We discuss the role of mixed-integer value functions in the theoretical analysis of stochastic integer programs. It is shown how the interaction of value function properties with basic results from probability theory ...
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ISBN:
(纸本)3540005803
We discuss the role of mixed-integer value functions in the theoretical analysis of stochastic integer programs. It is shown how the interaction of value function properties with basic results from probability theory leads to structural statements in stochastic integer programming.
This paper considers online stochastic reservation problems, where requests come online and must be dynamically allocated to limited resources in order to maximize profit. Multi-knapsack problems with or without overb...
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ISBN:
(纸本)3540343067
This paper considers online stochastic reservation problems, where requests come online and must be dynamically allocated to limited resources in order to maximize profit. Multi-knapsack problems with or without overbooking are examples of such online stochastic reservations. The paper studies how to adapt the online stochastic framework and the consensus and regret algorithms proposed earlier to online stochastic reservation systems. On the theoretical side, it presents a constant sub-optimality approximation of multi-knapsack problems, leading to a regret algorithm that evaluates each scenario with a single mathematical programming optimization followed by a small number of dynamic programs for one-dimensional knapsacks. On the experimental side, the paper demonstrates the effectiveness of the regret algorithm on multi-knapsack problems (with and without overloading) based on the benchmarks proposed earlier.
This paper analyzes the market-clearing formulation with stochastic security developed in its companion paper through two case studies solved using mixed-integer linear programming techniques. The generation and reser...
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Modern insurance products are becoming increasingly complex, offering various guarantees, surrender options and bonus provisions. A case in point are the with-profits insurance policies offered by UK insurers. While t...
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Modern insurance products are becoming increasingly complex, offering various guarantees, surrender options and bonus provisions. A case in point are the with-profits insurance policies offered by UK insurers. While these policies have been offered in some form for centuries, in recent years their structure and management have become substantially more involved. The products are particularly complicated due to the wide discretion they afford insurers in determining the bonuses policyholders receive. In this paper, we study the problem of an insurance firm attempting to structure the portfolio underlying its with-profits fund. The resulting optimization problem, a non-linear program with stochastic variables, is presented in detail. Numerical results show how the model can be used to analyze the alternatives available to the insurer, such as different bonus policies and reserving methods. (c) 2005 Elsevier B.V. All rights reserved.
We consider optimization problems for minimizing conditional valueat-risk (CVaR) from a computational point of view, with an emphasis on financial applications. As a general solution approach, we suggest to reformulat...
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We consider optimization problems for minimizing conditional valueat-risk (CVaR) from a computational point of view, with an emphasis on financial applications. As a general solution approach, we suggest to reformulate these CVaR optimization problems as two-stage recourse problems of stochastic programming. Specializing the L-shaped method leads to a new algorithm for minimizing conditional value-at-risk. We implemented the algorithm as the solver CVaRMin. For illustrating the performance of this algorithm, we present some comparative computational results with two kinds of test problems. Firstly, we consider portfolio optimization problems with 5 random variables. Such problems involving conditional value at risk play an important role in financial risk management. Therefore, besides testing the performance of the proposed algorithm, we also present computational results of interest in finance. Secondly, with the explicit aim of testing algorithm performance, we also present comparative computational results with randomly generated test problems involving 50 random variables. In all our tests, the experimental solver, based on the new approach, outperformed by at least one order of magnitude all general-purpose solvers, with an accuracy of solution being in the same range as that with the LP solvers.
This paper addresses the location problem of distribution centers (DC) in a distribution network with unreliable suppliers and random demand. A two-period model is proposed in which selected suppliers are available in...
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ISBN:
(纸本)9781424403103
This paper addresses the location problem of distribution centers (DC) in a distribution network with unreliable suppliers and random demand. A two-period model is proposed in which selected suppliers are available in the first period and can fail in the second period. The facility location/supplier reliability problem is formulated as a stochastic programming problem for minimizing total fixed facility costs, transportation costs, DC replenishment costs, DC inventory and safety stock costs. Since the problem is NP-hard non linear stochastic optimization problem, we propose a Monte Carlo optimization approach combining the sample average approximation (SAA) scheme and an efficient heuristic based on Lagrangian relaxation approach for solving the related sample optimization problem. Computational results are provided to assess the efficiency of the proposed method.
The paper presents a daily planning algorithm for a multi-reservoir hydropower system coordinated with wind power. The planning algorithm applies to the real situation where wind power and hydropower are owned by diff...
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ISBN:
(纸本)9789171785855
The paper presents a daily planning algorithm for a multi-reservoir hydropower system coordinated with wind power. The planning algorithm applies to the real situation where wind power and hydropower are owned by different utilities, sharing same transmission lines, though, hydropower has a priority for transmission capacity. Coordination is, thus, necessary to minimize wind energy curtailments during the congestion situations. The planning algorithm considers an uncertainty of wind power forecast. Forecast error scenarios are modeled with ARMA series. A scenario reduction algorithm is applied to reduce computational time. Only the planning for the spot market is considered. Thus, once the hydropower production bid is placed on the market it cannot be changed. The solution of the stochastic optimization problem should, therefore, fulfill the transmission constraints for all wind power production scenarios. The developed planning algorithm is applied in a case study. The results are compared to the planning results without coordination.
The possibility of controlling risk in stochastic power optimization by incorporating special risk functionals, so-called polyhedral risk measures, into the objective is demonstrated. We present an exemplary optimizat...
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ISBN:
(纸本)9789171785855
The possibility of controlling risk in stochastic power optimization by incorporating special risk functionals, so-called polyhedral risk measures, into the objective is demonstrated. We present an exemplary optimization model for mean-risk optimization of an electricity portfolios of a price-taking retailer. stochasticity enters the model via uncertain electricity demand, heat demand, spot prices, and future prices. The objective is to maximize the expected overall revenue and, simultaneously, to minimize risk in terms of multiperiod risk measures, i.e., risk measures that take into account intermediate cash values in order to avoid liquidity problems at any time. We compare the effect of different multiperiod polyhedral risk measures that had been suggested in our earlier work.
A unit commitment problem has long been known in the class of short-term functions and decisions, inherited from vertically integrated utility. In the competitive environment, the problem has become more complicated d...
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ISBN:
(纸本)9781424402274
A unit commitment problem has long been known in the class of short-term functions and decisions, inherited from vertically integrated utility. In the competitive environment, the problem has become more complicated due to the fact that any action taken will now influence profitability of decision maker such as generation companies, load serving entities, and so forth. Thus, not only do economic agents face operational risks, but they also need to procure their operations against financial risks front volatility in fuel, contract, and electricity prices. This leads to the evolution of stochastic unit commitment in this paper integrating risk management tools, i.e., electricity derivatives, so as to reduce the impacts from both operational and financial risks in the short run. The planning model is structured of stochastic mixed-integer program with recourse cost. A case study will be addressed with preliminary result presenting an improved solution.
Electricity suppliers are always confronted with demand uncertainty even though the state-of-the-art forecast and sophisticated control systems are employed to ensure both security and reliability. With the emergence ...
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ISBN:
(纸本)9789171785855
Electricity suppliers are always confronted with demand uncertainty even though the state-of-the-art forecast and sophisticated control systems are employed to ensure both security and reliability. With the emergence of power market, the market participants such as generation companies, load serving entities, etc., even face higher degree of uncertainty in its operation planning. This is due to the unique characteristics of electricity which could result in unprecedented price spikes. A portfolio of supply contracts including forwards and options is a set of tools for reducing the impacts of both demand uncertainty and price volatility by increasing production flexibility. Thus, a procurement strategy can be implemented by providing more choices via contracting in addition to self generation and spot market transactions. In this framework, a two-stage planning model is developed for improving the short-term operation by incorporating risk hedging strategy in the planning problem so as to meet stochastic demand.
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