Catálogo de publicaciones - libros

Models describing diseases and pathologic processes in particular are considered. There are presented basic uncertainties arising in such systems. There is shown why is it so necessary to take into account these uncertainties.

In this article we discuss a stochastic optimization model used for evaluation of long-term energy development. The model includes the following features:

In particular, this allows us to identify robust dynamic technology portfolios, which supply (in a sense) potential energy demand, while minimizing adjusted to risks expected costs together with investment and environmental risks. Formally, the discussed problem involves a non-convex, large-scale stochastic optimization model requiring special global optimization technique which takes advantage of the specific structure of the problem.

This article primarily concentrated with main motivations, critical importance of non-convexity (increasing returns) and explicit treatment of uncertainty by using stochastic optimization approach.

Electric energy systems have always been a continuous source of applications of planning under uncertainty. Stochastic parameters that may strongly affect the electric system are demand, natural hydro inflows and fuel prices, among others. A review of some estimation methods used to approximate those parameters is presented. Reliability and stochastic optimisation are widespread techniques used to incorporate random parameters in the decision-making process in electric companies. A unit commitment, a market-based unit commitment, a hydrothermal coordination and a risk management model are typical models that can incorporate uncertainty in the decision framework.

Main drawback of the traditional PERT modeling is that the probabilistic characteristics determined for the project completion time are only valid when it is supposed that any activity can be started promtly after executing all of its predecessor activities. This is possible in the case of scheduling computer tasks, however it is hardly possible in many other cases, like architectural project planning what is one of the the most important applicational areas of PERT modeling. In the paper a stochastic programming based PERT modeling will be introduced. This modeling will produce deterministic earliest starting times for the activities of the project. These deterministic starting times will be attainable with prescribed probability. So we also get an estimated project completion time what is attainable with the same prescribed probability. Numerical examples will be given for comparing the traditional and the newly introduced PERT modeling techniques.

The concept of implementable nonlinear stochastic programming by finite series of Monte-Carlo samples is surveyed addressing the topics related with stochastic differentiation, stopping rules, conditions of convergence, rational setting of the parameters of algorithms, etc. Our approach distinguishes itself by treatment of the accuracy of solution in a statistical manner, testing the hypothese of optimality according to statistical criteria, and estimating confidence intervals of the objective and constraint functions. The rule for adjusting the Monte-Carlo sample size is introduced which ensures the convergence with the linear rate and enables us to solve the stochastic optimization problem using a reasonable number of Monte-Carlo trials. The issues of implementation of the developed approach in optimal decision making, portfolio optimization, engineering are considered, too.

We analyze the effects of risks and learning on climate change decisions. Using a new two-stage, dynamic, climate change stabilization model with random time horizons, we show that the explicit incorporation of ex-post learning and safety constraints induces risk aversion in ex-ante decisions. This risk aversion takes the form in linear models of VaR- and CVaR-type risk measures. We also analyze extensions of the model that account for the possibility of nonlinear costs, limited emissions abatement capacity, and partial learning. We find that in all cases, even in linear models, any conclusion about the effect of learning can be reversed. Namely, learning may lead to either less- or more restrictive ex-ante emission reductions depending on model assumptions regarding costs, the distributions describing uncertainties, and assumptions about what might be learned. We analyze stylized elements of the model in order to identify the key factors driving outcomes and conclude that, unlike in most previous models, the quantiles of probability distributions play a critical role in solutions.

This paper deals with project evaluation from a portfolio perspective. The chief motivation stems from pricing bundles of related projects, all affected by uncertainty, when markets are imperfect or absent.

Novelties come by construing single projects as “players” of a transferableutility, stochastic, cooperative game. Stochastic programming then provides statedependent Lagrange multipliers associated to coupling constraints. Granted concave payoff functions, these multipliers not only emulate market clearing and formation of contingent, Arrow-Debreu prices; they also generate core solutions and project evaluations.

In this article we discuss a stochastic optimization model used for evaluation of long-term energy development. The model includes the following features:

In particular, this allows us to identify robust dynamic technology portfolios, which supply (in a sense) potential energy demand, while minimizing adjusted to risks expected costs together with investment and environmental risks. Formally, the discussed problem involves a non-convex, large-scale stochastic optimization model requiring special global optimization technique which takes advantage of the specific structure of the problem.

This article primarily concentrated with main motivations, critical importance of non-convexity (increasing returns) and explicit treatment of uncertainty by using stochastic optimization approach.