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  • Articles  (13)
  • stochastic programming  (13)
  • Springer  (13)
  • American Geophysical Union (AGU)
  • Annual Reviews
  • 2000-2004  (9)
  • 1980-1984  (4)
  • 1935-1939
  • Economics  (13)
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  • Articles  (13)
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  • Springer  (13)
  • American Geophysical Union (AGU)
  • Annual Reviews
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  • 1
    Electronic Resource
    Electronic Resource
    A framework for the probabilistic analysis of hierarchical planning systems (1984)
    Springer
    Annals of operations research 1 (1984), S. 23-42 
    Details
    ISSN: 1572-9338
    Keywords: Hierarchical planning problem ; stochastic programming ; heuristic ; performance measure ; probabilistic analysis ; asymptotic optimality ; machine scheduling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract As we have argued in previous papers, multi-level decision problems can often be modeled as multi-stage stochastic programs, and hierarchical planning systems designed for their solution, when viewed as stochastic programming heuristics, can be subjected to analytical performance evaluation. The present paper gives a general formulation of such stochastic programs and provides a framework for the design and analysis of heuristics for their solution. The various ways to measure the performance of such heuristics are reviewed, and some relations between these measures are derived. Our concepts are illustrated on a simple two-level planning problem of a general nature and on a more complicated two-level scheduling problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01874450
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  • 2
    Electronic Resource
    Electronic Resource
    Confidence intervals in the solution of stochastic integer linear programming problems (1984)
    Springer
    Annals of operations research 1 (1984), S. 67-78 
    Details
    ISSN: 1572-9338
    Keywords: Integer linear programming ; stochastic programming ; probabilistic analysis ; computational complexity ; order statistics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A method is proposed to estimate confidence intervals for the solution of integer linear programming (ILP) problems where the technological coefficients matrix and the resource vector are made up of random variables whose distribution laws are unknown and only a sample of their values is available. This method, based on the theory of order statistics, only requires knowledge of the solution of the relaxed integer linear programming (RILP) problems which correspond to the sampled random parameters. The confidence intervals obtained in this way have proved to be more accurate than those estimated by the current methods which use the integer solutions of the sampled ILP problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01874453
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  • 3
    Electronic Resource
    Electronic Resource
    On justification of use of stochastic functions for multimodal optimization models (1984)
    Springer
    Annals of operations research 1 (1984), S. 129-134 
    Details
    ISSN: 1572-9338
    Keywords: Statistical models ; multimodal optimization ; stochastic programming ; decision theory ; Bayesian problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A model of a complicated function under uncertainty is constructed axiomatically, formalizing suppositions on rationality of information on a considered function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01876143
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  • 4
    Electronic Resource
    Electronic Resource
    Subroutines for Computing Normal Probabilities of Sets—Computer Experiences (2000)
    Springer
    Annals of operations research 100 (2000), S. 103-122 
    Details
    ISSN: 1572-9338
    Keywords: multidimensional normal distribution ; stochastic programming ; reliability theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A subroutine package, called NORSET, has been prepared, that—via Monte Carlo integration—is suitable for evaluating several types of probabilities related to the n-dimensional normal distribution. The following probabilities can be computed: the distribution function value, the probabilities of rectangles, convex polyhedra, hyperellipsoids and circular cones in case of normal distribution. Probabilities accurate to three digits can be computed in less than 0.3 sec for up to 20 dimensions and in less than 10 secs for up to 100 dimensions. The description of the subroutines, results of computer testing and experimentations together with the conclusions are presented here.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019215116991
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  • 5
    Electronic Resource
    Electronic Resource
    Building and Solving Large-Scale Stochastic Programs on an Affordable Distributed Computing System (2000)
    Springer
    Annals of operations research 99 (2000), S. 167-187 
    Details
    ISSN: 1572-9338
    Keywords: algebraic modeling language ; decomposition methods ; distributed systems ; large-scale optimization ; stochastic programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We present an integrated procedure to build and solve big stochastic programming models. The individual components of the system – the modeling language, the solver and the hardware – are easily accessible, or a least affordable to a large audience. The procedure is applied to a simple financial model, which can be expanded to arbitrarily large sizes by enlarging the number of scenarios. We generated a model with one million scenarios, whose deterministic equivalent linear program has 1,111,112 constraints and 2,555,556 variables. We have been able to solve it on the cluster of ten PCs in less than 3 hours.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019245101545
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  • 6
    Electronic Resource
    Electronic Resource
    Modeling and solution strategies for unconstrained stochastic optimization problems (1984)
    Springer
    Annals of operations research 1 (1984), S. 3-22 
    Details
    ISSN: 1572-9338
    Keywords: Stochastic optimization ; subgradient ; stochastic programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We review some modeling alternatives for handling risk in decision-making processes for unconstrained stochastic optimization problems. Solution strategies are discussed and compared.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01874449
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  • 7
    Electronic Resource
    Electronic Resource
    Stochastic Nonstationary Optimization for Finding Universal Portfolios (2000)
    Springer
    Annals of operations research 100 (2000), S. 165-188 
    Details
    ISSN: 1572-9338
    Keywords: constant rebalanced portfolios ; optimal growth ; stochastic programming ; nonstationary optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We apply ideas from stochastic optimization for defining universal portfolios. Universal portfolios are that class of portfolios which are constructed directly from the available observations of the stocks behavior without any assumptions about their statistical properties. Cover [7] has shown that one can construct such portfolio using only observations of the past stock prices which generates the same asymptotic wealth growth as the best constant rebalanced portfolio which is constructed with the full knowledge of the future stock market behavior. In this paper we construct universal portfolios using a different set of ideas drawn from nonstationary stochastic optimization. Our portfolios yield the same asymptotic growth of wealth as the best constant rebalanced portfolio constructed with the perfect knowledge of the future and they are less demanding computationally compared to previously known universal portfolios. We also present computational evidence using New York Stock Exchange data which shows, among other things, superior performance of portfolios which explicitly take into account possible nonstationary market behavior.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019271201970
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  • 8
    Electronic Resource
    Electronic Resource
    Term Structure Models in Multistage Stochastic Programming: Estimation and Approximation (2000)
    Springer
    Annals of operations research 100 (2000), S. 189-209 
    Details
    ISSN: 1572-9338
    Keywords: stochastic programming ; approximation ; term structure models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper investigates some common interest rate models for scenario generation in financial applications of stochastic optimization. We discuss conditions for the underlying distributions of state variables which preserve convexity of value functions in a multistage stochastic program. One- and multi-factor term structure models are estimated based on historical data for the Swiss Franc. An analysis of the dynamic behavior of interest rates generated with these models reveals several deficiencies which have an impact on the performance of investment policies derived from the stochastic program. While barycentric approximation is used here for the generation of scenario trees, these insights may be generalized to other discretization techniques as well.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019223318808
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  • 9
    Electronic Resource
    Electronic Resource
    Valuing Flexibility in Offshore Petroleum Projects (2000)
    Springer
    Annals of operations research 99 (2000), S. 325-349 
    Details
    ISSN: 1572-9338
    Keywords: flexibility ; real options ; oil ; field development ; stochastic programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The average size of discovered petroleum reserves on the Norwegian continental shelf has declined steadily over the last years. As a consequence, the fields have become economically more marginal, and new and flexible development strategies are required. This paper describes a stochastic dynamic programming model for project evaluation under uncertainty, where emphasis is put on flexibility and its value. Both market risk and reservoir uncertainty are handled by the model, as well as different flexibility types. The complexity of the problem is a challenge and calls for simple descriptions of the main variables in order to obtain a manageable model size. Results from a case study reveal significant value of flexibility, and clearly illustrate the shortcoming of today's common evaluation methods. Particularly capacity flexibility should not be neglected in future development projects where uncertainty surrounding the reservoir properties is substantial.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019284119505
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  • 10
    Electronic Resource
    Electronic Resource
    A Stochastic Programming Model for Currency Option Hedging (2000)
    Springer
    Annals of operations research 100 (2000), S. 227-249 
    Details
    ISSN: 1572-9338
    Keywords: stochastic programming ; currency options ; hedging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper we use a stochastic programming approach to develop currency option hedging models which can address problems with multiple random factors in an imperfect market. The portfolios considered in our model are rebalanced at the end of each time period, and reinvestments are allowed during the hedging process. These sequential decisions (reinvestments) are based on the evolution of random parameters such as exchange rates, interest rates, etc. We also allow the inclusion of a variety of instruments in the hedging portfolio, including short term derivative securities, short term options, and futures. These instruments help generate strategies that provide good liquidity and low trade intensity. One of the important features of the model is that it incorporates constraints on sensitivity measures such as Delta and Gamma. By ensuring that these hedge parameters track a desired trajectory (e.g., the parameters of a target option), the new model provides investment strategies that are robust with respect to the perturbations measured by Delta and Gamma. In order to manage the explosion of scenarios due to multiple random factors, we incorporate sampling within a scenario aggregation algorithm. We illustrate that when compared with other myopic hedging methods in imperfect markets, the new stochastic programming model can provide better performance. Our examples also illustrate stochastic programming as a practical computational tool for realistic hedging problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019296422231
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  • 11
    Electronic Resource
    Electronic Resource
    Capacity Planning Model for a Multipurpose Water Reservoir with Target-Priority Operation (2000)
    Springer
    Annals of operations research 100 (2000), S. 273-303 
    Details
    ISSN: 1572-9338
    Keywords: stochastic programming ; decision rules ; target-priority policy ; chance constrained goal programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We consider the capacity determination problem of a hydro reservoir. The reservoir is to be used primarily for hydropower generation; however, commitments on release targets for irrigation as well as mitigation of downstream flood hazards are also secondary objectives. This paper is concerned with studying the complex interaction among various system reliabilities (power, flood, irrigation, etc.) and to provide decision makers a planning tool for further investigation. The main tool is an optimization model that recognizes the randomness in streamflow. The model incorporates a special target-priority policy according to given system reliabilities. Optimized values are then used in a simulation model to investigate the system behavior. Detailed computational results are provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019200623139
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  • 12
    Electronic Resource
    Electronic Resource
    Some Aspects of Stability in Stochastic Programming (2000)
    Springer
    Annals of operations research 100 (2000), S. 55-84 
    Details
    ISSN: 1572-9338
    Keywords: stochastic programming ; parametric optimization ; stability analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Some developments in structure and stability of stochastic programs during the last decade together with interrelations to optimization theory and stochastics are reviewed. With weak convergence of probability measures as a backbone we discuss qualitative and quantitative stability of recourse models that possibly involve integer variables. We sketch stability in chance constrained stochastic programming and provide some applications in statistical estimation. Finally, an outlook is devoted to issues that were not discussed in detail and to some open problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019258932012
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  • 13
    Electronic Resource
    Electronic Resource
    Stability Properties of a Bond Portfolio Management Problem (2000)
    Springer
    Annals of operations research 99 (2000), S. 251-265 
    Details
    ISSN: 1572-9338
    Keywords: stochastic programming ; bond portfolio management ; interest ratescenarios ; stability ; sensitivity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The bond portfolio management problem is formulated as a multiperiod two-stage or multistage stochastic program based on interest rate scenarios. These scenarios depend on the available market data, on the applied estimation and sampling techniques, etc., and are used to evaluate coefficients of the resulting large scale mathematical program. The aim of the contribution is to analyze stability and sensitivity of this program on small changes of the coefficients – the (scenario dependent) values of future interest rates and prices. We shall prove that under sensible assumptions, the scenario subproblems are stable linear programs and that also the optimal first-stage decisions and the optimal value of the considered stochastic program possess acceptable continuity properties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019275817688
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