A two-stagestochastic model with binary choice in the first stage has been developed to optimise the upgrading of a real-world forest road network, geographically located in the middle of Sweden. We have compared the...
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A two-stagestochastic model with binary choice in the first stage has been developed to optimise the upgrading of a real-world forest road network, geographically located in the middle of Sweden. We have compared the model with solutions to the same problem from deterministic scenario analysis. Upgrade policies can be achieved swiftly using both approaches, since the road network is of moderate size. However, a deterministic approach is considerably faster when larger problems are involved. The study here, furthermore, indicates that deterministic scenario analysis provides us with quick, near-optimal solutions to the stochastic model, which are of reasonable good quality. We conclude that the model used here is rather insensitive to uncertainty in critical period length, such as the length of spring thaw, at least when applied to the medium-sized problem presented here. Nevertheless, we strongly recommend the use of the stochastic model whenever possible, since the stochastic and deterministic solutions differ, due to the hedging effect in the stochastic solution. (C) 2006 Elsevier B.V. All rights reserved.
In this paper, we discuss here-and-now type stochastic programs with equilibrium constraints. We give a general formulation of such problems and study their basic properties such as measurability and continuity of the...
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In this paper, we discuss here-and-now type stochastic programs with equilibrium constraints. We give a general formulation of such problems and study their basic properties such as measurability and continuity of the corresponding integrand functions. We discuss also the consistency and rate of convergence of sample average approximations of such stochastic problems.
An inexact two-stage stochastic programming (ITSP) model is proposed for water resources management under uncertainty. The model is a hybrid of inexact optimization and two-stage stochastic programming. It can reflect...
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An inexact two-stage stochastic programming (ITSP) model is proposed for water resources management under uncertainty. The model is a hybrid of inexact optimization and two-stage stochastic programming. It can reflect not only uncertainties expressed as probability distributions but also those being available as intervals. The solution method for ITSP is computationally effective, which makes it applicable to practical problems. The ITSP is applied to a hypothetical case study of water resources system operation. The results indicate that reasonable solutions have been obtained. They are further analyzed and interpreted for generating decision alternatives and identifying significant factors that affect the system's performance. The information obtained through these post-optimality analyses can provide useful decision support for water managers.
This paper proposes a modification to the decomposition algorithm of Ierapetritou and Pistikopoulos (1994) for process optimization under uncertainty. The key feature of our approach is to avoid imposing constraints o...
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This paper proposes a modification to the decomposition algorithm of Ierapetritou and Pistikopoulos (1994) for process optimization under uncertainty. The key feature of our approach is to avoid imposing constraints on the uncertain parameters, thus allowing a more realistic modeling of uncertainty. A theoretical analysis of the earlier algorithm leads to the development of an improved algorithm which successfully avoids getting trapped in local minima while accounting more accurately for the trade-offs between cost and flexibility. In addition, the improved algorithm is 3-6 times faster, on the problems tested, than the original one. This is achieved by avoiding the solution of feasibility subproblems, the number of which is exponential in the number of uncertain parameters. (C) 2000 Elsevier Science Ltd. All rights reserved.
The traditional supply chain network planning problem is stated as a multi-period resource allocation model involving 0-1 discrete strategic decision variables. The MIP structure of this problem makes it fairly intrac...
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The traditional supply chain network planning problem is stated as a multi-period resource allocation model involving 0-1 discrete strategic decision variables. The MIP structure of this problem makes it fairly intractable for practical applications, which involve multiple products, factories, warehouses and distribution centres (DCs). The same problem formulated and studied under uncertainty makes it even more intractable. In this paper we consider two related modelling approaches and solution techniques addressing this issue. The first involves scenario analysis of solutions to "wait and see" models and the second involves a two-stage integer stochasticprogramming (ISP) representation and solution;of the same problem. We show how the results from the former can be used in the solution of the latter model. We also give some computational results based on serial and parallel implementations of the algorithms. (C) 2000 Elsevier Science B.V. All rights reserved.
Using the theory of generalized gradients for locally Lipschitz functions, optimality conditions for two-stage problems of stochasticprogramming with constraints that have to be satisfied almost surely- and constrain...
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