting natural parameters of a partial order P. For example, if every interval [a,b] contains at most λ maximal chains, if some antichain has cardinality v, and if there are χ1 chains whose union is cofinal and coinitial in P, then the chain decomposition number for P is ⩽χ1λv (Theorem 2.2), and the inequality is sharp in a certain sense (Section 3).
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    Order 4 (1987), S. 37-42 
    ISSN: 1572-9273
    Keywords: 06A10 ; Partially ordered sets ; Van der Waerden's arithmetic sequence
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    Topics: Mathematics
    Notes: Abstract Van der Waerden's arithmetic sequence theorem—in particular, the ‘density version’ of Szemerédi—is generalized to partially ordered sets in the following manner. Let w and t be fixed positive integers and ε〉0. Then for every sufficiently large partially ordered set P of width at most w, every subset S of P satisfying |S|≥ε|P| contains a chain a 1, a 2,..., a 1 such that the cardinality of the interval [a i, a i+1] in P is the same for each i.
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    Order 5 (1988), S. 163-171 
    ISSN: 1572-9273
    Keywords: 05C45 ; 05C70 ; 06A10 ; Boolean lattice ; Hamiltonian cycle ; matching
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    Topics: Mathematics
    Notes: Abstract New classes of explicit matchings for the bipartite graph ℬ(k) consisting of the middle two levels of the Boolean lattice on 2k+1 elements are constructed and counted. This research is part of an ongoing effort to show that ℬ(k) is Hamiltonian.
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    Order 6 (1989), S. 59-68 
    ISSN: 1572-9273
    Keywords: 06A10 ; Poset ; minimal cutset ; chain complete ; special points ; regular posets ; Menger's theorem
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    Topics: Mathematics
    Notes: Abstract If P is a poset, the associated PT-order is the quasi order ⊴ in which a ⊴ b holds if every maximal chain of P which passes through a also passes through b. P is special if whenever A is a chain in P and a=sup A or inf A, then there is b ∈ A such that b ⊴ a. It is proved that if P is chain complete and special then the set of ⊴-maximal elements is ⊴-dominating and contains a minimal cutset. As corollaries of this, we give partial answers to (i) a question of Rival and Zaguia by showing that if P is regular and special every element is in a minimal cutset and (ii) a question of Brochet and Pouzet by showing that if P is chain complete and special then it has the Menger property.
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    Order 7 (1990), S. 145-167 
    ISSN: 1572-9273
    Keywords: 06A10 ; 08A40 ; 08B10 ; 08C05 ; 08C15 ; Order-primal ; clone ; congruence-distributive ; duality ; category equivalence ; near-unanimity function
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    Topics: Mathematics
    Notes: Abstract A finite, nontrivial algebra is order-primal if its term functions are precisely the monotone functions for some order on the underlying set. We show that the prevariety generated by an order-primal algebra P is relatively congruence-distributive and that the variety generated by P is congruence-distributive if and only if it contains at most two non-ismorphic subdirectly irreducible algebras. We also prove that if the prevarieties generated by order-primal algebras P and Q are equivalent as categories, then the corresponding orders or their duals generate the same order variety. A large class of order-primal algebras is described each member of which generates a variety equivalent as a category to the variety determined by the six-element, bounded ordered set which is not a lattice. These results are proved by considering topological dualities with particular emphasis on the case where there is a monotone near-unanimity function.
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    Order 7 (1990), S. 249-266 
    ISSN: 1572-9273
    Keywords: 05C99 ; 06A10 ; Covering graph ; partially ordered set
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    Topics: Mathematics
    Notes: Abstract We give a construction of lattices whose covering graphs can be oriented as a graded order with bottom v for any vertex v in the lattice.
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    Order 7 (1990), S. 329-339 
    ISSN: 1572-9273
    Keywords: 06A10 ; 60C05 ; Partially ordered set ; random order ; dimension
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    Topics: Mathematics
    Notes: Abstract A relationship is established between (partially) ordered sets of dimension 2 chosen randomly on a labelled set, chosen randomly by isomorphism type, or generated by pairs of random linear orderings. As a consequence we are able to determine the limiting probability (in each of the above sample spaces) that a two-dimensional order is rigid, is uniquely realizable, or has uniquely orientable comparability graph; all these probabilities lie strictly between 0 and 1. Finally, we show that the number of 2-dimensional (partial) orderings of a labelled n-element set is $$(1 + o(1))n!^2 /(2\sqrt e ).$$ .
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    Order 7 (1990), S. 353-359 
    ISSN: 1572-9273
    Keywords: 06A10 ; 68C15 ; Linear extension ; jump number
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    Topics: Mathematics
    Notes: Abstract An ordered set P is called K-free if it does not contain a four-element subset {a, b, c, d} such that a 〈 b is the only comparability among these elements. In this paper we present a polynomial algorithm to find the jump number of K-free ordered sets.
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    Order 6 (1990), S. 313-318 
    ISSN: 1572-9273
    Keywords: 06A10 ; Partial order ; linear extension ; majority cycle
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    Topics: Mathematics
    Notes: Abstract For points x and y in a poset (X, 〉) let x〉 p y mean that more linear extensions of the poset have x above y than y above x. It has been known for some time that 〉 p can have cycles when the height of the poset is two or more. Moreover, the smallest posets with a 〉 p cycle have nine points and heights of 2, 3 and 4. We show here that height-1 posets can also have 〉 p cycles. Our smallest example for this phenomenon has 15 points.
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    Order 6 (1990), S. 351-366 
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    Keywords: 05A17 ; 06A10 ; Young's lattice ; matching ; partially ordered set
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    Topics: Mathematics
    Notes: Abstract If the level sets of a ranked partially ordered set are totally ordered, the greedy match between adjacent levels is defined by successively matching each vertex on one level to the first available unmatched vertex, if any, on the next level. Aigner showed that the greedy match produces symmetric chains in the Boolean algebra. We extend that result to partially ordered sets which are products of chains. It is widely thought that for Young's lattices corresponding to rectangles, the greedy match is complete. We show here that the greedy match is, in fact, complete for n×2, n×3 and n×4 rectangles but not for n×k rectangles if k≥5 and n is sufficiently large.
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    Order 7 (1990), S. 5-9 
    ISSN: 1572-9273
    Keywords: 06A10 ; 05C25 ; 20B25 ; 20B27 ; Automorphism group ; comparability graph ; covering graph
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    Topics: Mathematics
    Notes: Abstract Let G be a group and H a subgroup of G. It is shown that there exists a partially ordered set (X, ⩽) such that G is isomorphic to the group of all automorphisms of the comparability graph of (X, ⩽) and such that under this isomorphism H is mapped onto the group of all order-automorphisms of (X, ⩽). There also exists a partially ordered set (Y, ⩽) such that G is isomorphic to the group of all automorphisms of the covering graph of (Y, ⩽) and such that under this isomorphism H is mapped onto the group of all order-automorphisms of (Y, ⩽). In this representation X and Y can be taken to be finite if G is finite and of the same cardinality as G if G is infinite.
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    Order 7 (1990), S. 267-273 
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    Keywords: 06A10 ; Linear extension ; realization
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    Notes: Abstract A k-realization of an ordered set P is a sequence of k linear orderings of the underlying set of P, whose intersection is (the order relation of) P. We determine the status of the number of k-realizations with respect to comparability invariance, and we show that among all orders on the set {1, 2, ..., n}, the antichain has the most k-realizations, for any k〉1. The latter intuitively reasonable result rests ultimately on an observation related to comparability invariance for numbers of linear extensions.
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    Order 7 (1990), S. 349-352 
    ISSN: 1572-9273
    Keywords: 68C15 ; 06A10 ; Posets ; preemptive ; scheduling
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    Topics: Mathematics
    Notes: Abstract Optimal preemptive schedules of jobs with unit completion times and given precedence constraints may require arbitrarily many short intervals of work on a single task.
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    Order 8 (1991), S. 63-75 
    ISSN: 1572-9273
    Keywords: 06A10 ; Infinite ordered set ; spanned ; maximal chain ; disjoint family ; cutset-number
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    Topics: Mathematics
    Notes: Abstract We say that an ordered set P is spanned by a family C of chains if P=(P, ⩽) is the transitive closure of ∪{(C, ≤ | C) C ∈ C. It is shown that there is a function h: ω→ω such that if P is spanned by k〈ω chains, then P has a finite cutset-number ⩽h(k) (i.e. for any x∈P, there is a finite set F of size |F|⩽h(k)−1, such that the elements of F are incomparable with x and {x}∪F meets every maximal chain of P). The function h is exponentially bounded but eventually dominates any polynomial function, even if it is only required that there are at most h(k) pairwise disjoint maximal chains in P, whenever P is spanned by k〈ω chains.
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    Order 9 (1992), S. 367-396 
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    Keywords: 06A05 ; 06A10 ; 06A99 ; Ordering ; axiomatization ; closure properties ; transitivity
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    Topics: Mathematics
    Notes: Abstract A set of six axioms for sets of relations is introduced. All well-known sets of specific orderings, such as linear and weak orderings, satisfy these axioms. These axioms impose criteria of closedness with respect to several operations, such as concatenation, substitution and restriction. For operational reasons and in order to link our results with the literature, it is shown that specific generalizations of the transitivity condition give rise to sets of relations which satisfy these axioms. Next we study minimal extensions of a given set of relations which satisfy the axioms. By this study we come to the fundamentals of orderings: They appear to be special arrangements of several types of disorder. Finally we notice that in this framework many new sets of relations have to be regarded as a set of orderings and that it is not evident how to minimize the number of these new sets of orderings.
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    Annals of operations research 3 (1985), S. 355-377 
    ISSN: 1572-9338
    Keywords: Flexible manufacturing systems ; scheduling ; manufacturing systems ; simulation ; computer integrated manufacturing
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    Topics: Mathematics , Economics
    Notes: Abstract This paper presents a new two-phase (TP) approximate method for real-time scheduling in a flexible manufacturing system (FMS). This method combines a reduced enumeration schedule generation algorithm with a 0–1 optimization algorithm. In order to make the combined algorithm practicable, heuristic rules are introduced for the selection of jobs to be scheduled. The relative performance of the TP method vis-a-vis conventional heuristic dispatching rules such as SPT, LPT, FCFS, MWKR, and LWKR is investigated using combined process-interaction/discrete-event simulation models. An efficient experimental procedure is designed and implemented using these models, and the statistical analysis of the results is presented. For the particular case investigated, the conclusions are very encouraging. In terms of mean flow time, the TP method performs significantly better than any other tested heuristic dispatching rules. Also, the experimental results show that using global information significantly improves the FMS performance.
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    Annals of operations research 3 (1985), S. 13-21 
    ISSN: 1572-9338
    Keywords: Flexible manufacturing systems ; queueing models ; simulation ; performance evaluation
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    Topics: Mathematics , Economics
    Notes: Abstract Flexible manufacturing systems (FMSs) are a class of automated systems which can be used to improve productivity in discrete parts manufacturing. Due to the complexity of these systems, it is useful to have models that can aid in the design and operation of FMSs. We specifically differentiate here betweengenerative (or prescriptive) models, whichfind candidate decisions, andevaluative (or descriptive) models, whichevaluate a given set of decisions. We briefly cover, in a practical context, the pros and cons of these two classes of models. Then we focus on the latter class of models. Evaluative models for FMSs fall into five main classes, based on the technique used, namely: static allocation, queueing network theory, simulation, perturbation analysis, and Petri nets. Each of these approaches is briefly described, advantages and disadvantages mentioned, and references given to more detailed papers.
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    Annals of operations research 39 (1992), S. 157-172 
    ISSN: 1572-9338
    Keywords: Score function method ; likelihood ratio ; sensitivity analysis ; simulation ; Monte Carlo methods ; conditioning
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    Topics: Mathematics , Economics
    Notes: Abstract We consider first a discrete event static system that is to be simulated at values of a parameter or vector of parametersθ. The system is assumed driven by an inputX, where typicallyX is a vector of variables whose densityf θ (x) depends on the parameterθ. For the purpose of optimizing, finding roots, or graphing the expected performanceE θ L(X) for performance measureL, it is useful to estimate not only the expected value but also its gradient. An unbiased estimator for the latter is the score function estimator $$L(X)S(\theta ) = L(X)\frac{\partial }{{\partial \theta }}\ln f_\theta (x).$$ This estimator and likelihood ratio analogues typically require variance reduction, and we consider conditioning on the value of the score function for this purpose. The efficiency gains due to performing the Monte Carlo conditionally can be very large. Extension to discrete event dynamic systems such as theM/G/1 queue and other more complicated systems is considered.
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    Annals of operations research 53 (1994), S. 175-197 
    ISSN: 1572-9338
    Keywords: Variance reduction ; simulation ; control variates ; importance sampling ; common random numbers ; stratification ; conditioning ; efficiency
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    Topics: Mathematics , Economics
    Notes: Abstract This paper provides an overview of the five most commonly used statistical techniques for improving the efficiency of stochastic simulations: control variates, common random numbers, importance sampling, conditional Monte Carlo, and stratification. The paper also describes a mathematical framework for discussion of efficiency issues that quantifies the trade-off between lower variance and higher computational time per observation.
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    Keywords: integer programming ; discriminant analysis ; simulation
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    Notes: Abstract Although there have been several journal articles on the classificatory performance of mathematical programming approaches to the two-group discriminant problem, there has been no simulation study on the classificatory performance of mathematical programming approaches to the multiple-group problem reported in the literature. This study reports the results of a simulation experiment on the classificatory performance of a single-function and a multiple-function mathematical programming model relative to that of the standard parametric procedures for the three-group problem with small training samples. The effect of second-order terms on the classificatory performance of the mathematical programming models for the three-group problem is also investigated. Furthermore, this study theoretically examines the range of parameter values of a multiple-function mathematical programming model for which its number of misclassifications in the training sample cannot exceed that of a single-function model.
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    Annals of operations research 74 (1997), S. 321-332 
    ISSN: 1572-9338
    Keywords: simulation ; modeling ; aerospace ; air route structure ; free flight ; clustering
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    Topics: Mathematics , Economics
    Notes: Abstract Recent work performed for the Federal Aviation Administration to support the development of future concepts of air traffic management has involved simulation modeling of patterns of airspace usage by commercial and business air traffic. The objective of these efforts has been to investigate the impacts of a pattern of airspace usage known as "free flight", whereby pilots and flight dispatchers have much more freedom to choose, say, direct or wind-optimal routing through airspace. One of the figures of merit investigated is a count of "convergence pairs" as a measure of the complexity of various traffic patterns. These are cases when aircraft in the simulation model fly close to each other. Interestingly, geographic plots of convergence pairs accumulated over time bring out certain features or patterns of congested air traffic flows or flight alignments. However, these plots are also thick with "noise" or extraneous convergence pairs, whose presence detracts from the ability to perceive congested air traffic flows. Cluster analysis has been found to be an effective method of filtering these displays so that the congested flow features are discernible. The process developed for this purpose is based on a two-pass clustering approach. The process has worked well for the simulation modeling performed to date. Classification of the locations of convergence pairs into congested flow corridors is visually appealing, and has helped distinguish differences in contrasting scenarios of airspace usage. The paper presents graphical results and describes the clustering algorithms employed.
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    International journal of flexible manufacturing systems 5 (1993), S. 53-88 
    ISSN: 1572-9370
    Keywords: manufacturing control software ; software methodologies ; planning ; scheduling ; monitoring ; simulation
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The complexity and diversity of manufacturing software and the need to adapt this software to the frequent changes in the production requirements necessitate the use of a systematic approach to developing this software. The software life-cycle model (Royce, 1970) that consists of specifying the requirements of a software system, designing, implementing, testing, and evolving this software can be followed when developing large portions of manufacturing software. However, the presence of hardware devices in these systems and the high costs of acquiring and operating hardware devices further complicate the manufacturing software development process and require that the functionality of this software be extended to incorporate simulation and prototyping. This paper reviews recent methods for planning, scheduling, simulating, and monitoring the operation of manufacturing systems. A synopsis of the approaches to designing and implementing the real-time control software of these systems is presented. It is concluded that current methodologies support, in a very restricted sense, these planning, scheduling, and monitoring activities, and that enhanced performance can be achieved via an integrated approach.
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    International journal of flexible manufacturing systems 5 (1993), S. 301-323 
    ISSN: 1572-9370
    Keywords: flexible manufacturing systems ; automated guided vehicles ; scheduling ; dispatching ; simulation
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Although extensive research has been conducted to solve design and operational problems of automated manufacturing systems, many of the problems still remain unsolved. This article investigates the scheduling problems of flexible manufacturing systems (FMSs). Specifically, the relative performances of machine and automated guided vehicle (AGV) scheduling rules are analyzed against various due-date criteria. First, the relevant literature is briefly reviewed, and then the rules are tested under different experimental conditions by using a simulation model of an FMS. The sensitivity to AGV workload, buffer capacity, and processing-time distribution is also investigated to assess the robustness of the scheduling rules.
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    International journal of flexible manufacturing systems 7 (1995), S. 339-360 
    ISSN: 1572-9370
    Keywords: Petri net ; FMS ; modeling ; simulation ; tool ; analysis ; animation
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract We propose a CAD tool, XPN-FMS, which is primarily based on a unique Petri net (PN) synthesis method, called the knitting technique, developed by the authors. Petri net theory has been applied to specification, validation, performance analysis, control code generation, and simulation for manufacturing systems. The analysis of flexible manufacturing systems (FMSs) based on PNs suffers from the complexity problem of reachability analysis (Peterson, 1981). CAD tools are urgently needed. There is no existing CAD tool for FMSs as comprehensive as XPN-FMS, in the sense that the latter integrates the functions of drawing, analysis, reduction (Chao and Wang, 1992; Murata and Koh, 1980), synthesis, property queries, and animation of FMS operations in one software package. Using the X window graphical interface and animation, XPN-FMS makes the modeling and analysis of an FMS visualizable and easy to understand and manipulate. It lets a user draw the factory layout of an FMS on the screen of a monitor using the supplied tools. A corresponding PN model can also be drawn on the monitor screen. XPN-FMS can animate and simulate the overall operating process of the FMS. It is useful for FMS specification, validation, and exploration of different design alternatives, status monitoring, and control. Using XPN-FMS with various inputs and comparing the resulting outputs, the user can determine how to improve efficiency, reduce cost, and pinpoint bottlenecks. For the PN models of FMSs that are decision free, we extend the theory and algorithm of a unique matrix-based method (Chao and Wang, 1993b) to search for subcritical loops (including types A and B) and to support scheduling and dealing with transition periods. XPN-FMS implements this extended method to find the minimum cycle time, critical loop, subcritical loops, next critical loop, and scheduling ranges to avoid the transient period for static scheduling. This is implemented in XPN-FMS for the input sequence control.
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    International journal of flexible manufacturing systems 8 (1996), S. 23-43 
    ISSN: 1572-9370
    Keywords: FMS ; simulation ; scheduling ; dispatch ; heuristics
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The objective of the research, presented herein, was to determine whether or not the makespan performance of an FMS could be improved by a methodology which draws parallels with the actions of a human chess player in resolving decision problems in an environment where optimal solutions were computationally intractable with current processing technologies. The methodology was given the acronym CHESS (Control Heuristic Embedded System Simulator) and provides a mechanism for using short-term simulation look-aheads to resolve contention problems. The research also sought to determine the relationship between performance improvement and “look-ahead distance.” The results of the research highlight the fact that the methodology could provide considerable reductions in the number of contentions and the makespan time for a given range of part types (approximately 20 percent for the test-case applications). The most pertinent results, however, are those that highlight the effectiveness of look-ahead distance in terms of improving system performance, and these may have a potential to provide a significant impact in a range of different areas.
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    Annals of operations research 8 (1987), S. 363-381 
    ISSN: 1572-9338
    Keywords: Probability ; simulation ; petroleum ; resources ; appraisal
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    Topics: Mathematics , Economics
    Notes: Abstract An analytic probabilistic methodology for resource appraisal of undiscovered oil and gas resources in play analysis is presented. This play-analysis methodology is a geostochastic system for petroleum resource appraisal in explored as well as frontier areas. An objective was to replace an existing Monte Carlo simulation method in order to increase the efficiency of the appraisal process. Underlying the two methods is a single geologic model which considers both the uncertainty of the presence of the assessed hydrocarbon and its amount if present. The results of the model are resource estimates of crude oil, nonassociated gas, dissolved gas, and gas for a geologic play in terms of probability distributions. The analytic method is based upon conditional probability theory and a closed form solution of all means and standard deviations, along with the probabilities of occurrence.
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    Order 1 (1985), S. 235-247 
    ISSN: 1572-9273
    Keywords: 06A10 ; Chain ; antichain ; cutset
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    Topics: Mathematics
    Notes: Abstract A subset A of an ordered set P is a cutset if each maximal chain of P meets A; if, in addition, A is an antichain call it an antichain cutset. Our principal result is a characterization, by means of a ‘forbidden configuration’, of those finite ordered sets, which can be expressed as the union of antichain cutsets.
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    Order 1 (1985), S. 317-331 
    ISSN: 1572-9273
    Keywords: 06A10 ; 60C05 ; Partially ordered set ; probabilistic methods ; dimension
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    Topics: Mathematics
    Notes: Abstract Letk andn be positive integers and fix a setS of cardinalityn; letP k (n) be the (partial) order onS given by the intersection ofk randomly and independently chosen linear orders onS. We begin study of the basic parameters ofP k (n) (e.g., height, width, number of extremal elements) for fixedk and largen. Our object is to illustrate some techniques for dealing with these ‘random orders’ and to lay the groundwork for future research, hoping that they will be found to have useful properties not obtainable by known constructions.
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    Order 1 (1985), S. 371-375 
    ISSN: 1572-9273
    Keywords: 06A10 ; Poset ; chain ; antichain ; cutset
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    Topics: Mathematics
    Notes: Abstract It is shown that ifP is a poset containing noN, then every minimal cutset inP is an antichain, that the converse also holds whenP is finite, and that this converse fails in general.
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    Order 11 (1994), S. 197-210 
    ISSN: 1572-9273
    Keywords: 06A10 ; 68C25 ; On-line algorithm ; lattice of maximal antichains
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    Topics: Mathematics
    Notes: Abstract We consider the on-line computation of the lattice of maximal antichains of a finite poset $$\tilde P$$ . This on-line computation satisfies what we call the “linear extension hypothesis”: the new incoming vertex is always maximal in the current subposet of $$\tilde P$$ . In addition to its theoretical interest, this abstraction of the lattice of antichains of a poset has structural properties which give it interesting practical behavior. In particular, the lattice of maximal antichains may be useful for testing distributed computations, for which purpose the lattice of antichains is already widely used. Our on-line algorithm has a run time complexity of $$\mathcal{O}((\left| P \right| + \omega ^2 (P))\omega (P)\left| {MA(P)} \right|),$$ , where |P| is the number of elements of the poset, $$\tilde P$$ , |MA(P)| is the number of maximal antichains of $$\tilde P$$ and ω(P) is the width of $$\tilde P$$ . This is more efficient than the best off-line algorithms known so far.
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    Order 11 (1994), S. 309-316 
    ISSN: 1572-9273
    Keywords: 90B35 ; 06A10 ; Scheduling ; communication delays ; parallel processors ; precedence constraints
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    Topics: Mathematics
    Notes: Abstract We show that a greedy algorithm for scheduling unit time jobs on two machines with unit communication delays produces an optimal schedule when the precedence constraints are given by a rooted forest. We also give a min/max relationship for the length of such a schedule. The min/max result (for forests and two machines) shows that the addition of unit communication delays increases the optimal schedule length by at most one.
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    Order 2 (1985), S. 25-40 
    ISSN: 1572-9273
    Keywords: 06A10 ; 05C20 ; 05C38 ; Order ; diagram ; graph ; orientation ; cycle
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    Topics: Mathematics
    Notes: Abstract We study some equivalent and necessary conditions for a finite graph to be the covering graph of a (partially) ordered set. For each κ≥1, M. Aigner and G. Prins have introduced a notion of a vertex colouring, here called κ-good colouring, such that a 1-good colouring is the usual concept and graphs that have a 2-good colouring are precisely covering graphs. We present some inequalities for the corresponding chromatic numbers χκ, especially for x 2. There exist graphs that satisfy these inequalities for κ=2 but are not covering graphs. We show also that x 2 cannot be bounded by a function of x=x 1. A construction of Nešetřil and Rödl is used to show that x 2 is not bounded by a function of the girth.
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    Order 2 (1985), S. 387-402 
    ISSN: 1572-9273
    Keywords: 06A10 ; Poset ; linear extension ; correlation ; universal correlation ; Graham, Yao, and Yao inequality ; xyz inequality
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    Topics: Mathematics
    Notes: Abstract Posets $$A,{\text{ }}B \subseteq X{\text{ x }}X$$ are said to be correlated with respect to another poset R on X (we write A↑ R B) if P(R∪A) P(R∪B)≤P(R∪A∪B) P(R). Here P(S) is the probability that a randomly chosen bijection from X to the totally ordered set with |X| elements is a linear extension of S. We study triples (A, B, R) such that A ↑ R B holds for all extensions S of R (we write A $$\begin{array}{*{20}c} \uparrow \\ \uparrow \\ \end{array}$$ R B). Two well-known correlation inequalities, the xyz inequality and an inequality of Graham, Yao, and Yao, can be considered as giving cases when this relation holds. We show when the Graham, Yao, and Yao inequality holds strictly. Our main result is a classification of all R such that (a, b) $$\begin{array}{*{20}c} \uparrow \\ \uparrow \\ \end{array}$$ R (c, d) holds, where a, b, c, d are elements of X.
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    Order 3 (1986), S. 15-20 
    ISSN: 1572-9273
    Keywords: 06A10 ; Partially ordered set
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    Topics: Mathematics
    Notes: Abstract Let P be a partially ordered set. Define k = k (P) = max p∈ |{x ∈ P : p 〈 x or p = x}|, i.e., every element is comparable with at most k others. Here it is proven that there exists a constant c (c 〈 50) such that dim P 〈 ck(log k)2. This improves an earlier result of Rödl and Trotter (dim P ≤2 k 2+2). Our proof is nonconstructive, depending in part on Lovász' local lemma.
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    Order 2 (1985), S. 269-274 
    ISSN: 1572-9273
    Keywords: 06A10 ; Partial order ; fixed point ; comparability graph
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    Topics: Mathematics
    Notes: Abstract We show that the fixed point property is comparability invariant for finite ordered sets; that is, if P and Q are finite ordered sets with isomorphic comparability graphs, then P has the fixed point property if and only if Q does. In the process we give a characterization of comparability invariants which can also be used to give shorter proofs of some known results.
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    Order 5 (1988), S. 21-22 
    ISSN: 1572-9273
    Keywords: 06A10 ; Dimension ; width ; chain-covering number
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    Topics: Mathematics
    Notes: Abstract A partially ordered set with no infinite antichains may have arbitrarily large dimension.
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    Order 3 (1986), S. 21-38 
    ISSN: 1572-9273
    Keywords: 06A10 ; Ladder ; cutset ; 2-cutset property ; chain ; antichain
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    Topics: Mathematics
    Notes: Abstract An ordered set P is said to have the 2-cutset property if for every element x of P there is a subset S of P whose elements are noncomparable to x, such that |S|≤2 and such that every maximal chain in P meets {x}∪S. It is shown that if P has the 2-cutset property and has width n then P contains a ladder of length [1/2(n−3)].
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    Order 4 (1988), S. 315-318 
    ISSN: 1572-9273
    Keywords: 06A10 ; Circle containment order ; poset
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    Topics: Mathematics
    Notes: Abstract A partially ordered set is called acircle containment order provided one can assign to each element of the poset a circle in the plane so thatx≤y iff the circle assigned tox is contained in the circle assigned toy. It has been conjectured that every finite three-dimensional partially ordered set is a circle containment order. We show that the infinite three dimensional posetZ 3 isnot a circle containment order.
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    Order 5 (1988), S. 173-186 
    ISSN: 1572-9273
    Keywords: 06A10 ; Ordered set ; retract ; variety ; obstruction
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    Topics: Mathematics
    Notes: Abstract We use the technique of ‘χ-Embeddings’ to study retracts and varieties of ordered sets. We investigate the class of all ordered sets $$Q$$ which are retract of every ordered set in which $$Q$$ is ‘χ-Embedded’.
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    Order 5 (1989), S. 369-380 
    ISSN: 1572-9273
    Keywords: 06A10 ; Poset ; linear extension ; semiorder ; 1/3–2/3 conjecture ; partially ordered set
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    Topics: Mathematics
    Notes: Abstract A well-known conjecture of Fredman is that, for every finite partially ordered set (X, 〈) which is not a chain, there is a pair of elements x, y such that P(x〈y), the proportion of linear extensions of (X, 〈) with x below y, lies between 1/3 and 2/3. In this paper, we prove the conjecture in the special case when (X, 〈) is a semiorder. A property we call 2-separation appears to be crucial, and we classify all locally finite 2-separated posets of bounded width.
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    Order 6 (1989), S. 31-37 
    ISSN: 1572-9273
    Keywords: 05A05 ; 06A10 ; Cutset ; Boolean lattice
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    Topics: Mathematics
    Notes: Abstract An informative new proof is given for the theorem of Nowakowski that determines for all n and k the minimum size of a cutset for an element A with |A|=k of the Boolean algebra B n of all subsets of {1,...,n}, ordered by inclusion. An inequality is obtained for cutsets for A that is reminiscent of Lubell's inequality for antichains in B n. A new result that is provided by this approach is a list of all minimum cutsets for A.
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    Order 5 (1989), S. 349-361 
    ISSN: 1572-9273
    Keywords: 05C10 ; 06A10 ; Convex Hasse representations ; Kuratowski type results for Hasse diagrams
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    Topics: Mathematics
    Notes: Abstract A plane Hasse representation of an acyclic oriented graph is a drawing of the graph in the Euclidean plane such that all arcs are straight-line segments directed upwards and such that no two arcs cross. We characterize completely those oriented graphs which have a plane Hasse representation such that all faces are bounded by convex polygons. From this we derive the Hasse representation analogue, due to Kelly and Rival of Fary's theorem on straight-line representations of planar graphs and the Kuratowski type theorem of Platt for acyclic oriented graphs with only one source and one sink. Finally, we describe completely those acyclic oriented graphs which have a vertex dominating all other vertices and which have no plane Hasse representation, a problem posed by Trotter.
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    Order 6 (1989), S. 265-275 
    ISSN: 1572-9273
    Keywords: 05C75 ; O5C99 ; 06A10 ; Upper bound graph ; multigraph ; poset ; chordal graph ; interval graph
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    Topics: Mathematics
    Notes: Abstract The study of upper bound graphs of posets can be extended naturally to multigraphs. This paper characterizes such upper bound multigraphs, shows they determine the associated posets up to isomorphism, and extends results of D. Scott to characterize posets having chordal or interval upper bound multigraphs.
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    Order 5 (1988), S. 235-237 
    ISSN: 1572-9273
    Keywords: 06A10 ; Circle containment order ; poset
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    Topics: Mathematics
    Notes: Abstract A partially ordered set P is called a circle containment order provided one can assign to each x∈P a circle C x so that $$x \leqslant y \Leftrightarrow C_x \subseteq C_y $$ . We show that the infinite three-dimensional poset N 3 is not a circle containment order and note that it is still unknown whether or not [n]3 is such an order for arbitrarily large n.
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    Order 7 (1990), S. 101-102 
    ISSN: 1572-9273
    Keywords: 06A10 ; Dimension of a poset ; direct product ; strict product
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    Topics: Mathematics
    Notes: Abstract It is shown that the dimension of a poset is the smallest cardinal number λ such that there is an embedding of the poset into a strict product of λ linear orders.
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    Order 7 (1990), S. 133-143 
    ISSN: 1572-9273
    Keywords: 06A10 ; Order ; diagram ; slope ; degree ; cover ; bend ; crooked
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    Topics: Mathematics
    Notes: Abstract A natural and practical criterion in the preparation of diagrams of ordered sets is to minimize the number of different slopes used for the edges. For any diagram this is at least the maximum number of upper covers and of lower covers of any element. While this maximum degree is not always enough we show that it is as long as any edge joining a covering pair may be bent, to produce a crooked diagram.
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    Order 6 (1989), S. 1-14 
    ISSN: 1572-9273
    Keywords: 06A10 ; Fixed point ; irreducible element ; dismantlability ; cutset ; retraction ; crown
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    Topics: Mathematics
    Notes: Abstract There exist exactly eleven (up to isomorphism and duality) ordered sets of size ≤10 with the fixed point property and containing no irreducible elements.
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    Order 6 (1989), S. 39-47 
    ISSN: 1572-9273
    Keywords: 06A10 ; Inclusion orders ; circle orders ; angle orders
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    Topics: Mathematics
    Notes: Abstract A poset is a circle order if its points can be mapped into circular disks in the plane so that x〈y in the poset precisely when x's circular disk is properly included in y's; the poset is an angle order if its points can be mapped into unbounded angular regions that preserve 〈 by proper inclusion. It is well known that many finite angle orders are not circle orders, but has been open as to whether every finite circle order is an angle order. This paper proves that there are finite circle orders that are not angle orders.
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    Order 6 (1989), S. 91-99 
    ISSN: 1572-9273
    Keywords: 08A40 ; 06A10 ; Clones ; crowns ; tences ; generators
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    Topics: Mathematics
    Notes: Abstract In this paper we study the clones of all order preserving operations for crowns and fences. By presenting explicit generating sets, we show that these clones are finitely generated. The case of crowns is particularly interesting because they admit no order preserving near unanimity operations. Various related questions are also discussed. For example, we give a new proof of a theorem of Duffus and Rival which states that crowns are irreducible.
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    Order 6 (1989), S. 235-240 
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    Keywords: 06A10 ; 52A37 ; Order ; sphere ; partially ordered set ; space-time
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    Topics: Mathematics
    Notes: Abstract Ann-sphere order is a finite partially ordered set representable by containment ofn-spheres in Euclidean (n+1)-space. We present a sequence {P i } of ordered sets such that eachP i is ann-sphere order only forn≥i; one consequence is that we are able to determine the dimension of a Euclidean space-time manifold from the finite suborders of its causality order.
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    Annals of operations research 53 (1994), S. 391-418 
    ISSN: 1572-9338
    Keywords: Autoregressive process ; confidence interval ; output analysis ; simulation ; statistics ; time series
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    Topics: Mathematics , Economics
    Notes: Abstract We revisit and update the autoregressive-output-analysis method for constructing a confidence interval for the steady-state mean of a simulated process by using Rissanen's predictive least-squares criterion to estimate the autoregressive order of the process. This order estimator is strongly consistent when the output is autoregressive. The order estimator is combined with the standard autoregressive-output-analysis method to form a confidence-interval procedure. Alternatives for estimating the degrees of freedom for the procedure are investigated. The main result is an asymptotically valid confidence-interval procedure that, empirically, has good small-sample properties.
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    Annals of operations research 67 (1996), S. 183-210 
    ISSN: 1572-9338
    Keywords: Capacity planning ; emergency services ; health care ; simulation
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    Topics: Mathematics , Economics
    Notes: Abstract Due to its highly stochastic nature and complex interaction between services involved, health care has been a demanding area of application for computer simulation. This paper includes details and results of a simulation study realized in the Surgical Emergency Department at Istanbul University School of Medicine. The purpose is to suggest new bed capacities to improve the current system, and also to provide the management with guidelines for their expansion plans. For this aim, arrival rates, treatment procedures, inpatient admittance, and service durations have been carefully analyzed and modeled. The model, coded in SLAM-II simulation language, has been run under several bed capacity scenarios, and resulting queueing and waiting patterns have been discussed in detail.
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    Computational & mathematical organization theory 3 (1998), S. 219-247 
    ISSN: 1572-9346
    Keywords: computational models of organizations ; organizational ecology ; cellular automata ; simulation
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    Notes: Abstract Research on the ecological dynamics oforganizational populations has demonstrated that competitiveconditions at the time of founding have enduring effects onorganizational survival. According to ecological theories,organizational life chances are systematically affected by density (the number of organizations in a population) at thetime of founding because the lower resource endowments thatcharacterize organizations appearing in periods of highpopulation density tend to become self-reinforcing, and—over time—amplify differences in mortality rates oforganizations founded under different conditions. However,credible arguments have been offered that could justify both positive and negative effects of the delayed effectsof population density on organizational mortality rates, andreceived empirical research in part reflects this ambiguity.To develop new insight into this issue and to explore theboundaries of received empirical results, in this study wepresent a computational model of organizational evolutionaccording to which the global dynamics of organizationalpopulations emerge from the iteration of simple rules oflocal interaction among individual organizations. We use the synthetic data produced by simulation to estimate eventhistory models of organizational mortality, and compare theparameter estimates with those reported in the most recentempirical studies of actual organizational populations. Theconclusions supported by the model qualify and extendreceived empirical results, and suggest that delayed effectsof density are highly sensitive the details of local structure of connections among members of organizationalpopulations.
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    Computational & mathematical organization theory 4 (1998), S. 43-69 
    ISSN: 1572-9346
    Keywords: simulation ; organization ; computational model ; formal logic ; cognition
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    Topics: Mathematics
    Notes: Abstract A programming language which is optimized for modelling multi-agent interaction within articulated social structures such as organizations is described with several examples of its functionality. The language is SDML, a strictly declarative modelling language which has object-oriented features and corresponds to a fragment of strongly grounded autoepistemic logic. The virtues of SDML include the ease of building complex models and the facility for representing agents flexibly as models of cognition as well as modularity and code reusability. Two representations of cognitive agents within organizational structures are reported and a Soar-to-SDML compiler is described. One of the agent representations is a declarative implementation of a Soar agent taken from the Radar-Soar model of Ye and Carley (1995). The Ye-Carley results are replicated but the declarative SDML implementation is shown to be much less computationally expensive than the more procedural Soar implementation. As a result, it appears that SDML supports more elaborate representations of agent cognition together with more detailed articulation of organizational structure than we have seen in computational organization theory. Moreover, by representing Soar-cognitive agents declaratively within SDML, that implementation of the Ye-Carley specification is necessarily consistent and sound with respect to the formal logic to which SDML corresponds.
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    Computational & mathematical organization theory 3 (1997), S. 151-171 
    ISSN: 1572-9346
    Keywords: organizational performance ; planned organizational change ; resistance to change ; system dynamics ; simulation
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    Topics: Mathematics
    Notes: Abstract This paper suggests that an induction of change program leads to atemporary impairment of organizational performance. A System Dynamics Modelportrays the process of planned organizational change. A set of keyvariables that facilitate or impede change is identified, quantified, andintegrated into the model. Three data sets, reproduced by simulation,demonstrate that the model is internally consistent and empiricallyadequate. The paper discusses theoretical and practical implications of the‘initial dip’ phenomenon in processes of planned change.
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    International journal of flexible manufacturing systems 11 (1999), S. 271-289 
    ISSN: 1572-9370
    Keywords: random flexible manufacturing systems ; scheduling ; simulation
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The increased use of flexible manufacturing systems to efficiently provide customers with diversified products has created a significant set of operational challenges for managers. Many issues concerning procedures and policies for the day-to-day operation of these systems still are unresolved. Previous studies in this area have concentrated on various problems by isolating or simplifying the systems under study. The primary objective of this study is to extend previous research by examining the effects of scheduling rules and routing flexibility on the performance of a constrained, random flexible manufacturing system (FMS). Other experimental factors considered are shop load, shop configuration, and system breakdowns. Within the bounds of this experiment, the results indicate that, in the presence of total routing flexibility, the effects of shop load, system breakdowns, and scheduling rules are significantly dampened. In particular, when total routing flexibility exists, the choice of scheduling rules is not critical. We also show that the behavior of scheduling rules in a more constrained FMS environment (i.e., where system breakdowns occur and material handling capability is limited) is consistent with the findings of previous research conducted under less constrained environments. Finally, results indicate that the shop configuration factor has little or no impact on a system's flow-time performance.
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    International journal of flexible manufacturing systems 7 (1995), S. 27-46 
    ISSN: 1572-9370
    Keywords: automatic assembly systems ; genetic algorithms ; simulation ; stochastic optimization
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract This paper presents the application of genetic algorithms to the performance optimization of asynchronous automatic assembly systems (AAS). These stochastic systems are subject to blocking and starvation effects that make complete analytic performance modeling difficult. Therefore, this paper extends genetic algorithms to stochastic systems. The performance of the genetic algorithm is measured through comparison with the results of stochastic quasi-gradient (SQM) methods to the same AAS. The genetic algorithm performs reasonably well in obtaining good solutions (as compared with results of SQM) in this stochastic optimization example, even though genetic algorithms were designed for application to deterministic systems. However, the genetic algorithm's performance does not appear to be superior to SQM.
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    International journal of flexible manufacturing systems 7 (1995), S. 255-286 
    ISSN: 1572-9370
    Keywords: productivity ; design process ; robotic assembly ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The design of production systems is generally based on economic considerations, which are related to certain technical criteria, such as capacity, availability, and reliability. To realize a cost-effective design, these technical and economic criteria should be considered in their mutual coherence during the conceptual design process. This paper focuses on a productivity model, which is related to this subject. This model allows an opinion to be formed about the technical and economic performance of conceptual robotic assembly cells, during the process of design. First, the system design process is discussed in brief, after which the productivity variables are presented. An illustration of the model is used to assess the technical and economic behavior of alternative system structures for the assembly of a power plug assortment.
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    Computational & mathematical organization theory 5 (1999), S. 167-192 
    ISSN: 1572-9346
    Keywords: rational choice ; friendship ; Markov processes ; random utility models ; simulation ; empirical test
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We propose a class of actor-oriented statistical models for closed social networks in general, and friendship networks in particular. The models are random utility models developed within a rational choice framework. Based on social psychological and sociological theories about friendship, mathematical functions capturing expected utility of individual actors with respect to friendship are constructed. Expected utility also contains a random (unexplained) component. We assume that, given their restrictions and contact opportunities, individuals evaluate their utility functions and behave such that they maximize the expected amount of utility. The behavior under consideration is the expression of like and dislike (choice of friends). Theoretical mechanisms that are modelled are, e.g., the principle of diminishing returns, the tendency towards reciprocated choices, and the preference for friendship relations with similar others. Constraints imposed on individuals are, e.g., the structure of the existing network, and the distribution of personal characteristics over the respondents. The models are illustrated by means of a data-set collected among university freshmen at 7 points in time during 1994 and 1995.
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    International journal of flexible manufacturing systems 11 (1999), S. 19-35 
    ISSN: 1572-9370
    Keywords: integration ; process planning ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Many studies on integration of process planning and production scheduling have been carried out during the last decade. While various integration approaches and algorithms have been proposed, the implementation of these approaches is still a difficult issue. To achieve successful implementation, it is important to examine and evaluate integration approaches or algorithms beforehand. Based on an object-oriented integration testbed, a simulation study that compares different integration algorithms is presented in this paper. Separated planning method and integrated planning methods are examined. Also, situations of both fixed and variable processing times are simulated, and useful results have been observed. The successful simulation with the object-oriented integration testbed eventually will be extended to include other new planning algorithms for examining their effectiveness and implementation feasibility.
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    International journal of flexible manufacturing systems 4 (1992), S. 113-127 
    ISSN: 1572-9370
    Keywords: Flexible manufacturing ; simulation ; rules ; heuristics ; fuzzy logic
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract This article reports an investigation into part-input methods for an implemented flexible flow system (FFS). Two new dynamic methods—look-ahead simulation and a fuzzy heuristic rule base—are compared to three simple myopic static sequencing rules and one dynamic rule. It is shown using simulation that for the existing system, the best sequence generated from the minimum production set performs very well, but the dynamic methods outperform the sequence when the system is modified and the sequence is unaltered. It is concluded that for a stable FFS, the static determination of the best input sequence is appropriate, but that a rapidly changing FFS—due to machine breakdown, changes in production requirements, etc.—may benefit from a dynamic part-input method. The look-ahead simulation outperforms the fuzzy rule base, and appears to be a more promising dynamic method. Suggestions for future research and evaluation are given.
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    Order 2 (1985), S. 165-171 
    ISSN: 1572-9273
    Keywords: 06A10 ; 60C05 ; Partially ordered set ; diameter ; random structures
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let P k (n) be the (partial) order determined by intersecting k random linear orderings of a set of size n; equivalently, let P k (n) consist of n points chosen randomly and independently from the unit cube in ℝ k , with the induced product order. We show for each fixed k〉1, that with probability approaching 1 as n→∞, the comparability graph of P k (n) is connected and has diameter 3.
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    Order 2 (1985), S. 129-144 
    ISSN: 1572-9273
    Keywords: 06A10 ; Poset ; linear extension ; correlation ; universal correlation ; Winkler's Theorem ; universal negative correlation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Posets A, B⫇X×X, with X finite, are said to be universally correlated (A↑B) if, for all posets R over X, (i.e., all posets R⫇Y×Y with X⫇Y), we have P(R∪A) P(R∪B)≤P(R∪A∪B) P(R). Here P(R∪A), for instance, is the probability that a randomly chosen bijection from Y to the totally ordered set with |Y| elements is a linear extension of R∪A. We show that A↑B iff, for all posets R over X, P(R∪A) P(R∪B)≤P(R∪A∪B) P(R∪(A∩B)). Winkler proved a theorem giving a necessary and sufficient condition for A↑B. We suggest an alteration to his proof, and give another condition equivalent to A↑B. Daykin defined the pair (A, B) to be universally negatively correlated (A B) if, for all posets R over X, P(R∪A) P(R∪B)≥P(R∪A∪B) P(R∪(A∩B)). He suggested a condition for A↓B. We give a counterexample to that conjecture, and establish the correct condition. We write A↓B if, for all posets R over X, P(R∪A) P(R∪B)≥P(R∪A∪B) P(R). We give a necessary and sufficient condition for A↓B. We also give constructive techniques for listing all pairs (A, B) satisfying each of the relations A↑B, A↓B, and A↓B.
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    Order 2 (1985), S. 321-322 
    ISSN: 1572-9273
    Keywords: 06A10 ; 05C99 ; Covering graph ; order orientation ; extremal problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Every graph G may be transformed into a covering graph either by deletion of edges or by subdivision. Let Π E (G) and Π V (G) denote corresponding minimal numbers. We prove Π E (G) = Π V (G) for every graph G.
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    Order 2 (1985), S. 1-8 
    ISSN: 1572-9273
    Keywords: 06A10 ; Poset ; N-free poset ; linear extension ; Jump number ; matroid ; greedy algorithm ; Rado-Edmonds theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let L=x 1 x 2...x n be a linear extension of a poset P. Each pair (x i , x i+1) such that x i ≮ x i+1in P is called a jump of L. It is well known that for N-free posets a natural ‘greedy’ procedure constructing linear extensions yields a linear extension with a minimum number of jumps. We show that there is a matroid corresponding to any N-free poset and apply the Rado-Edmonds Theorem to obtain another proof of this result.
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    Order 2 (1985), S. 61-67 
    ISSN: 1572-9273
    Keywords: 06A10 ; Ordered set ; multifunction ; fixed point ; chain-completeness
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Sufficient conditions for the fixed point property for products of two partially ordered sets are proved. These conditions are formulated in terms of multifunctions (functions with non-empty sets as values).
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    Order 2 (1985), S. 119-122 
    ISSN: 1572-9273
    Keywords: 06A10 ; 68C25 ; Chordal bipartite graph ; elimination scheme ; crown
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove that a bipartite graph is chordal if and only if it has an elimination scheme. This leads to a polynomial algorithm to recognize whether an ordered set is cycle-free.
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    Order 2 (1985), S. 145-164 
    ISSN: 1572-9273
    Keywords: 06A05 ; 06A10 ; Ordered sets ; linear extension ; greedy dimensions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Every linear extension L: [x 1〈x 2〈...〈x m ] of an ordered set P on m points arises from the simple algorithm: For each i with 0≤i〈m, choose x i+1 as a minimal element of P−{x j :j≤i}. A linear extension is said to be greedy, if we also require that x i+1 covers x i in P whenever possible. The greedy dimension of an ordered set is defined as the minimum number of greedy linear extensions of P whose intersection is P. In this paper, we develop several inequalities bounding the greedy dimension of P as a function of other parameters of P. We show that the greedy dimension of P does not exceed the width of P. If A is an antichain in P and |P−A|≥2, we show that the greedy dimension of P does not exceed |P−A|. As a consequence, the greedy dimension of P does not exceed |P|/2 when |P|≥4. If the width of P−A is n and n≥2, we show that the greedy dimension of P does not exceed n 2+n. If A is the set of minimal elements of P, then this inequality can be strengthened to 2n−1. If A is the set of maximal elements, then the inequality can be further strengthened to n+1. Examples are presented to show that each of these inequalities is best possible.
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    Order 2 (1985), S. 243-248 
    ISSN: 1572-9273
    Keywords: 06A10 ; Ordered set ; chain ; antichain ; width ; cutset
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The partially ordered set P is an (α, β, γ) ordered set if the width of P≥α, the length of any chain of P≤β and the cut-set number ≤γ. We will prove that if P is an (α, β, γ) ordered set then P contains a ‘simple’ (α, β, γ) ordered set and use this result to prove that if P has the 3 cutset property, then width of P ≤ length of P+3.
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