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  • 1
    Electronic Resource
    Electronic Resource
    Separable Markovian decision problems (1992)
    Springer
    OR spectrum 14 (1992), S. 43-52 
    Details
    ISSN: 1436-6304
    Keywords: Markov decision processes ; linear programming ; Markovsche Entscheidungsprozesse ; lineare Programmierung
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Separabele Markoffsche Entscheidungsprobleme haben die Eigenschaft, daß für gewisse Paare (i, a) von Zuständeni und zugehörigen Aktionena gilt: (i) die unmittelbare Auszahlung ist die Summe zweier Terme, von denen der eine nur vom Zustand und der andere nur von der Aktion abhängt (ria=si+ta), (ii) die Übergangswahrscheinlichkeiten hängen nur von der Aktion ab und nicht vom Zustand, in dem diese Aktion gewählt wurde. Dieses Modell wurde schon gegen Ende der Sechziger Jahre untersucht. Es wurde bewiesen, daß diskontierte Probleme und undiskontierte Probleme mit nur einer rekurrenten Klasse als lineare Programme mit weniger Variablen als im allgemeinen Modell formuliert werden können. Es war bisher unbekannt, ob auch für undiskontierte Modelle mit mehreren rekurrenten Klassen eine Formulierung mit weniger Variablen existiert. Dieses Problem wird in der vorliegenden Arbeit gelöst: eine solche Formulierung ist möglich. Abschließend werden einige Anwendungen von separablen Modellen angegeben.
    Notes: Summary Separable Markovian decision problems have the property that for certain pairs (i, a) of a statei and an actiona: (i) the immediate reward is the sum of terms due to the current state and action (ria=Si+ta), (ii) the transition probability depends only on the action and not on the state from which the transition occurs. The separable model was studied already in the late sixties. For the discounted case and the unichain undiscounted case a reduced LP formulation was given, which involves a substantially smaller number of variables than in the LP formulation of a general Markov decision problem. It was unknown whether such an efficient formulation was also possible in the multichain case. This paper solves this problem: such an efficient formulation can be obtained. Some applications of separable models are also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01783501
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  • 2
    Electronic Resource
    Electronic Resource
    Optimal consumption and arbitrage in incomplete, finite state security markets (1993)
    Springer
    Annals of operations research 45 (1993), S. 349-372 
    Details
    ISSN: 1572-9338
    Keywords: Incomplete market ; trading constraints ; linear programming ; optimal portfolio ; duality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We study a consistent treatment for both the multi-period portfolio selection problem and the option attainability problem by a dual approach. We assume that time is discrete, the horizon is finite, the sample space is finite and the number of securities is less than that of the possible securities price transitions, i.e. an incomplete security market. The investor is prohibited from investing stocks more than given linear investment amount constraints at any time and he maximizes an expected additive utility function for the consumption process. First we give a set of budget feasibility conditions so that a consumption process is attainable by an admissible portfolio process. To establish this relation, we used an algorithmic approach which has a close connection with the linear programming duality. Then we prove the unique existence of a primal optimal solution from the budget feasibility conditions. Finally, we formulate a dual control problem and establish the duality between primal and dual control problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02282058
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  • 3
    Electronic Resource
    Electronic Resource
    Bounds on the number of vertices of perturbed polyhedra (1993)
    Springer
    Annals of operations research 46-47 (1993), S. 249-269 
    Details
    ISSN: 1572-9338
    Keywords: Convex polytopes ; degeneracy ; linear programming ; simplex method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Finding the incident edges to a degenerate vertex of a polyhedron is a non-trivial problem. So pivoting methods generally involve a perturbation argument to overcome the degeneracy problem. But the perturbation entails a bursting of each degenerate vertex into a cluster of nondegenerate vertices. The aim of this paper is to give some bounds on the number of these perturbed vertices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02023098
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  • 4
    Electronic Resource
    Electronic Resource
    An exterior point simplex algorithm for (general) linear programming problems (1993)
    Springer
    Annals of operations research 46-47 (1993), S. 497-508 
    Details
    ISSN: 1572-9338
    Keywords: Simplex method ; linear programming ; pivoting ; degeneracy ; exterior point algorithms ; cycling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We present an exterior point simplex type algorithm that possesses a new monotonic property. A dual feasible basic solution is required to start with. Intermediate solutions are neither primal nor dual feasible. Cycling-free pivoting rules and an exponentional example are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02023111
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  • 5
    Electronic Resource
    Electronic Resource
    An effective non-Archimedean anti-degeneracy/cycling linear programming method especially for data envelopment analysis and like models (1993)
    Springer
    Annals of operations research 46-47 (1993), S. 271-278 
    Details
    ISSN: 1572-9338
    Keywords: Degeneracy/cycling ; non-Archimedean data envelopment analysis ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A non-Archimedean effective anti-degeneracy/cycling method for linear programming models, especially Data Envelopment Analysis (DEA), processing networks and advertising media mix models is herein developed. It has given a tenfold speed increase plus elimination of cycling difficulties over conventional Marsden or Kennington/Ali LP software modules in a 1000 LP DEA application.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02023099
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  • 6
    Electronic Resource
    Electronic Resource
    On some properties of o-degeneracy graphs (1993)
    Springer
    Annals of operations research 46-47 (1993), S. 393-408 
    Details
    ISSN: 1572-9338
    Keywords: Degeneracy ; linear programming ; degeneracy graphs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Degenerate optima in linear programming problems lead in a canonical way to so-called o-degeneracy graphs as subgraphs of degeneracy graphs induced by the set of optimal bases. Fundamental questions about the structure of o-degeneracy graphs suggest the closer inspection of some properties of these graphs, such as, for example, the connectivity and the complexity. Finally, some open questions are pointed out.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02023106
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  • 7
    Electronic Resource
    Electronic Resource
    PROMISE: A DSS for multiple objective stochastic linear programming problems (1994)
    Springer
    Annals of operations research 51 (1994), S. 45-59 
    Details
    ISSN: 1572-9338
    Keywords: Multiple objective ; linear programming ; stochastic ; decision support system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Most of the multiple objective linear programming (MOLP) methods which have been proposed in the last fifteen years suppose deterministic contexts, but because many real problems imply uncertainty, some methods have been recently developed to deal with MOLP problems in stochastic contexts. In order to help the decision maker (DM) who is placed before such stochastic MOLP problems, we have built a Decision Support System called PROMISE. On the one hand, our DSS enables the DM to identify many current stochastic contexts: risky situations and also situations of partial uncertainty. On the other hand, according to the nature of the uncertainty, our DSS enables the DM to choose the most appropriate interactive stochastic MOLP method among the available methods, if such a method exists, and to solve his problem via the chosen method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02032080
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  • 8
    Electronic Resource
    Electronic Resource
    Well management in the North Sea (1993)
    Springer
    Annals of operations research 43 (1993), S. 427-441 
    Details
    ISSN: 1572-9338
    Keywords: Petroleum production ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The purpose of this paper is to describe a planning model for the management of approximately 130 petroleum-producing wells in the North Sea. The objective is to form a better basis for the decisions about which wells to produce from and which to shut down during a period. Every well is dealt with individually as the production potential and chemical composition are different. The total flow consists of six saleable components: gas, four NGL products, and oil. The production may be curtailed due to the capacities of the platforms, gathering centre, pipelines and refinery plants. The total gas production is available for fulfilling the gas contracts, injecting the gas into the reservoirs or using the gas as fuel. There exist contracts for some of the NGL products, while the rest of the NGL products and oil are sold on the free market. The well-management model is solved by means of a standard mathematical programming code, and computational results are given for a planning problem with four different data sets.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02024840
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  • 9
    Electronic Resource
    Electronic Resource
    Project analysis using a linear approach (P.A.U.L.A.) (1993)
    Springer
    Decisions in economics and finance 16 (1993), S. 73-86 
    Details
    ISSN: 1129-6569
    Keywords: project analysis ; linear programming ; internal financial law (IFL) ; financial leverage ; discounted cash-flows (DCF) decomposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Riassunto Si definisce un modello generale (PAULA) per la valutazione, selezione e gestione ottimale di progetti certi alternativi. Sfruttando i risvolti formali e finanziari dei problemi lineari associati (diretto e duale), si formulano poi due proposte per definire una legge finanziaria interna (IFL) ottimale, utili sia per abbattere la molteplicità intrinseca delleIFL, sia per evitare risultati economicamente arbitrari nel loro uso.
    Notes: Abstract We define a general model (called PAULA) for the valuation, optimal management and selection among mutually exclusive safe projects. By exploiting the formal and financial features of the associated linear problems (primal and dual), we put forward two proposals to define an optimal internal financial law (IFL). They may be used to reduce the multiplicity of the IFLs and to avoid economically arbitrary outcomes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02086763
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  • 10
    Electronic Resource
    Electronic Resource
    LPL: A mathematical programming language (1993)
    Springer
    OR spectrum 15 (1993), S. 43-55 
    Details
    ISSN: 1436-6304
    Keywords: Modeling ; linear programming ; compiler ; MPS ; Modellierung ; lineare Programmierung ; Compiler ; MPS
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Dieser Artikel beschreibt die neue Version der Modellierungssprache LPL (Linear Programming Language), die sich dazu eignet, mathematische Modelle aufzubauen, zu warten und zu dokumentieren. Die LPL-Sprache wurde zum Erstellen von MPS-InputDateien und Resultate-Tabellen größerer LP-Modelle erfolgreich eingesetzt. Der LPL-Compiler übersetzt ein LPL-Programm, das ein vollständiges Modell repräsentiert, in den Eingabecode eines LP/MIP-Lösungsprogramms, ruft den Lösungsalgorithmus auf, liest die Lösung, und ein integrierter Tabellengenerator gibt vom Benutzer definierte Resultate-Tabellen aus. Außerdem erlaubt ein Dateneingabe-Generator, die Daten in verschiedenen Formaten zu lesen.
    Notes: Summary This paper describes the new version of the modeling language, named LPL (Linear Programming Language). It may be used to build, modify and document mathematical models. The LPL language has been successfully applied to generate automatically MPS input files and reports of large LP models. The available LPL compiler translates LPL programs to the input code of any LP/MIP solver, calls the solver automatically, reads the solution back to its internal representation, and the integrated Report Generator produces the user defined reports of the model. Furthermore, an Input Generator can read the data from many formats.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01783416
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