We consider power system expansion planning under uncertainty. In our approach, integer programming and stochastic programming provide a basic framework. We develop a multistage stochastic programming model in which s...
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We consider power system expansion planning under uncertainty. In our approach, integer programming and stochastic programming provide a basic framework. We develop a multistage stochastic programming model in which some of the variables are restricted to integer values. By utilizing the special property of the problem, called block separable recourse, the problem is transformed into a two-stage stochastic program with recourse. The electric power capacity expansion problem is reformulated as the problem with first stage integer variables and continuous second stage variables. The L-shaped algorithm to solve the problem is proposed.
stochastic programming is a branch of mathematical programming that considers optimization in the presence of uncertainty. In this paper, both single-objective and multi-objective stochastic programming problems are c...
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stochastic programming is a branch of mathematical programming that considers optimization in the presence of uncertainty. In this paper, both single-objective and multi-objective stochastic programming problems are considered, where the right hand side parameters follow Pareto distribution with known mean and variance. Both the stochastic programming methods namely, chance constrained programming and two-stage stochastic programming are used. In order to solve these stochastic programming problems;we convert these problems into some equivalent deterministic models. Then we use standard mathematical programming techniques for solving single-objective deterministic model. We use fuzzy programming technique to solve the multi-objective deterministic model. The solution procedures are illustrated with an example.
In intensity-modulated radiotherapy (IMRT), a treatment is designed to deliver high radiation doses to tumors, while avoiding the healthy tissue. Optimization-based treatment planning often produces sharp dose gradien...
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In intensity-modulated radiotherapy (IMRT), a treatment is designed to deliver high radiation doses to tumors, while avoiding the healthy tissue. Optimization-based treatment planning often produces sharp dose gradients between tumors and healthy tissue. Random shifts during treatment can cause significant differences between the dose in the "optimized" plan and the actual dose delivered to a patient. An IMRT treatment plan is delivered as a series of small daily dosages, or fractions, over a period of time (typically 35 days). It has recently become technically possible to measure variations in patient setup and the delivered doses after each fraction. We develop an optimization framework, which exploits the dynamic nature of radiotherapy and information gathering by adapting the treatment plan in response to temporal variations measured during the treatment course of a individual patient. The resulting (suboptimal) control policies, which re-optimize before each fraction, include two approximate dynamic programming schemes: certainty equivalent control (CEC) and open-loop feedback control (OLFC). Computational experiments show that resulting individualized adaptive radiotherapy plans promise to provide a considerable improvement compared to non-adaptive treatment plans, while remaining computationally feasible to implement.
Portfolio managers in the new fixed-income securities have to cope with various forms of uncertainty, in addition to the usual interest rate changes. Uncertainy in the timing and amount of cashflows, changes in the de...
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Portfolio managers in the new fixed-income securities have to cope with various forms of uncertainty, in addition to the usual interest rate changes. Uncertainy in the timing and amount of cashflows, changes in the default and other risk premia and so on, complicate the portfolio manager's problem. We develop here a multi-period, dynamic, portfolio optimization model to address this problem. The model specifies a sequence of investment decisions over time that maximize the expected utility of return at the end of the planning horizon. The model is a two-stage stochastic program with recourse. The dynamics of interest rates, cashflow uncertainty, and liquidity, default and other risk premia, are explicitly modeled through postulated scenarios. Simulation procedures are developed to generate these scenarios, The optimization models are then integrated with the simulation procedures. Extensive validation experiments are carried out to establish the effectiveness of the model in dealing with uncertainty. In particular the model is compared against the popular portfolio immunization strategy, and against a portfolio based on mean-absolute deviation optimization.
We present how to use stochastic programming to best fund a pool of similar fixed-rate mortgages through issuing bonds, callable and non-callable, of various maturities. We discuss the estimation of expected net prese...
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We present how to use stochastic programming to best fund a pool of similar fixed-rate mortgages through issuing bonds, callable and non-callable, of various maturities. We discuss the estimation of expected net present value and (downside) risk for different funding instruments using Monte Carlo simulation techniques, and the optimization of the funding using single- and multi-stage stochastic programming. Using realistic data we computed efficient frontiers of expected net present value versus downside risk for the single- and the multi-stage model, and studied the underlying funding strategies. Constraining the duration and convexity of the mortgage pool and the funding portfolios to match at any decision point, we computed duration and convexity hedged funding strategies and compared them with those from the multi-stage stochastic programming model without duration and convexity constraints. The out-of-sample results for the different data assumptions demonstrate that multi-stage stochastic programming yields significantly larger net present values at the same or at a lower level of risk compared with single-stage optimization and with duration and convexity hedging. We found that the funding strategies obtained from the multi-stage model differed significantly from those from the single-stage model and were again significantly different to funding strategies obtained from duration and convexity hedging. Using multi-stage stochastic programming for determining the best funding of mortgage pools will lead, in the average, to significantly higher profits compared with using single-stage funding strategies, or using duration and convexity hedging. An efficient method for the out-of-sample evaluation of strategies obtained from multi-stage stochastic programming models is presented.
As a kind of particular programming problem, transportation problem attracts much attention in many fields, such as energy development, materials management, etc. In this paper, after analyzing the essence of stochast...
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The application of Information Technology (IT) and Information Systems (IS) have been crucial in enhancing the operating flexibility and resiliency of refineries. In particular, the Process Systems Engineering (PSE) c...
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This paper introduces a framework for the quantitative analysis of collaborative service platforms. Services built around platforms require the coordinated collaboration of several independent agents, each from a diff...
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This paper introduces a framework for the quantitative analysis of collaborative service platforms. Services built around platforms require the coordinated collaboration of several independent agents, each from a different field or area of expertise and each providing one or more components to the overall service. One of these agents takes the further role of platform coordinator, whose role consists in assembling the services from components provided by other agents and sharing the revenue between the participants. The agents decide which services to make a contribution to by selecting service portfolios that maximize their expected profit under constraints on risk and capacity. The coordinator selects the revenue-sharing scheme that balances the offers from other agents and ensures the functioning of the platform. We develop two stochastic optimization models with bilevel structure for the analysis of the collaborative service platform provision, analyse the properties of the solutions and provide numerical experiments that show the qualitative difference of the profit/risk trade-off in the multiagent case compared with the classical single agent case.
There are two types of random phenomena modeled in stochastic programs. One type is what we may term "external" or "natural" random variables, such as temperature or the roll of a dice. But in many...
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There are two types of random phenomena modeled in stochastic programs. One type is what we may term "external" or "natural" random variables, such as temperature or the roll of a dice. But in many other cases, random variables are used to reflect the behavior of other market participants. This is the case for such as price and demand of a product. Using simple game theoretic models, we demonstrate that stochastic programming may not be appropriate in these cases, as there may be no feasible way to replace the decisions of others by a random variable, and arrive at the correct decision. Hence, this simple note is a warning against certain types of stochastic programming models. stochastic programming is unproblematic in pure forms of monopoly and perfect competition, and also with respect to external random phenomena. But if market power is involved, such as in oligopolies, the modeling may not be appropriate.
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