Quantitative stability of optimal values and solution sets to stochastic programming problems is studied when the Underlying probability distribution varies in some metric space of probability measures. We give condit...
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Quantitative stability of optimal values and solution sets to stochastic programming problems is studied when the Underlying probability distribution varies in some metric space of probability measures. We give conditions that imply that a stochastic program behaves stable with respect to a minimal information (m.i.) probability metric that is naturally associated with the data of the program. Canonical metrics bounding the m.i. metric are derived for specific models, namely for linear two-stage, mixed-integer two-stage and chance-constrained models. The corresponding quantitative stability results as well as some consequences for asymptotic properties of empirical approximations extend earlier results in this direction. In particular, rates of convergence in probability are derived under metric entropy conditions. Finally, we study stability properties of stable investment portfolios having minimal risk with respect to the spectral measure and stability index of the underlying stable probability distribution.
One of the important issues in range query (RQ) retrieval problems is to determine the key's resolution for multiattribute records. Conventional models need to be improved because of potential degeneracy, less des...
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One of the important issues in range query (RQ) retrieval problems is to determine the key's resolution for multiattribute records. Conventional models need to be improved because of potential degeneracy, less desired computability, and possible inconsistency with the partial match query (PMQ) models. This paper presents a new RQ model to overcome these drawbacks and introduces a new methodology, stochastic programming (SP), to conduct the optimization process. The model is established by using a monotone increasing function to. characterize range sizes. Three SP approaches, wait-and-see (WS), here-and-now (HN), and scenario tracking (ST) methods are integrated into this RQ model. Analytical expressions of the optimal solution are derived. It seems that HN has advantage over WS because the latter usually involves complicated multiple summations or integrals. For the ST method, a nonlinear programming software package is designed. Results of numerical experiments are presented that optimized a 10-dimensional RQ model and tracked a middle size (100) and a large size (1,000) scenarios.
Uncertainty is one of the characteristics of product recovery networks. in particular the strategic design of their logistic infrastructure has to take uncertain information into account. In this paper we present a st...
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Uncertainty is one of the characteristics of product recovery networks. in particular the strategic design of their logistic infrastructure has to take uncertain information into account. In this paper we present a stochastic programming based approach by which a deterministic location model for product recovery network design may be extended to explicitly account for the uncertainties. Such a stochastic model seeks a solution which is appropriately balanced between some alternative scenarios identified by field experts. We apply the stochastic models to a representative real case study on recycling sand from demolition waste in The Netherlands. The interpretation of the results is meant to give more insight into decision-making under uncertainty for reverse logistics. (C) 2003 Elsevier B.V. All rights reserved.
Bunker fuel oil, one of the products of petroleum refining, has a strong impact on the production process because it drives the availability of heavy residues that depend on the crude quality. Based on the uncertainty...
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ISBN:
(纸本)9974002745
Bunker fuel oil, one of the products of petroleum refining, has a strong impact on the production process because it drives the availability of heavy residues that depend on the crude quality. Based on the uncertainty of its demand, a stochastic model is proposed, where the benefit of the production is optimized, taking decision on the more suitable raw material, intermediate products and its final blend in order to fulfill the quality and demand requirements of final products. Three different crude qualities are supposed to be available for the first stage decision and their prices include an estimation of the storage cost for different scenarios. The optimum implies the most expensive quality to be bought due to a lack of incentive in the production of extra amounts of fuel oil at a non attractive price. Results are compared with the solution of a deterministic model with mean demand. In spite of being more complex than the deterministic model, the stochastic model solution's shows how the refinery should operate for each scenario of bunker fuel oil demand. Relative value between raw material and products, storage cost and some constraints in the demand have strong impact in the solution. Finally, a first approach to a procedure for building a stochastic model for linear programming packages, of common use in the refining industry, is exposed.
We consider capacity expansion of a telecommunications network in the face of uncertain future demand and potential future failures of network components. The problem is formulated as a bicriteria stochastic program w...
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We consider capacity expansion of a telecommunications network in the face of uncertain future demand and potential future failures of network components. The problem is formulated as a bicriteria stochastic program with recourse in which the total cost of the capacity expansion and the probability of future capacity requirements to be violated are simultaneously minimized. Assuming the existence of a finite number of possible future states of the world, an algorithm for the problem is elaborated. The algorithm determines all non-dominated solutions to the problem by a reduced feasible region method, solving a sequence of restricted subproblems by a cutting plane procedure. Computational results are reported for three different problem instances, one of which is a real-life problem faced by SONOFON, a Danish communications network operator.
We study a dynamic portfolio management problem over a finite horizon with transaction costs and a risk averse objective function. We assume that the uncertainty faced by the investor can be modelled or approximated u...
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We study a dynamic portfolio management problem over a finite horizon with transaction costs and a risk averse objective function. We assume that the uncertainty faced by the investor can be modelled or approximated using discrete probability distributions via a scenario approach. To solve the resulting optimization problem we use stochastic programming techniques;in particular a scenario decomposition approach. To take advantage of the structure of the portfolio problem we propose a further decomposition obtained by means of a discrete version of the Maximum Principle. The result is a double decomposition of the original problem: The first, given by the scenario approach, focuses on the stochastic aspect of the problem while the second, using the discrete Maximum Principle, concerns the dynamics over time. Applying the double decomposition to our portfolio problem yields a simpler and more direct solution approach which we illustrate with examples. (C) 2004 Elsevier B.V. All rights reserved.
In this paper we consider the problem of computing decentralized control policies in a discrete stochastic decision problem. For the problem we consider, computation of optimal decentralized policies is NP-hard. We pr...
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ISBN:
(纸本)0780390989
In this paper we consider the problem of computing decentralized control policies in a discrete stochastic decision problem. For the problem we consider, computation of optimal decentralized policies is NP-hard. We present a relaxation method for this problem which computes suboptimal decentralized policies as well as bounds on the optimal achievable value. We then show that policies computed from this relaxation are guaranteed to be within a fixed bound of optimal. The relaxation is derived from an equivalent formulation of this decentralized decision problem as a polynomial optimization problem. The method is illustrated by an example of decentralized detection.
We propose an SOS transition rule format for the generative model of probabilistic processes. Transition rules are partitioned in several strata, giving rise to an ordering relation analogous to those introduced by Ul...
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ISBN:
(数字)9783540319825
ISBN:
(纸本)3540253882
We propose an SOS transition rule format for the generative model of probabilistic processes. Transition rules are partitioned in several strata, giving rise to an ordering relation analogous to those introduced by Ulidowski and Phillips for classic process algebras. Our rule format guarantees that probabilistic bisimulation is a congruence w.r.t. process algebra operations. Moreover, our rule format guarantees that process algebra operations preserve semistochasticity of processes, i.e. the property that the sum of the probability of the moves of any process is either 0 or 1. Finally, we show that most of operations of the probabilistic process algebras studied in the literature are captured by our format, which, therefore, has practical applications.
We apply stochastic bounding methods with a partial order on the state space to the analysis of memory overflow in a router. Usually, stochastic bounds are associated to a total order implying useless constraints and ...
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ISBN:
(纸本)3540294147
We apply stochastic bounding methods with a partial order on the state space to the analysis of memory overflow in a router. Usually, stochastic bounds are associated to a total order implying useless constraints and decreasing the tightness of bounds. Here we present the basic methodology of sample path comparison with a partial order and some numerical results to show the accuracy of the results. We analyze the probability of a buffer overflow with two types of packets, a Pushout access mechanism and Markov modulated batch arrivals. This problem is strongly related to the memory rejection out a Fiber Delay Loop in an all optical router using deflection routing.
We study the interaction between non-deterministic and probabilistic behaviour in systems with continuous state spaces, arbitrary probability distributions and uncountable branching. Models of such systems have been p...
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ISBN:
(数字)9783540319825
ISBN:
(纸本)3540253882
We study the interaction between non-deterministic and probabilistic behaviour in systems with continuous state spaces, arbitrary probability distributions and uncountable branching. Models of such systems have been proposed previously. Here, we introduce a model that extends probabilistic automata to the continuous setting. We identify the class of schedulers that ensures measurability properties on executions, and show that such measurability properties are preserved by parallel composition. Finally, we demonstrate how these results allow us to define an alternative notion of weak bisimulation in our model.
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