stochastic programs are usually hard to solve when applied to real-world problems;a common approach is to consider the simpler deterministic program in which random parameters are replaced by their expected values, wi...
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stochastic programs are usually hard to solve when applied to real-world problems;a common approach is to consider the simpler deterministic program in which random parameters are replaced by their expected values, with a loss in terms of quality of the solution. The Value of the stochastic Solution-VSS-is normally used to measure the importance of using a stochastic model. But what if VSS is large, or expected to be large, but we cannot solve the relevant stochastic program? Shall we just give up? In this paper we investigate very simple methods for studying structural similarities and differences between the stochastic solution and its deterministic counterpart. The aim of the methods is to find out, even when VSS is large, if the deterministic solution carries useful information for the stochastic case. It turns out that a large VSS does not necessarily imply that the deterministic solution is useless for the stochastic setting. Measures of the structure and upgradeability of the deterministic solution such as the loss using the skeleton solution and the loss of upgrading the deterministic solution will be introduced and basic inequalities in relation to the standard VSS are presented and tested on different cases.
A random optimization problem (GRAPHICS) is approximated by a sequence of random surrogate problems (P-n)(n is an element of N) with (GRAPHICS) ([Omega, Sigma, P] a given probability space). We investigate the converg...
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A random optimization problem (GRAPHICS) is approximated by a sequence of random surrogate problems (P-n)(n is an element of N) with (GRAPHICS) ([Omega, Sigma, P] a given probability space). We investigate the convergence almost surely and in probability of the optimal values and the solution sets. The results can be regarded as random versions of well-known stability statements of parametric programming. Semicontinuous convergence (almost surely, in probability) of sequences of random functions is a crucial assumption in this framework and will be investigated in more detail.
This paper deals with the problem of scenario tree reduction for stochastic programming problems. In particular, a reduction method based on cluster analysis is proposed and tested on a portfolio optimization problem....
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This paper deals with the problem of scenario tree reduction for stochastic programming problems. In particular, a reduction method based on cluster analysis is proposed and tested on a portfolio optimization problem. Extensive computational experiments were carried out to evaluate the performance of the proposed approach, both in terms of computational efficiency and efficacy. The analysis of the results shows that the clustering approach exhibits good performance also when compared with other reduction approaches.
In this paper, a model for finding optimal contribution rates and portfolio allocations takes into account the funding situation of the fund. Using the CVaR risk measure, the model can be solved with dynamic stochasti...
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In this paper, a model for finding optimal contribution rates and portfolio allocations takes into account the funding situation of the fund. Using the CVaR risk measure, the model can be solved with dynamic stochastic programming techniques. Our model improves Kouwenberg's and Bogentoft's dynamic stochastic programming ALM model. And by adding CVaR constraints and considering the real situation of pension funds in China, we ultimately construct a new ALM model on DB enterprise pension funds. We build two models according to two different periods within the initial time and the stable period of pension funds and through optimisation methods to analyse the optimal investment strategy and obtain some useful conclusions.
Disaster response involves the planning, coordination, and distribution of supplies in an effective manner to people in need. Recent natural hazards, such as hurricane Harvey, have exposed the complexities and challen...
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Disaster response involves the planning, coordination, and distribution of supplies in an effective manner to people in need. Recent natural hazards, such as hurricane Harvey, have exposed the complexities and challenges associated with those tasks. In this paper, a stochastic programming model is presented which considers prepositioning strategies among food bank facilities located in high-risks areas for hurricanes. The model considers the uncertainty associated with the impact of the hurricane at each facility in terms of the number of available supplies, donations received at the facility, and the expected demand for their service region. The first-stage decision attempts to minimize the number of people not receiving the needed supplies by prepositioning the existing supplies at each facility. Second-stage decisions maximize the system responsiveness by trying to satisfy the observed demand for the scenarios under consideration. The experiments consider scenarios in which one or two food bank facilities are shut down after the natural phenomenon and study the impact of prepositioning supplies.
作者：
Ivanov, S.V.
Volokolamskoe shosse 4 Moscow125993 Russia
Under study is a bilevel stochastic linear programming problem with quantile criterion. Bilevel programming problems can be considered as formalization of the process of interaction between two parties. The first part...
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The author considers the use of risk measures that allows combining stochastic programming and robust optimization problems within the overall approach. Constructions for the class of polyhedral coherent risk measures...
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The author considers the use of risk measures that allows combining stochastic programming and robust optimization problems within the overall approach. Constructions for the class of polyhedral coherent risk measures are described. It is shown how the use of such measures can reduce problems of linear optimization under uncertainty to deterministic linear programming problems.
Unit commitment seeks the most cost effective generator commitment schedule for an electric power system to meet net load, defined as the difference between the load and the output of renewable generation, while satis...
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Unit commitment seeks the most cost effective generator commitment schedule for an electric power system to meet net load, defined as the difference between the load and the output of renewable generation, while satisfying the operational constraints on transmission system and generation resources. stochastic programming and robust optimization are the most widely studied approaches for unit commitment under net load uncertainty. We incorporate risk considerations in these approaches and investigate their comparative performance for a multi-bus power system in terms of economic efficiency as well as the risk associated with the commitment decisions. We explicitly account for risk, via Conditional Value at Risk (CVaR) in the stochastic programming objective function, and by employing a CVaR-based uncertainty set in the robust optimization formulation. The numerical results indicate that the stochastic program with CVaR evaluated in a low-probability tail is able to achieve better cost-risk trade-offs than the robust formulation with less conservative preferences. The CVaR-based uncertainty set with the most conservative parameter settings outperforms an uncertainty set based only on ranges.
This paper focuses on the energy optimal operation problem of microgrids (MGs) under stochastic environment. The deterministic method of MGs operation is often uneconomical because it fails to consider the high random...
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We consider a class of stochastic nonlinear complementarity problems. We first reformulate the stochastic complementarity problem as a stochastic programming model. Based on the reformulation, we then propose a penalt...
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We consider a class of stochastic nonlinear complementarity problems. We first reformulate the stochastic complementarity problem as a stochastic programming model. Based on the reformulation, we then propose a penalty-based sample average approximation method and prove its convergence. Finally, we report on some numerical test results to show the efficiency of our method.
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