A supply chain network-planning problem is presented as a two-stage resource allocation model with 0-1 discrete variables. In contrast to the deterministic mathematical programming approach, we use scenarios. to repre...
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A supply chain network-planning problem is presented as a two-stage resource allocation model with 0-1 discrete variables. In contrast to the deterministic mathematical programming approach, we use scenarios. to represent the uncertainties in demand. This formulation leads to a very large scale mixed integer-programming problem which is intractable. We apply Lagrangian relaxation and its corresponding decomposition of the initial problem in a novel way, whereby the Lagrangian relaxation is reinterpreted as a column generator and the integer feasible solutions are used to approximate the given problem. This approach addresses two closely related problems of scenario analysis and two-stage stochastic programs. Computational solutions for large data instances of these problems are carried out successfully and their solutions analysed and reported. The model and the solution system have been applied to study supply chain capacity investment and planning.
We discuss the problem of hedging between the natural gas and electric power markets. Based on multiple forecasts for natural gas prices, natural gas demand, and electricity prices, a stochastic optimization model adv...
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We discuss the problem of hedging between the natural gas and electric power markets. Based on multiple forecasts for natural gas prices, natural gas demand, and electricity prices, a stochastic optimization model advises a decision maker on when to buy or sell natural gas and when to transform gas into electricity. For relatively small models, branch-and-bound solves the problem to optimality. Larger models are solved using Benders decomposition and Lagrangian relaxation. We apply our approach to the system of an electric utility and succeed in solving problems with 50 000 binary variables in less than 4 minutes to within 1.16% of the optimal value.
We prove that the multivariate standard normal probability distribution function is concave for large argument values. The method of proof allows for the derivation of similar statements for other types of multivariat...
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We prove that the multivariate standard normal probability distribution function is concave for large argument values. The method of proof allows for the derivation of similar statements for other types of multivariate probability distribution functions too. The result has important application, e.g., in probabilistic constrained stochastic programming problems. 2001 Elsevier Science B.V. All rights reserved.
An algorithm incorporating the Logarithmic barrier into the Benders decomposition technique is proposed for solving two-stage stochastic programs. Basic properties concerning the existence and uniqueness of the soluti...
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An algorithm incorporating the Logarithmic barrier into the Benders decomposition technique is proposed for solving two-stage stochastic programs. Basic properties concerning the existence and uniqueness of the solution and the underlying path are studied. When applied to problems with a finite number of scenarios, the algorithm is shown to converge globally and to run in polynomial-time.
Based on the MPS standard for linear programs, data conventions for the description of multi-stage stochastic linear programs were described by Birge et al. [3]. This paper proposes extensions to the so-called SMPS st...
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Based on the MPS standard for linear programs, data conventions for the description of multi-stage stochastic linear programs were described by Birge et al. [3]. This paper proposes extensions to the so-called SMPS standard, in order to address known shortcomings and to extend the range of problems that can be expressed within the standard.
In this paper we study a Monte Carlo simulation based approach to stochastic discrete optimization problems. The basic idea of such methods is that a random sample is generated and the expected value function is appro...
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In this paper we study a Monte Carlo simulation based approach to stochastic discrete optimization problems. The basic idea of such methods is that a random sample is generated and the expected value function is approximated by the corresponding sample average function. The obtained sample average optimization problem is solved, and the procedure is repeated several times until a stopping criterion is satisfied. We discuss convergence rates, stopping rules, and computational complexity of this procedure and present a numerical example for the stochastic knapsack problem.
Subsidized housing policy in the United States must increasingly account for a greater use of tenant-based housing subsidies in place of traditional high-rise public housing. This paper focuses on design of policies t...
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Daily bidding is an activity of paramount importance for generation companies operating in day-ahead electricity markets. The authors have developed a strategic bidding procedure based on stochastic programming to obt...
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By using fuzzy random lifetimes as basic variables, three types of system performances-expected system lifetime, (alpha,beta)-system lifetime and system reliability-evaluated by fuzzy random theory are presented respe...
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ISBN:
(纸本)078037293X
By using fuzzy random lifetimes as basic variables, three types of system performances-expected system lifetime, (alpha,beta)-system lifetime and system reliability-evaluated by fuzzy random theory are presented respectively. Some fuzzy random simulations are designed to estimate these system performances. Further, a spectrum of redundancy optimization models are constructed for redundancy optimization problems. In order to solve the proposed models, a hybrid intelligent algorithm is designed. Finally, a multistage system is provided for the sake of illustration.
Integrals of optimal values of random optimization problems depending on a finite dimensional parameter are approximated by using empirical distributions instead of the original measure. Under fairly broad conditions,...
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Integrals of optimal values of random optimization problems depending on a finite dimensional parameter are approximated by using empirical distributions instead of the original measure. Under fairly broad conditions, it is proved that uniform convergence of empirical approximations of the right hand sides of the constraints implies uniform convergence of the optimal values in the linear and convex case.
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