Models and algorithms for risk neutral and risk averse power optimization under uncertainty are presented. The approach differs from previous ones by incorporating the transmission network explicitly.
Models and algorithms for risk neutral and risk averse power optimization under uncertainty are presented. The approach differs from previous ones by incorporating the transmission network explicitly.
We develop a two-stage stochastic integer programming model for the simultaneous optimization of power production and day-ahead power trading in a hydro-thermal system. The model rests on mixed-integer linear formulat...
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We develop a two-stage stochastic integer programming model for the simultaneous optimization of power production and day-ahead power trading in a hydro-thermal system. The model rests on mixed-integer linear formulations for the unit commitment problem and for the price clearing mechanism at the power exchange. Foreign bids enter as random components into the model. We solve the stochasticinteger program by a decomposition method combining Lagrangian relaxation of nonanticipativity with branch-and-bound in the spirit of global optimization. Finally, we report some first computational experiences.
We consider a scheduling problem where each job requires multiple classes of resources, which we refer to as the multiple resource constrained scheduling problem(MRCSP). Potential applications include team scheduling ...
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We consider a scheduling problem where each job requires multiple classes of resources, which we refer to as the multiple resource constrained scheduling problem(MRCSP). Potential applications include team scheduling problems that arise in service industries such as consulting and operating room scheduling. We focus on two general cases of the problem. The first case considers uncertainty of processing times, due dates, and resource availabilities consumption, which we denote as the stochastic MRCSP with uncertain parameters (SMRCSP-U). The second case considers uncertainty in the number of jobs to schedule, which arises in consulting and defense contracting when companies bid on future contracts but may or may not win the bid. We call this problem the stochastic MRCSP with job bidding (SMRCSP-JB).We first provide formulations of each problem under the framework of two-stage stochasticprogramming with recourse. We then develop solution methodologies for both problems. For the SMRCSP-U, we develop an exact solution method based on the L-shaped method for problems with a moderate number of scenarios. Several algorithmic enhancements are added to improve efficiency. Then, we embed the L-shaped method within a sampling-based solution method for problems with a large number of scenarios. We modify a sequential sampling procedure to allowfor approximate solution of integer programs and prove desired properties. The sampling-based method is applicable to two-stage stochasticinteger programs with integer first-stage variables. Finally, we compare the solution methodologies on a set of test *** SMRCSP-JB, we utilize the disjunctive decomposition (D2 ) algorithm for stochasticinteger programs with mixed-binary subproblems. We develop several enhancements to the D2 algorithm. First, we explore the use of a cut generation problem restricted to a subspace of the variables, which yields significant computational savings. Then, we examine generating alternative disjunc
We consider the problem min(X epsilon(0, 1)n) {c'x : a'(j)x <= b(j), j = 1,..., m), where the a(j) are random vectors with unknown distributions. The only information we are given regarding the random vecto...
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We consider the problem min(X epsilon(0, 1)n) {c'x : a'(j)x <= b(j), j = 1,..., m), where the a(j) are random vectors with unknown distributions. The only information we are given regarding the random vectors aj are their moments, up to order k. We give a robust formulation, as a function of k, for the 0-1 integer linear program under this limited distributional information. (C) 2007 Elsevier B.V. All rights reserved.
The bilateral contract selection and bids definition constitute a strategic issue for electric energy producers that operate in competitive markets, as the liberalized electricity ones. In this paper we propose a two-...
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The bilateral contract selection and bids definition constitute a strategic issue for electric energy producers that operate in competitive markets, as the liberalized electricity ones. In this paper we propose a two-stage stochastic integer programming model for the integrated optimization of power production and trading which include a specific measure accounting for risk management. We solve the model by means of a novel enumerative solution approach that exploits the particular problem structure. Finally, we report some preliminary computational experiments. (c) 2007 Elsevier Ltd. All rights reserved.
We consider a strategic supply chain planning problem formulated as a two-stage stochastic integer programming (SIP) model. The strategic decisions include site locations, choices of production, packing and distributi...
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We consider a strategic supply chain planning problem formulated as a two-stage stochastic integer programming (SIP) model. The strategic decisions include site locations, choices of production, packing and distribution lines, and the capacity increment or decrement policies. The SIP model provides a practical representation of real-world discrete resource allocation problems in the presence of future uncertainties which arise due to changes in the business and economic environment. Such models that consider the future scenarios (along with their respective probabilities) not only identify optimal plans for each scenario, but also determine a hedged strategy for all the scenarios. We (1) exploit the natural decomposable structure of the SIP problem through Benders' decomposition, (2) approximate the probability distribution of the random variables using the generalized lambda distribution, and (3) through simulations, calculate the performance statistics and the risk measures for the two models, namely the expected-value and the here-and-now.
We propose a new class of stochasticinteger programs whose special features are dominance constraints induced by mixed-integer linear recourse. For these models, we establish closedness of the constraint set mapping ...
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We propose a new class of stochasticinteger programs whose special features are dominance constraints induced by mixed-integer linear recourse. For these models, we establish closedness of the constraint set mapping with the underlying probability measure as a parameter. In the case of finite probability spaces, the models are shown to be equivalent to large-scale, block-structured, mixed-integer linear programs. We propose a decomposition algorithm for the latter and discuss computational results.
We identify multistage stochasticinteger programs with risk objectives where the related wait-and-see problems enjoy similiar separability as in the risk neutral case. For models belonging to this class, we present a...
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We identify multistage stochasticinteger programs with risk objectives where the related wait-and-see problems enjoy similiar separability as in the risk neutral case. For models belonging to this class, we present a solution method combining branch-and-bound with relaxation of non-anticipativity and constraint branching along non-anticipativity subspaces.
A long distance transportation problem was abstracted to a resource flow allocation problem upon a stochastic-flow network with unreliable nodes. The objectives were the probability that transmission was successful an...
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A long distance transportation problem was abstracted to a resource flow allocation problem upon a stochastic-flow network with unreliable nodes. The objectives were the probability that transmission was successful and transportation cost. In order to solve constructed model, a multi-objective genetic algorithm was propounded. Tested by examples, the algorithm well solved the flow allocation problem in a stochastic-flow network.
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