We consider convex stochastic programming problems with probabilistic constraints involving integer-valued random variables. The concept of a p-efficient point of a probability distribution is used to derive various e...
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We consider convex stochastic programming problems with probabilistic constraints involving integer-valued random variables. The concept of a p-efficient point of a probability distribution is used to derive various equivalent problem formulations. Next we introduce the concept of r-concave discrete probability distributions and analyse its relevance for problems under consideration. These notions are used to derive lower and upper bounds for the optimal value of probabilistically constrained convex stochastic programming problems with discrete random variables.
We consider convex stochastic programming problems with probabilistic constraints involving integer-valued random variables. The concept of a p-efficient point of a probability distribution is used to derive various e...
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We consider convex stochastic programming problems with probabilistic constraints involving integer-valued random variables. The concept of a p-efficient point of a probability distribution is used to derive various equivalent problem formulations. Next we introduce the concept of r-concave discrete probability distributions and analyse its relevance for problems under consideration. These notions are used to derive lower and upper bounds for the optimal value of probabilistically constrained convex stochastic programming problems with discrete random variables.
We consider the problem of optimizing inventories for problems where the demand distribution is unknown, and where it does not necessarily follow a standard form such as the normal. We address problems where the proce...
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We consider the problem of optimizing inventories for problems where the demand distribution is unknown, and where it does not necessarily follow a standard form such as the normal. We address problems where the process of deciding the inventory, and then realizing the demand, occurs repeatedly. The only information we use is the amount of inventory left over. Rather than attempting to estimate the demand distribution, we directly estimate the value function using a technique called the Concave, Adaptive Value Estimation (CAVE) algorithm. CAVE constructs a sequence of concave piecewise linear approximations using sample gradients of the recourse function at different points in the domain. Since it is a sampling-based method, CAVE does not require knowledge of the underlying sample distribution. The result is a nonlinear approximation that is more responsive than traditional linear stochastic quasi-gradient methods and more flexible than analytical techniques that require distribution information. In addition, we demonstrate near-optimal behavior of the CAVE approximation in experiments involving two different types of stochastic programs the newsvendor stochastic inventory problem and two-stage distribution problems.
The bond portfolio management problem is formulated as a multiperiod stochastic program using interest rate scenarios. The scenarios are sampled from the binomial lattice from a Black-Derman-Toy model. The paper analy...
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The bond portfolio management problem is formulated as a multiperiod stochastic program using interest rate scenarios. The scenarios are sampled from the binomial lattice from a Black-Derman-Toy model. The paper analyzes the sensitivity of the solution of the resulting large-scale mathematical program with respect to the model inputs. The numerical results are for the Italian bond market. (C) 2001 Elsevier Science BN. All rights reserved.
The legal regulations for the life insurance business in Norway have recently been, and still are, under revision. The government's intention is to secure the interests of the customers in life insurance companies...
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The legal regulations for the life insurance business in Norway have recently been, and still are, under revision. The government's intention is to secure the interests of the customers in life insurance companies. However, there has been debate as to whether the regulations really are in the customers' best interest, We apply an asset-liability management (ALM) model to analyze the implications of the regulations. The model is multistage, stochastic and integrates assets and liabilities. We employ a four stage model to analyze the legal regulations, and conclude that the current legal framework is not in the insurance holders' best interests. (C) 2001 Elsevier Science B.V. All rights reserved.
On one hand, PSA results are increasingly used in decision making, system management and optimization of system design. On the other hand, when severe accidental transients are considered, dynamic reliability appears ...
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On one hand, PSA results are increasingly used in decision making, system management and optimization of system design. On the other hand, when severe accidental transients are considered, dynamic reliability appears appropriate to account for the complex interaction between the transitions between hardware configurations, the operator behavior and the dynamic evolution of the system. This paper presents an exploratory work in which the estimation of the system unreliability in a dynamic context is coupled with an optimization algorithm to determine the "best" safety policy. Because some reliability parameters are likely to be distributed, the cost function to be minimized turns out to be a random variable. stochastic programming techniques are therefore envisioned to determine an optimal strategy. Monte Carlo simulation is used at all stages of the computations, from the estimation of the system unreliability to that of the stochastic quasi-gradient. The optimization algorithm is illustrated on a HNO3 supply system. (C) 2001 Elsevier Science Ltd. All rights reserved.
An ergodic theorem for random lsc (lower semicontinuous) functions is obtained by relying on a "scalarization" of such functions. In the process, Kolmogorov's extension theorem for random lsc functions i...
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An ergodic theorem for random lsc (lower semicontinuous) functions is obtained by relying on a "scalarization" of such functions. In the process, Kolmogorov's extension theorem for random lsc functions is established. Applications to statistical estimation problems, composite materials, and stochastic optimization problems are briefly noted.
We present a stochastic optimization model for planning capacity expansion under capacity deterioration and demand uncertainty. The paper focuses on the electric sector, although the methodology can be used in other a...
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We present a stochastic optimization model for planning capacity expansion under capacity deterioration and demand uncertainty. The paper focuses on the electric sector, although the methodology can be used in other applications. The goals of the model are deciding which energy types must be installed, and when. Another goal is providing an initial generation plan for short periods of the planning horizon that might be adequately modified in real time assuming penalties in the operation cost. Uncertainty is modeled under the assumption that the demand is a random vector. The cost of the risk associated with decisions that may need some tuning in the future is included in the objective function. The proposed scheme to solve the nonlinear stochastic optimization model is Generalized Benders' decomposition. We also exploit the Benders' subproblem structure to solve it efficiently. Computational results for moderate-size problems are presented along with comparison to a general-purpose nonlinear optimization package. (C) 2001 John Wiley & Sons, Inc.
An aggregation technique for constraints with values in Hilbert spaces is suggested. The technique allows us to replace the original optimization problem by a sequence of subproblems having scalar or finite-dimensiona...
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An aggregation technique for constraints with values in Hilbert spaces is suggested. The technique allows us to replace the original optimization problem by a sequence of subproblems having scalar or finite-dimensional constraints. Applications to optimal control, games, and stochastic programming are discussed in detail.
In a great many situations, the data for optimization problems cannot be known with certainty and furthermore the decision process will take place in multiple time stages as the uncertainties al e resolved, This gives...
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In a great many situations, the data for optimization problems cannot be known with certainty and furthermore the decision process will take place in multiple time stages as the uncertainties al e resolved, This gives rise to a need for stochastic prog ramming (SP) methods that create solutions that ale hedged against future uncertainty. The progressive hedging algorithm (PHA) of Rockafellar and Wets is a general method for SP. We cast the PHA ill a meta-heuristic framework with the sub-problems generated for each scenario solved heuristically. Rather than using an approximate search algorithm for the exact problem as is typically the case in the meta-heuristic literature, we use an algorithm for sub-problems that is exact in its usual context but serves as a heuristic for our meta-heuristic. Computational results reported for stochastic lot-sizing problems, demonstrate that the method is effective, (C) 2001 Elsevier Science B.V. All rights reserved.
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