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  • HU Berlin  (238)
  • SB Ludwigsfelde
  • Informationszentrum DGAP
  • SB Schwedt
  • Bibliothek Wandlitz
  • Higle, Julie L.  (238)
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  • HU Berlin  (238)
  • SB Ludwigsfelde
  • Informationszentrum DGAP
  • SB Schwedt
  • Bibliothek Wandlitz
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  • 1
    Online Resource
    Online Resource
    Fenchel Decomposition for Stochastic Mixed-IntegerProgramming (2009)
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    Details
    UID:
    edochu_18452_9054
    Format: 1 Online-Ressource (22 Seiten)
    Series Statement: Stochastic Programming E-Print Series 2009,2009,4
    Content: This paper introduces a new cutting plane method for two-stage stochastic mixed-integer programming (SMIP) called Fenchel decomposition (FD). FD usesa class of valid inequalities termed, FD cuts, which are derived based on Fenchel cutting planes from integer programming. We derive FD cuts based on both the first and second stage variables, and devise an FD algorithm for SMIP with binary first stage and establish finite convergence for mixed-binary second stage. We also derive alternative FD cuts based on the second stage variables only and use an idea from disjunctive programming to lift the cuts to the higher dimension space including the first stage variables. We then devise an FD-L algorithm based on the lifted FD cuts. Finally, we report on preliminary computational results based on example instances from the literature. The results are promising and show the lifted FD cuts to have better performance than the regular FD cuts. Furthermore, both the FD and FD-L algorithms outperform a standard solver on large-scaleinstances.
    Language: English
    DOI: 10.18452/8402
    URN: urn:nbn:de:kobv:11-10098678
    URL: Volltext  (kostenfrei)
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    HU Berlin
  • 2
    Online Resource
    Online Resource
    Multistage stochastic convex programs : Duality and its implications (2002)
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    Details
    UID:
    edochu_18452_8918
    Format: 1 Online-Ressource (23 Seiten)
    Series Statement: Stochastic Programming E-Print Series 2002,2002,2
    Content: In this paper, we study alternative primal and dual formulations of multistage stochastic convex programs (SP). The alternative dual problems which can be traced to the alterna-tive primal representations, lead to stochastic analogs of standard deterministic constructs such as conjugate functions and Lagrangians. One of the by-products of this approach is that the development does not depend on dynamic programming (DP) type recursive arguments, and is therefore applicable to problems in which the objective function is non-separable (in the DP sense). Moreover, the treatment allows us to handle both continuous and discrete random variables with equal ease. We also investigate properties of the ex-pected value of perfect information (EVPI) within the context of SP, and the connection between EVPI and nonanticipativity of optimal multipliers. Our study reveals that there exist optimal multipliers that are nonanticipative if, and only if, the EVPI is zero. Finally, we provide interpretations of the retroactive nature of the dual multipliers.
    Language: English
    DOI: 10.18452/8266
    URN: urn:nbn:de:kobv:11-10058335
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    HU Berlin
  • 3
    Online Resource
    Online Resource
    Adaptive and nonadaptive samples in solving stochastic linear programs : A computational investigation (2005)
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    Details
    UID:
    edochu_18452_8993
    Format: 1 Online-Ressource (26 Seiten)
    Series Statement: Stochastic Programming E-Print Series 2005,2005,12
    Content: Large scale stochastic linear programs are typically solved using a combination of mathematical programming techniques and sample-based approximations. Some methods are designed to permit sample sizes to adapt to information obtained during the solution process, while others are not. In this paper, we experimentally examine the relative merits of approximations based on adaptive samples and those based on non-adaptive samples. We begin with an examination of two versions of an adaptive technique, Stochastic Decomposition (SD), and conclude with a comparison to a nonadaptive technique, the Sample Average Approximation method (SAA). Our results indicate that there is minimal di®erence in the quality of the solutions provided by SD and SAA, although SAA requires substantially more time to execute.
    Language: English
    DOI: 10.18452/8341
    URN: urn:nbn:de:kobv:11-10059872
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    HU Berlin
  • 4
    Online Resource
    Online Resource
    A model for dynamic chance constraints in hydro power reservoir management (2009)
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    Details
    UID:
    edochu_18452_9051
    Format: 1 Online-Ressource (18 Seiten)
    Series Statement: Stochastic Programming E-Print Series 2009,2009,1
    Content: In this paper, a model for (joint) dynamic chance constraints is proposed and applied to an optimization problem in water reservoir management. The model relies on discretization of the decision variables but keeps the probability distribution continuous. Our approach relies on calculating probabilities of rectangles, which isparticularly useful in the presence of independent random variables but works for a moderate number of stages equally well in case of correlated variables. Numerical results are provided for two and three stages.
    Language: English
    DOI: 10.18452/8399
    URN: urn:nbn:de:kobv:11-10097382
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  • 5
    Online Resource
    Online Resource
    A branch-and-cut algorithm for the stochastic uncapacitated lot-sizing problem (2004)
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    Details
    UID:
    edochu_18452_8965
    Format: 1 Online-Ressource (28 Seiten)
    Series Statement: Stochastic Programming E-Print Series 2004,2004,6
    Content: This paper addresses a multi-stage stochastic integer programming formulation of the uncapacitated lot-sizing problem under uncertainty. We show that the classical $(\mathcal{l}, S)$ inequalities for the deterministic lot-sizing polytope are also valid for the stochastic lot-sizing polytope. We then extend the $(\mathcal{l}, S)$ inequalities to a general class of valid inequalities, called the $(Q, S_Q)$ inequalities, and we establish necessary and sufficient conditions which guarantee that the $(Q, S_Q)$ inequalities are facet-defining. A separation heuristic for $(Q, S_Q )$ inequalities is developed and incorporated into a branch and cut algorithm. A computational study verifies the usefulness of the $(Q, S_Q)$ inequalities as cuts.
    Language: English
    DOI: 10.18452/8313
    URN: urn:nbn:de:kobv:11-10059453
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    HU Berlin
  • 6
    Online Resource
    Online Resource
    Cutting planes for multi-stage stochastic integer programs (2006)
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    Details
    UID:
    edochu_18452_9019
    Format: 1 Online-Ressource (23 Seiten)
    Series Statement: Stochastic Programming E-Print Series 2006,2006,18
    Content: This paper addresses the problem of finding cutting planes for multi-stage stochastic integer programs.We give a general method for generating cutting planes for multi-stage stochastic integer programs basedon combining inequalities that are valid for the individual scenarios. We apply the method to generatecuts for a stochastic version of a dynamic knapsack problem and to stochastic lot sizing problems. Wegive computational results which show that these new inequalities are very effective in a branch-and-cutalgorithm.
    Language: English
    DOI: 10.18452/8367
    URN: urn:nbn:de:kobv:11-10071635
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    HU Berlin
  • 7
    Online Resource
    Online Resource
    The C 3 theorem and a D 2 algorithm for large scale stochastic integer programming : Set convexification (2000)
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    Details
    UID:
    edochu_18452_8902
    Series Statement: Stochastic Programming E-Print Series 2000,2000,26
    Content: This paper considers the two stage stochastic integer programming problems, with an emphasis on problems in which integer variables appear in the second stage. Drawing heavily on the theory of disjunctive programming, we characterize convexifications of the second stage problem and develop a decomposition-based algorithm for the solution of such problems. In particular, we verify that problems with fixed recourse are characterized by scenario-dependent second stage convexifications that have a great deal in common. We refer to this characterization as the C^3 (Common Cut Coefficients) Theorem. Based on the C^3 Theorem, we develop an algorithmic methodology that we refer to as Disjunctive Decomposition (D^2). We show that when the second stage consists of 0-1 MILP problems , we can obtain accurate second stage objective function estimates afer finitely many steps. We also set the stage for comparisions between problems in which the first stage includes only 0-1 variables and those that allow both continuous and integer variables in the first stage.
    Language: English
    DOI: 10.18452/8250
    URN: urn:nbn:de:kobv:11-110-18452/8902-0
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    HU Berlin
  • 8
    Online Resource
    Online Resource
    Finite capacity production planning with random demand and limited information (2000)
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    Details
    UID:
    edochu_18452_8882
    Format: 1 Online-Ressource (24 Seiten)
    Series Statement: Stochastic Programming E-Print Series 2000,2000,6
    Content: Production planning has a fundamental role in any manufacturing operation. The problem is to decide what type of, and how much, product should be produced in future time periods. The decisions should be based on many factors, including period machine capacity, profit margins, holding costs, etc. Of primary importance is the estimate of demand for manufacturer's products in upcoming periods.Our focus is to address the production planning problem by including in our models the randomness that exists in our estimates for future demands. We solve the problem with two variants of Monte Carlo sampling based optimization techniques, to which we refer as "simulation based optimization" methods. The first variant assumes that we know the actual demand distribution (assumed to be continuous) with which we approximate the true optimal solution by averaging sample estimates of the corresponding expected value function. The second approach is useful when we have limited information about the demand distribution. We illustrate the robustness of the approach by comparing a three mass-point approximation of the continuous distribution to the results obtained using the continuous distribution. This second approach is particularly appealing as it results in a solution that is close to optimal while being much faster than the continuous distribution approach.
    Language: English
    DOI: 10.18452/8230
    URN: urn:nbn:de:kobv:11-10057558
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    HU Berlin
  • 9
    Online Resource
    Online Resource
    Confidence level solutions for stochastic programming (2000)
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    Details
    UID:
    edochu_18452_8886
    Format: 1 Online-Ressource (15 Seiten)
    Series Statement: Stochastic Programming E-Print Series 2000,2000,10
    Content: We propose an alternative approach to stochastic programming based on Monte-Carlo sampling and stochastic gradient optimization. The procedure is by essence probabilistic and the computed solution is a random variable. The associated objective value is doubly random, since it depends on two outcomes: the event in the stochastic program and the randomized algorithm. We propose a solution concept in which the probability that the randomized algorithm produces a solution with an expected objective value departing from the optimal one by more than $\epsilon$ is small enough. We derive complexity bounds for this process. We show that by repeating the basic process on independent sample, one can significantly sharpen the complexity bounds.
    Language: English
    DOI: 10.18452/8234
    URN: urn:nbn:de:kobv:11-10057628
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    HU Berlin
  • 10
    Online Resource
    Online Resource
    Structure and stability of probabilistic storage level constraints (2000)
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    Details
    UID:
    edochu_18452_8899
    Series Statement: Stochastic Programming E-Print Series 2000,2000,23
    Content: We consider the structure of probabilistic storage level constraints as well as the stability of solutions to optimization problems involving such constraints. Apart from the general case, special structures with and without discretization are analyzed. Structures of the feasible set are characterized in terms of convexity and/or connectedness. Stability of solution sets with respect to perturbations of the probability measure is formulated by means of upper and lower semicontinuity of the associated multivalued mapping.
    Language: English
    DOI: 10.18452/8247
    URN: urn:nbn:de:kobv:11-110-18452/8899-8
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    HU Berlin
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