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  • 1
    Online Resource
    Online Resource
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    UID:
    edochu_18452_9002
    Format: 1 Online-Ressource (16 Seiten)
    Series Statement: Stochastic Programming E-Print Series 2006,2006,1
    Content: We analyze an extension of the classical multi-period, single-item, linear cost inventory problem where the objective function is a coherent risk measure. Properties of coherent risk measures allow us to offer a unifying treatment of risk averse and min-max type formulations. For the single period newsvendor problem, we show that the structure of the optimal solution of the risk averse model is similar to that of the classical expected value problem. For a finite horizon dynamic inventory model, we show that, again, the optimal policy has a similar structure as that of the expected value problem. This result carries over even to the case when there is a fixed ordering cost. We also analyze monotonicity properties of the optimal order quantity with respect to the degree of risk aversion for certain risk measures.
    Language: English
    URL: Volltext  (kostenfrei)
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  • 2
    Online Resource
    Online Resource
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    UID:
    edochu_18452_8983
    Format: 1 Online-Ressource (15 Seiten)
    Series Statement: Stochastic Programming E-Print Series 2005,2005,2
    Content: We consider probabilistic constrained linear programs with general distributions for the uncertain parameters. These problems generally involve non-convex feasible sets. We develop a branch and bound algorithm that searches for a global solution to this problem by successively partitioning the non-convex feasible region and by using bounds on the objective function to fathom inferior partitions. This basic algorithm is enhanced by domain reduction and cutting plane strategies to reduce the size of the partitions and hence tighten bounds. The proposed branch-reduce-cut algorithm exploits the monotonicity properties inherent in the problem, and requires solving linear programming subproblems. We provide convergence proofs for the algorithm. Some illustrative numerical results involving problems with discrete distributions are presented.
    Language: English
    URL: Volltext  (kostenfrei)
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  • 3
    Online Resource
    Online Resource
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    UID:
    edochu_18452_8949
    Format: 1 Online-Ressource (26 Seiten)
    Series Statement: Stochastic Programming E-Print Series 2003,2003,15
    Content: This paper proposes a stochastic programming model and solution algorithm for solving sup-ply chain network design problems of a realistic scale. Existing approaches for these problems are either restricted to deterministic environments or can only address a modest number of scenarios for the uncertain problem parameters. Our solution methodology integrates a recently proposed sampling strategy, the Sample Average Approximation scheme, with an accelerated Benders de-composition algorithm to quickly compute high quality solutions to large-scale stochastic supply chain design problems with a huge (potentially infinite) number of scenarios. A computational study involving two real supply chain networks are presented to highlight the significance of the stochastic model as well as the efficiency of the proposed solution strategy.
    Language: English
    URL: Volltext  (kostenfrei)
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  • 4
    Online Resource
    Online Resource
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    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
    URL: Volltext  (kostenfrei)
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  • 5
    Online Resource
    Online Resource
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    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
    URL: Volltext  (kostenfrei)
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  • 6
    Online Resource
    Online Resource
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    UID:
    edochu_18452_8892
    Format: 1 Online-Ressource (30 Seiten)
    Series Statement: Stochastic Programming E-Print Series 2000,2000,16
    Content: This paper addresses a general class of two-stage stochastic programs with integer recourse and discrete distributions. We exploit the structure of the value function of the second stage integer problem to develop a novel global optimization algorithm. The proposed scheme departs from those in the current literature in that it avoids explicit enumeration of the search space while guaranteeing finite termination. Our computational results indicate superior performance of the proposed algorithm in comparison to the existing literature.
    Language: English
    URL: Volltext  (kostenfrei)
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  • 7
    Online Resource
    Online Resource
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    UID:
    edochu_18452_8908
    Format: 1 Online-Ressource (23 Seiten)
    Series Statement: Stochastic Programming E-Print Series 2001,2001,5
    Content: This paper addresses a multi-period investment model for capacity expansion in an uncertain environment. Using a scenario tree approach to model the evolution of uncertain demand and cost parameters, and fixed-charge cost functions to model the economies of scale in expansion costs, we develop a multi-stage stochastic integer programming formulation for the problem. A reformulation of the problem is proposed using variable disaggregation to exploit the lot-sizing substructure of the problem. The reformulation significantly reduces the LP relaxation gap of this large scale integer program. A heuristic scheme is presented to perturb the LP relaxation solutions to produce good quality integer solutions. Finally, we outline a branch and bound algorithm that makes use of the reformulation strategy as a lower bounding scheme, and the heuristic as an upper bounding scheme, to solve the problem to global optimality. Our preliminary computational results indicate that the proposed strategy has significant advantages over straightforward use of commercial solvers.
    Language: English
    URL: Volltext  (kostenfrei)
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  • 8
    Online Resource
    Online Resource
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    UID:
    edochu_18452_8969
    Format: 1 Online-Ressource (15 Seiten)
    Series Statement: Stochastic Programming E-Print Series 2004,2004,10
    Content: Traditional stochastic programming is risk neutral in the sense that it is concerned with the optimization of an expectation criterion. A common approach to addressing risk in decision making problems is to consider a weighted mean-risk objective, where some dispersion statistic is used as a measure of risk. We investigate the computational suitability of various mean-risk objective functions in addressing risk in stochastic programming models. We prove that the classical mean-variance criterion leads to computational intractability even in the simplest stochastic programs. On the other hand, a number of alternative mean-risk functions are shown to be computationally tractable using slight variants of existing stochastic programming decomposition algorithms. We propose a parametric cutting plane algorithm to generate the entire mean-risk efficient frontier for a particular mean-risk objective.
    Language: English
    URL: Volltext  (kostenfrei)
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  • 9
    Online Resource
    Online Resource
    Berlin : Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
    UID:
    edochu_18452_8996
    Format: 1 Online-Ressource (32 Seiten)
    Series Statement: Stochastic Programming E-Print Series 2005,2005,15
    Content: This paper addresses a general class of capacity planning problems under uncertainty, which arises, for example, in semiconductor tool purchase planning. Using a scenario tree to model the evolution of the uncertainties, we develop a multi-stage stochastic integer programming formulation for the problem. In contrast to earlier two-stage approaches, the multi-stage model allows for revision of the capacity expansion plan as more information regarding the uncertainties is revealed. We provide analytical bounds for the value of multi-stage stochastic programming (VMS) afforded over the two-stage approach. By exploiting a special lot-sizing substructure inherent in the problem, we develop an effient approximation scheme for the diffult multi-stage stochastic integer program and prove that the proposed scheme is asymptotically optimal. Computational experiments with realistic-scale problem instances suggest that the VMS for this class of problems is quite high. Moreover the quality and performance of the approximation scheme is very satisfactory. Fortunately, this is more so for instances for which the VMS is high.
    Language: English
    URL: Volltext  (kostenfrei)
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  • 10
    Online Resource
    Online Resource
    Philadelphia, Pennsylvania :Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104),
    UID:
    almahu_9947979234102882
    Format: 1 PDF (xxxiv, 678 pages).
    ISBN: 9781611974683 , 1611974682
    Series Statement: MOS-SIAM series on optimization
    Content: Optimization is of critical importance in engineering. Engineers constantly strive for the best possible solutions, the most economical use of limited resources, and the greatest efficiency. As system complexity increases, these goals mandate the use of state-of-the-art optimization techniques. In recent years, the theory and methodology of optimization have seen revolutionary improvements. Moreover, the exponential growth in computational power, along with the availability of multicore computing with virtually unlimited memory and storage capacity, has fundamentally changed what engineers can do to optimize their designs. This is a two-way process: engineers benefit from developments in optimization methodology, and challenging new classes of optimization problems arise from novel engineering applications. Advances and Trends in Optimization with Engineering Applications reviews 10 major areas of optimization and related engineering applications, providing a broad summary of state-of-the-art optimization techniques most important to engineering practice. Each part provides a clear overview of a specific area and discusses a range of real-world problems. The book provides a solid foundation for engineers and mathematical optimizers alike who want to understand the importance of optimization methods to engineering and the capabilities of these methods.
    Note: Foreword -- Preface -- I. Linear and quadratic optimization -- II. Mixed-integer linear optimization -- III. Conic linear optimization -- IV. Global optimization -- V. Nonlinear optimization -- VI. Mixed-integer nonlinear optimization -- VII. Robust optimization -- VIII. Stochastic optimization -- IX. Inventory and supply chain optimization -- X. Methodologies and applications in black-box and derivative-free optimization. , Also available in print version. , Mode of access: World Wide Web. , System requirements: Adobe Acrobat Reader.
    Additional Edition: Print version: ISBN 9781611974676
    Language: English
    URL: SIAM
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