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  • Articles  (17)
  • linear programming  (17)
  • Springer  (17)
  • Blackwell Publishers Ltd
  • Blackwell Publishing Ltd
  • International Union of Crystallography
  • 1995-1999  (12)
  • 1985-1989  (5)
  • 1965-1969
  • 1997  (12)
  • 1989  (5)
  • Economics  (8)
  • Computer Science  (7)
  • Geography  (3)
  • Energy, Environment Protection, Nuclear Power Engineering  (1)
  • Natural Sciences in General
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  • Articles  (17)
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  • Springer  (17)
  • Blackwell Publishers Ltd
  • Blackwell Publishing Ltd
  • International Union of Crystallography
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  • 1995-1999  (12)
  • 1985-1989  (5)
  • 1965-1969
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  • 1
    Electronic Resource
    Electronic Resource
    Workload planning in small lot printed circuit board assembly (1997)
    Springer
    OR spectrum 19 (1997), S. 147-157 
    Details
    ISSN: 1436-6304
    Keywords: Key words: production ; scheduling ; printed circuit board assembly ; modelling ; linear programming ; aggregational error ; decision support ; Schlüsselwörter: Produktion ; Ablaufplanung ; Leiterplattenbestückung ; Modellierung ; lineare Programmierung ; Aggregationsfehler ; Entscheidungsunterstützung ; S′jm = Sjm ; SFj(r)(12)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung. Bei der Kleinserienmontage von Leiterplatten besteht das Problem der Einlastungsplanung darin, ein Tagesprogramm an Produktionsaufträgen zusammenzustellen, die gemeinsam in das Produktionssystem eingeschleust werden. Jeder Produktionsauftrag entspricht einem bestimmten Leiterplattentyp. Wechselt man bei der automatischen Bestückung von Leiterplatten zu einem neuen Leiterplattentyp, so fallen erhebliche Rüstzeiten an, die davon abhängen, wie viele Bauteilezuführungen im Magazin der Bestückungsautomaten ausgewechselt werden müssen. Zur Unterstützung dieses Entscheidungsproblems werden zwei unterschiedliche Modelle der linearen Optimierung entwickelt. Die beiden Modelle unterscheiden sich vor allem durch ihren Aggregationsgrad und ihren Rechenaufwand. Zur Verringerung des Aggregationsfehlers wird ein auf der Fuzzy-Set-Theorie beruhender Ansatz zur Abschätzung der bei automatischen SMD-Bestückungsautomanten auftretenden Rüstzeiten entwickelt. Hierbei wird als industrielles Anwendungsbeispiel die Leiterplattenbestückung in einem bedeutenden Elektronikunternehmen betrachtet. Die durchgeführte numerische Untersuchung zeigt, daß das hochaggregierte Fuzzy-LP-Modell zu hinreichend genauen Lösungen führt und erheblich geringeren Rechenaufwand verursacht als ein detaillierteres LP-Modell. Außerdem wird die praktische Eignung des Fuzzy-LP-Modells für den Einsatz innerhalb eines interaktiven Entscheidungsunterstützungssystems verdeutlicht.
    Notes: Abstract. The problem of workload planning in small lot printed circuit board (PCB) assembly concerns the determination of the daily mix of production orders to be released into the production system. When switching from one production order (board type) to another, a considerable set-up time is incurred based on the number of component feeders to be replaced in the component magazine of the assembly machines. To support the order-mix decision faced by a major electronics manufacturer, two versions of a linear programming model are developed. The models differ primarily in their degree of aggregation and their computational effort. In order to reduce the aggregational error incurred, a fuzzy approach is developed to estimate the number of component set-ups at automatic SMD placement machines. Our numerical investigation reveals that sufficiently accurate solutions may be obtained from a highly aggregate fuzzy LP-model and this is achieved with considerably less computational effort than with a more detailed LP-model. We also demonstrate the potential suitability of the fuzzy LP-model for implementation within an interactive decision support system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01545517
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  • 2
    Electronic Resource
    Electronic Resource
    Workload planning in small lot printed circuit board assembly (1997)
    Springer
    OR spectrum 19 (1997), S. 147-157 
    Details
    ISSN: 1436-6304
    Keywords: production ; scheduling ; printed circuit board assembly ; modelling ; linear programming ; aggregational error ; decision support ; Produktion ; Ablaufplanung ; Leiterplattenbestückung ; Modellierung ; lineare Programmierung ; Aggregationsfehler ; Entscheidungsunterstützung
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Bei der Kleinserienmontage von Leiterplatten besteht das Problem der Einlastungsplanung darin, ein Tagesprogramm an Produktionsaufträgen zusammenzustellen, die gemeinsam in das Produktionssystem eingeschleust werden. Jeder Produktionsauftrag entspricht einem bestimmten Leiterplattentyp. Wechselt man bei der automatischen Bestückung von Leiterplatten zu einem neuen Leiterplattentyp, so fallen erhebliche Rüstzeiten an, die davon abhängen, wie viele Bauteilezuführungen im Magazin der Bestückungsautomaten ausgewechselt werden müssen. Zur Unterstützung dieses Entscheidungsproblems werden zwei unterschiedliche Modelle der linearen Optimierung entwickelt. Die beiden Modelle unterscheiden sich vor allem durch ihren Aggregationsgrad und ihren Rechenaufwand. Zur Verringerung des Aggregationsfehlers wird ein auf der Fuzzy-Set-Theorie beruhender Ansatz zur Abschätzung der bei automatischen SMD-Bestückungsautomanten auftretenden Rüstzeiten entwickelt. Hierbei wird als industrielles Anwendungsbeispiel die Leiterplattenbestückung in einem bedeutenden Elektronikunternehmen betrachtet. Die durchgeführte numerische Untersuchung zeigt, daß das hochaggregierte Fuzzy-LP-Modell zu hinreichend genauen Lösungen führt und erheblich geringeren Rechenaufwand verursacht als ein detaillierteres LP-Modell. Außerdem wird die praktische Eignung des Fuzzy-LP-Modells für den Einsatz innerhalb eines interaktiven Entscheidungsunterstützungssystems verdeutlicht.
    Notes: Abstract The problem of workload planning in small lot printed circuit board (PCB) assembly concerns the determination of the daily mix of production orders to be released into the production system. When switching from one production order (board type) to another, a considerable set-up time is incurred based on the number of component feeders to be replaced in the component magazine of the assembly machines. To support the order-mix decision faced by a major electronics manufacturer, two versions of a linear programming model are developed. The models differ primarily in their degree of aggregation and their computational effort. In order to reduce the aggregational error incurred, a fuzzy approach is developed to estimate the number of component set-ups at automatic SMD placement machines. Our numerical investigation reveals that sufficiently accurate solutions may be obtained from a highly aggregate fuzzy LP-model and this is achieved with considerably less computational effort than with a more detailed LP-model. We also demonstrate the potential suitability of the fuzzy LP-model for implementation within an interactive decision support system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01545517
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  • 3
    Electronic Resource
    Electronic Resource
    Deckung des Klassenraumbedarfs an Hamburger Schulen (1997)
    Springer
    OR spectrum 19 (1997), S. 67-74 
    Details
    ISSN: 1436-6304
    Keywords: Deckung des Bedarfs an Klassenräumen ; lineare Optimierung ; gemischt ganzzahlige Optimierung ; Covering classroom requirements ; linear programming ; mixed integer programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Abstract The city of Hamburg expects for the next years enormously increasing rates of pupils. Covering the additional need of classrooms by new building is very expensive. It would be better to avoid this by making good use of the existing resources. The possible steps for covering the requirements and the restrictions are explained subsequently. There are a lot of alternatives, which must be coordinated for a “good” solution in a suitable way. The mathematical model for this problem is described furthermore. The model in question belongs to the class of mixed integer problems. Finally the standard optimization software SCICONIC, which is used for solving the mixed integer problem, is introduced and the embedding of SCICONIC into the architecture of the evolved planning system is described. Because the users of the system are officers without knowledge in electronic data processing and mathematical programming, a user friendly interface is of special importance in this case. This paper does not include new mathematical cognition, but describes the skilled use of known OR-techniques in a real software project.
    Notes: Zusammenfassung Die Stadt Hamburg sieht in den nächsten Jahren eine beträchtliche Schülerwelle auf sich zukommen. Daraus resultiert zusätzlicher Klassenraumbedarf, der durch Neubau nur sehr kostspielig gedeckt werden kann. Durch systematische Ausnutzung von bestehenden Raumreserven lassen sich teure Neubaumaßnahmen weitgehend vermeiden. Im folgenden werden zunächst die möglichen Maßnahmen zur Raumbedarfsdeckung mit ihren einschränkenden Bedingungen aufgezeigt. Die Maßnahmen erlauben eine Vielzahl von Handlungsalternativen, die zum wirksamen Einsatz optimal aufeinander abgestimmt werden müssen. Das mathematische Modell zur Lösung dieses Problems wird in der weiteren Folge beschrieben. Es handelt sich um ein gemischt ganzzahliges Optimierungsproblem. Abschließend wird die zur Lösung eingesetzte Standard-Optimierungs-Software SCICONIC vorgestellt und die Einbindung von SCICONIC in das entwickelte Raumplanungssystem geschildert. Da die Anwender des Systems Sachbearbeiter ohne DV- und OR-Erfahrung sind, hat hier Benutzerfreundlichkeit eine besonders hohe Bedeutung. Der vorliegende Aufsatz erhebt nicht den Anspruch auf neue mathematische Erkenntnisse, sondern er beschreibt die fachgerechte Anwendung bekannter OR-Verfahren in einem Software-Projekt der Praxis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01539812
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  • 4
    Electronic Resource
    Electronic Resource
    Deckung des Klassenraumbedarfs an Hamburger Schulen (1997)
    Springer
    OR spectrum 19 (1997), S. 67-74 
    Details
    ISSN: 1436-6304
    Keywords: Schlüsselwörter: Deckung des Bedarfs an Klassenräumen ; lineare Optimierung ; gemischt ganzzahlige Optimierung ; Key words: Covering classroom requirements ; linear programming ; mixed integer programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Abstract. The city of Hamburg expects for the next years enormously increasing rates of pupils. Covering the additional need of classrooms by new building is very expensive. It would be better to avoid this by making good use of the existing resources. The possible steps for covering the requirements and the restrictions are explained subsequently. There are a lot of alternatives, which must be coordinated for a ``good'' solution in a suitable way. The mathematical model for this problem is described furthermore. The model in question belongs to the class of mixed integer problems. Finally the standard optimization software SCICONIC, which is used for solving the mixed integer problem, is introduced and the embedding of SCICONIC into the architecture of the evolved planning system is described. Because the users of the system are officers without knowledge in electronic data processing and mathematical programming, a user friendly interface is of special importance in this case. This paper does not include new mathematical cognition, but describes the skilled use of known OR-techniques in a real software project.
    Notes: Zusammenfassung. Die Stadt Hamburg sieht in den nächsten Jahren eine beträchtliche Schülerwelle auf sich zukommen. Daraus resultiert zusätzlicher Klassenraumbedarf, der durch Neubau nur sehr kostspielig gedeckt werden kann. Durch systematische Ausnutzung von bestehenden Raumreserven lassen sich teure Neubaumaßnahmen weitgehend vermeiden. Im folgenden werden zunächst die möglichen Maßnahmen zur Raumbedarfsdeckung mit ihren einschränkenden Bedingungen aufgezeigt. Die Maßnahmen erlauben eine Vielzahl von Handlungsalternativen, die zum wirksamen Einsatz optimal aufeinander abgestimmt werden müssen. Das mathematische Modell zur Lösung dieses Problems wird in der weiteren Folge beschrieben. Es handelt sich um ein gemischt ganzzahliges Optimierungsproblem. Abschließend wird die zur Lösung eingesetzte Standard-Optimierungs-Software SCICONIC vorgestellt und die Einbindung von SCICONIC in das entwickelte Raumplanungssystem geschildert. Da die Anwender des Systems Sachbearbeiter ohne DV- und OR-Erfahrung sind, hat hier Benutzerfreundlichkeit eine besonders hohe Bedeutung. Der vorliegende Aufsatz erhebt nicht den Anspruch auf neue mathematische Erkenntnisse, sondern er beschreibt die fachgerechte Anwendung bekannter OR-Verfahren in einem Software-Projekt der Praxis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01539812
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  • 5
    Electronic Resource
    Electronic Resource
    Conical projection algorithms for linear programming (1989)
    Springer
    Mathematical programming 43 (1989), S. 151-173 
    Details
    ISSN: 1436-4646
    Keywords: Conical projection methods ; Karmarkar's LP algorithm ; linear programming ; poly-nomial-time algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The Linear Programming Problem is manipulated to be stated as a Non-Linear Programming Problem in which Karmarkar's logarithmic potential function is minimized in the positive cone generated by the original feasible set. The resulting problem is then solved by a master algorithm that iteratively rescales the problem and calls an internal unconstrained non-linear programming algorithm. Several different procedures for the internal algorithm are proposed, giving priority either to the reduction of the potential function or of the actual cost. We show that Karmarkar's algorithm is equivalent to this method in the special case in which the internal algorithm is reduced to a single steepest descent iteration. All variants of the new algorithm have the same complexity as Karmarkar's method, but the amount of computation is reduced by the fact that only one projection matrix must be calculated for each call of the internal algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582287
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  • 6
    Electronic Resource
    Electronic Resource
    An application of Karmarkar's interior-point linear programming algorithm for multi-reservoir operations optimization (1989)
    Springer
    Stochastic environmental research and risk assessment 3 (1989), S. 17-29 
    Details
    ISSN: 1436-3259
    Keywords: Stochastic optimization ; linear programming ; simplex method ; Karmarkar's method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Optimization of multi-reservoir systems operations is typically a very large scale optimization problem. The following are the three types of optimization problems solved using linear programming (LP): (i) deterministic optimization for multiple periods involving fine stage intervals, for example, from an hour to a week (ii) implicit stochastic optimization using multiple years of inflow data, and (iii) explicit stochastic optimization using probability distributions of inflow data. Until recently, the revised simplex method has been the most efficient solution method available for solving large scale LP problems. In this paper, we show that an implementation of the Karmarkar's interior-point LP algorithm with a newly developed stopping criterion solves optimization problems of large multi-reservoir operations more efficiently than the simplex method. For example, using a Micro VAX II minicomputer, a 40 year, monthly stage, two-reservoir system optimization problem is solved 7.8 times faster than the advanced simplex code in MINOS 5.0. The advantage of this method is expected to be greater as the size of the problem grows from two reservoirs to multiples of reservoirs. This paper presents the details of the implementation and testing and in addition, some other features of the Karmarkar's algorithm which makes it a valuable optimization tool are illuminated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01543425
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  • 7
    Electronic Resource
    Electronic Resource
    Toward Practical Query Evaluation for Constraint Databases (1997)
    Springer
    Constraints 2 (1997), S. 279-304 
    Details
    ISSN: 1572-9354
    Keywords: constraint programming ; databases ; database optimization ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Linear constraint databases (LCDBs) extend relational databases to include linear arithmetic constraints in both relations and queries. A LCDB can also be viewed as a powerful extension of linear programming (LP) where the system of constraints is generalized to a database containing constraints and the objective function is generalized to a relational query containing constraints. Our major concern is query optimization in LCDBs. Traditional database approaches are not adequate for combination with LP technology. Instead, we propose a new query optimization approach, based on statistical estimations and iterated trials of potentially better evaluation plans. The resulting algorithms are not only effective on LCDBs, but also applicable to existing query languages. A number of specific constraint algebra algorithms are also developed: select-project-join for two relations, constraint sort-join and constraint multi-join.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009795512753
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  • 8
    Electronic Resource
    Electronic Resource
    Dominant Competitive Factors for evaluating program efficiency in grouped data (1997)
    Springer
    Annals of operations research 73 (1997), S. 253-276 
    Details
    ISSN: 1572-9338
    Keywords: Data Envelopment Analysis ; game theory ; efficiency ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Dominant Competitive Factors, unique solutions to a new class of two-person ratio efficiency games, are introduced as a means for distinguishing exceptional aspects of individual performance. The vectors of input-output multipliers thus obtained may be analyzed collectively so that commonalities within groups and differences across groups may be discovered. The method is applied to "Program Follow-Through", the original impetus for developing Data Envelopment Analysis. Our results are compared with those of the earlier study, whereupon substantial new insights are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018933329202
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  • 9
    Electronic Resource
    Electronic Resource
    A Data Envelopment Analysis approach to Discriminant Analysis (1997)
    Springer
    Annals of operations research 73 (1997), S. 299-321 
    Details
    ISSN: 1572-9338
    Keywords: Discriminant Analysis ; linear programming ; Data Envelopment Analysis ; insurance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Data Envelopment Analysis (DEA) and Discriminant Analysis (DA) are similar in that both may be used to classify units as exhibiting either good or poor performance. Both use linear programming to select a set of factor weights that determines group membership relative to a "threshold" or hyperplane. This similarity was pointed out in an earlier paper, in which several methods which combine aspects of DA and DEA were suggested. This paper further develops one of these hybrid methods, which can be described as an efficiency approach to Discriminant Analysis. The various formulation options are considered with respect to their effects on solution quality and stability. The stability issue is raised by the fact that solution equivalence under data transformation (including both translation and rotation) is considered important in DA, and has significantly affected model formulation. Thus, the data transformation issue is studied for the hybrid method, and also for DEA. The hybrid method is applied to an insurance data set, where some firms are solvent and others in financial distress, to further evaluate the method and its possible formulations. DA methods are applied to the same data set to provide a basis for comparison. The hybrid method is shown to outperform the general discriminant models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018937430111
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  • 10
    Electronic Resource
    Electronic Resource
    Interior path following primal-dual algorithms. part I: Linear programming (1989)
    Springer
    Mathematical programming 44 (1989), S. 27-41 
    Details
    ISSN: 1436-4646
    Keywords: Interior-point methods ; linear programming ; Karmarkar's algorithm ; polynomial-time algorithms ; logarithmic barrier function ; path following
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We describe a primal-dual interior point algorithm for linear programming problems which requires a total of $$O\left( {\sqrt n L} \right)$$ number of iterations, whereL is the input size. Each iteration updates a penalty parameter and finds the Newton direction associated with the Karush-Kuhn-Tucker system of equations which characterizes a solution of the logarithmic barrier function problem. The algorithm is based on the path following idea.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01587075
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