In classical two-stage stochastic programming the expected value of the total costs is minimized. Recently, mean-risk models - studied in mathematical finance for several decades - have attracted attention in stochast...
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In classical two-stage stochastic programming the expected value of the total costs is minimized. Recently, mean-risk models - studied in mathematical finance for several decades - have attracted attention in stochastic programming. We consider Conditional Value-at-Risk as risk measure in the framework of two-stage stochastic integer programming. The paper addresses structure, stability, and algorithms for this class of models. In particular, we study continuity properties of the objective function, both with respect to the first-stage decisions and the integrating probability measure. Further, we present an explicit mixed-integer linear programming formulation of the problem when the probability distribution is discrete and finite. Finally, a solution algorithm based on Lagrangean relaxation of nonanticipativity is proposed.
The paper investigates the features of separately clearing the energy in the day-ahead market and then doing the same for the real-time market from the system operator's perspective. The analysis will show that th...
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ISBN:
(纸本)9781424401772
The paper investigates the features of separately clearing the energy in the day-ahead market and then doing the same for the real-time market from the system operator's perspective. The analysis will show that this separate clearing mechanism is not always the most economical. An alternative approach based on co-optimization of both energy markets is presented. Considering stochastic electric demand, a novel integrated energy dispatching model (IEDM) is proposed for system operators that schedules day-ahead energy trading taking possible real-time demand and prices into account to find an optimal day-ahead dispatching scheme so as to achieve the total purchase cost minimum. Mathematical analysis is provided to illustrate the IEDM is more economical than the conventional separate dispatching approach. The IEDM solution integrates Monte Carlo simulation and linear programming with Hooke and Jeeves pattern search method. A 6-unit system example is applied to illustrate that the IEDM provides a more economical approach.
The optimal scheduling of hydrothermal systems requires the representation of future inflows uncertainties for basically two reasons. Firstly, to define the present day commitment of thermal plants in order to hedge a...
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ISBN:
(纸本)9789171785855
The optimal scheduling of hydrothermal systems requires the representation of future inflows uncertainties for basically two reasons. Firstly, to define the present day commitment of thermal plants in order to hedge against adverse low inflows, and, secondly, to specify the volume of water storage in reservoirs to avoid spillage if high inflows occur. An inflow scenario tree must be correctly dimensioned so as to provide a parsimonious-but still representative-sample of the multivariate process underlying possible future inflows. In this article we propose a methodology to generate such a tree. The idea is to use principal component analysis to reduce the effective dimensionality of the scenario specification problem so that a discretization technique can be used in a smaller dimensional space. A stochastic hydrothermal schedulling optimization model was applied to the Brazilian interconnected power system to illustrate the proposed methodology. The quality of the reduced sample was evaluated by considering not only hydrological aspects, but also the solution stability of the stochastic problem.
This is a summary of the main results presented in the author's PhD thesis, supervised by D. Conforti and P. Beraldi and defended on March 2005. The thesis, written in English, is available from the author upon re...
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We introduce a modelling paradigm which integrates credit risk and market risk in describing the random dynamical behaviour of the underlying fixed income assets. We then consider an asset and liability management (AL...
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We introduce a modelling paradigm which integrates credit risk and market risk in describing the random dynamical behaviour of the underlying fixed income assets. We then consider an asset and liability management (ALM) problem and develop a multistage stochastic programming model which focuses on optimum risk decisions. These models exploit the dynamical multiperiod structure of credit risk and provide insight into the corrective recourse decisions whereby issues such as the timing risk of default is appropriately taken into consideration. We also present an index tracking model in which risk is measured (and optimised) by the CVaR of the tracking portfolio in relation to the index. In-sample as well as out-of-sample (backtesting) experiments are undertaken to validate our approach. The main benefits of backtesting, that is, ex-post analysis are that (a) we gain insight into asset allocation decisions, and (b) we are able to demonstrate the feasibility and flexibility of the chosen framework. (c) 2005 Published by Elsevier B.V.
This paper addresses the elective surgery planning problem when the operating rooms' capacity is shared between elective and emergency patients. The planning problem consists in determining the set of elective pat...
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ISBN:
(纸本)9781424403103
This paper addresses the elective surgery planning problem when the operating rooms' capacity is shared between elective and emergency patients. The planning problem consists in determining the set of elective patients that would be operated in each period over a planning horizon in order to minimize patients related costs and overtime costs of operating rooms. A stochastic integer programming model is proposed. Lagrangian relaxation is used to decompose the planning problem into period-level sub-problems that are solved by a dynamic programming method. The dual problem is solved iteratively using a sub-gradient algorithm. Feasible plans are derived from relaxed solutions using a heuristic and improved with a "local search heuristic". This approach results in both near-optimal solution and a lower bound to assess the degree of optimality. Numerical experimentations show that solutions within 1% of the optimum are obtained in a short computation time for problems of practical sizes.
We introduce and study the following model for routing uncertain demands through a network. We are given a capacitated multicommodity flow network with a single source and multiple sinks, and demands that have known v...
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ISBN:
(纸本)3540380442
We introduce and study the following model for routing uncertain demands through a network. We are given a capacitated multicommodity flow network with a single source and multiple sinks, and demands that have known values but unknown sizes. We assume that the sizes of demands are governed by independent distributions, and that we know only the means of these distributions and an upper bound on the maximum-possible size. Demands are irrevocably routed one-by-one, and the size of a demand is unveiled only after it is routed. A routing policy is a function that selects an unrouted demand and a path for it, as a function of the residual capacity in the network. Our objective is to maximize the expected value of the demands successfully routed by our routing policy. We distinguish between safe routing policies, which never violate capacity constraints, and unsafe policies, which can attempt to route a demand on any path with strictly positive residual capacity. We design safe routing policies that obtain expected value close to that of an optimal unsafe policy in planar graphs. Unlike most previous work on similar stochastic optimization problems, our routing policies are fundamentally adaptive. Our policies iteratively solve a sequence of linear programs to guide the selection of both demands and routes.
Criteria VaR (Value-at-Risk) and CVaR (Conditional Value-at-Risk), which are well-known in financial mathematics, are compared. Some connection between them is established. Ways of choice a level of confidence probabi...
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Criteria VaR (Value-at-Risk) and CVaR (Conditional Value-at-Risk), which are well-known in financial mathematics, are compared. Some connection between them is established. Ways of choice a level of confidence probability for the quantile optimization problem are suggested. The ways are based on some equations of balance between VaR and CVaR. Examples are discussed. (c) 2005 Elsevier B.V. All rights reserved.
In this paper we recall and further develop an inventory model formulated by the author [Prekopa, A., 1965. Reliability equation for an inventory problem and its asymptotic solutions. In: Prekopa, A. (Ed.), Colloquia ...
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In this paper we recall and further develop an inventory model formulated by the author [Prekopa, A., 1965. Reliability equation for an inventory problem and its asymptotic solutions. In: Prekopa, A. (Ed.), Colloquia Applied Mathematics in Economics. Publ. House of the Hung. Acad. Sci., Budapest, pp. 317-327;Prekopa, A., 1973. Generalizations of the theorems of Smirnov with application to a reliability type inventory problem. Math. Operationsforschung und Stat. 4, 283-297] and Ziermarm [Ziermann, M., 1964. Application of Smirnov's theorems for an inventory control problem. Publications of the Mathematical Institute of the Hungarian Academy of Sciences Ser. B 8, 509-518] that has had wide application in Hungary and elsewhere. The basic assumption made in connection with this model is that the delivery of the ordered amount takes place in an interval, according to some random process, rather than at one time epoch. The problem is to determine that minimum level of safety stock, that ensures continuous production, without disruption, by a prescribed high probability. The model is further developed first by its combination with another inventory control model, the order up to S model and then, by the formulations of a static and a dynamic type stochastic programming models. (c) 2005 Elsevier B.V. All rights reserved.
This paper aims at developing a decision making tool which can be potentially used by an IC design company to select the appropriate IC assembly factories and to allocate the outsourcing capacity among them. Herein a ...
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This paper aims at developing a decision making tool which can be potentially used by an IC design company to select the appropriate IC assembly factories and to allocate the outsourcing capacity among them. Herein a two-stage decision procedure is indicated to solve the outsourcing capacity allocation problem with uncertainty. In order to select the candidates of IC assembly factories, a fuzzy analytic hierarchy process is presented to generate the cooperation priority in the first stage model. In the second stage model, the outsourcing capacity allocation problem is formulated as a fuzzy stochastic programming model that is to minimize the total fuzzy weighted cost and subject to stochastic demand/supply. Finally, the proposed model is applied to an IC design company in the real world. The results of quantitative analysis and sensitivity analysis prove the superiority of the fuzzy stochastic outsourcing capacity allocation model.
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