The problem of adaptive routing in a network with failures is considered. The network may be in one of finitely many states characterized by different travel times along the arcs, and transitions between the states oc...
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The problem of adaptive routing in a network with failures is considered. The network may be in one of finitely many states characterized by different travel times along the arcs, and transitions between the states occur according to a continuous-time Markov chain. The objective was to develop a routing strategy that minimizes the total expected travel time. Dynamic programming models and flow-oriented models were developed and analyzed in the uncapacitated and the capacitated case. It is shown that the robust plan can be found from a special two-stage stochastic programming problem in which the second-stage models the rerouting problem after the state transition in the network. The models are illustrated on an example of the Sioux Falls transportation network. The computational results reveal striking properties of different routing policies and show that substantial improvements in both duration and size of jams can be achieved by employing robust strategies. (C) 2000 John Wiley & Sons, Inc.
We consider the capacity determination problem of a hydro reservoir. The reservoir is to be used primarily for hydropower generation: however, commitments on release targets for irrigation as well as mitigation of dow...
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We consider the capacity determination problem of a hydro reservoir. The reservoir is to be used primarily for hydropower generation: however, commitments on release targets for irrigation as well as mitigation of downstream hood hazards are also secondary objectives. This paper is concerned with studying the complex interaction among various system reliabilities (power. flood, irrigation, etc.) and to provide decision makers a planning tool for further investigation. The main tool is an optimization model that recognizes the randomness in streamflow. The model incorporates a special target-priority policy according to given system reliabilities. Optimized values are then used in a simulation model to investigate the system behavior. Detailed computational results are provided.
In this paper we give a variant of the Topkis-Veinott method for solving inequality constrained optimization problems. This method uses a linearly constrained positive semidefinite quadratic problem to generate a feas...
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In this paper we give a variant of the Topkis-Veinott method for solving inequality constrained optimization problems. This method uses a linearly constrained positive semidefinite quadratic problem to generate a feasible descent direction at each iteration. Under mild assumptions, the algorithm is shown to be globally convergent in the sense that every accumulation point of the sequence generated by the algorithm is a Fritz-John point of the problem. We introduce a Fritz-John (FJ) function, an FJ1 strong second-order sufficiency condition (FJ1-SSOSC), and an FJ2 strong second-order sufficiency condition (FJ2-SSOSC), and then show, without any constraint qualification (CQ), that (i) if an FJ point z satisfies the FJ1-SSOSC, then there exists a neighborhood N(z) of z such that, for any FJ point y is an element of N(z)\{z}, f(0)(y) not equal f(0)(z), where f(0) is the objective function of the problem;(ii) if an FJ point z satisfies the FJZ-SSOSC, then z is a strict local minimum of the problem. The result (i) implies that the entire iteration point sequence generated by the method converges to an FJ point. We also show that if the parameters are chosen large enough, a unit step length can be accepted by the proposed algorithm.
We present an integrated procedure to build and solve big stochastic programming models. The individual components of the system - the modeling language, the solver and the hardware - are easily accessible, or a least...
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We present an integrated procedure to build and solve big stochastic programming models. The individual components of the system - the modeling language, the solver and the hardware - are easily accessible, or a least affordable to a large audience. The procedure is applied to a simple financial model, which can be expanded to arbitrarily large sizes by enlarging the number of scenarios. We generated a model with one million scenarios, whose deterministic equivalent linear program has 1,111,112 constraints and 2,555,556 variables. We have been able to solve it on the cluster of ten PCs in less than 3 hours.
The average size of discovered petroleum reserves on the Norwegian continental shelf has declined steadily over the last years. As a consequence, the fields have become economically more marginal, and new and flexible...
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The average size of discovered petroleum reserves on the Norwegian continental shelf has declined steadily over the last years. As a consequence, the fields have become economically more marginal, and new and flexible development strategies are required. This paper describes a stochastic dynamic programming model for project evaluation under uncertainty, where emphasis is put on flexibility and its value. Both market risk and reservoir uncertainty are handled by the model, as well as different flexibility types. The complexity of the problem is a challenge and calls for simple descriptions of the main variables in order to obtain a manageable model size. Results from a case study reveal significant value of flexibility, and clearly illustrate the shortcoming of today's common evaluation methods. Particularly capacity flexibility should not be neglected in future development projects where uncertainty surrounding the reservoir properties is substantial.
A subroutine package. called NORSET, has been prepared. that-via Monte Carlo integration-is suitable for evaluating several types of probabilities related To the n-dimensional normal distribution. The following probab...
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A subroutine package. called NORSET, has been prepared. that-via Monte Carlo integration-is suitable for evaluating several types of probabilities related To the n-dimensional normal distribution. The following probabilities can be computed: the distribution function value, the probabilities of rectangles, convex polyhedra, hyperellipsoids and circular cones in case of normal distribution. Probabilities accurate to three digits can be computed in less than 0.3 sec for up to 20 dimensions and in less than 10 sees for up to 100 dimensions. The description of the subroutines, results of computer testing and experimentations together with the conclusions are presented here.
This paper is a summary of central and typical concepts, ideas and results in the field of sequential optimization and stochastic phenomena in forestry. The sequential optimization methods can be applied to all forest...
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This paper is a summary of central and typical concepts, ideas and results in the field of sequential optimization and stochastic phenomena in forestry. The sequential optimization methods can be applied to all forestry decisions. The text covers forestry decisions and forest economics issues that are based on sequential decision making. An illustration covers optimal decisions in the presence of stochastic market prices. stochastic (and/or deterministic but for different reasons unpredictable) changes in the economic and physical environments can be considered in decision making over time as soon as they are revealed. For this reason, the information and decision processes are sequential.
The bond portfolio management problem is formulated as a multiperiod two-stage or multistage stochastic program based on interest rate scenarios. These scenarios depend on the available market data, on the applied est...
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The bond portfolio management problem is formulated as a multiperiod two-stage or multistage stochastic program based on interest rate scenarios. These scenarios depend on the available market data, on the applied estimation and sampling techniques, etc., and are used to evaluate coefficients of the resulting large scale mathematical program. The aim of the contribution is to analyze stability and sensitivity of this program on small changes of the coefficients - the (scenario dependent) values of future interest rates and prices. We shall prove that under sensible assumptions, the scenario subproblems are stable linear programs and that also the optimal first-stage decisions and the optimal value of the considered stochastic program possess acceptable continuity properties.
The article is devoted to the 70th birthday of academician V.S. Mikhalevich and presents a survey of his fruitful activity as scientist and science organizer.
The article is devoted to the 70th birthday of academician V.S. Mikhalevich and presents a survey of his fruitful activity as scientist and science organizer.
Benders decomposition is a well-known technique for solving large linear programs with a special structure. In particular, it is a popular technique for solving multistage stochastic linear programming problems. Early...
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Benders decomposition is a well-known technique for solving large linear programs with a special structure. In particular, it is a popular technique for solving multistage stochastic linear programming problems. Early termination in the subproblems generated during Benders decomposition (assuming dual feasibility) produces valid cuts that are inexact in the sense that they are not as constraining as cuts derived from an exact solution. We describe an inexact cut algorithm, prove its convergence under easily verifiable assumptions, and discuss a corresponding Dantzig-Wolfe decomposition algorithm. The paper is concluded with some computational results from applying the algorithm to a class of stochastic programming problems that arise in hydroelectric scheduling.
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