The forest harvest and road construction planning problem consists fundamentally of managing land designated for timber production and divided into harvest cells. For each time period the planner must decide which cel...
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The forest harvest and road construction planning problem consists fundamentally of managing land designated for timber production and divided into harvest cells. For each time period the planner must decide which cells to cut and what access roads to build in order to maximize expected net profit. We have previously developed deterministic mixed integer linear programming models for this problem. The main contribution of the present work is the introduction of a multistage stochastic integer programming model. This enables the planner to make more robust decisions based on a range of timber price scenarios over time, maximizing the expected value instead of merely analyzing a single average scenario. We use a specialization of the Branch-and-Fix Coordination algorithmic approach. Different price and associated probability scenarios are considered, allowing us to compare expected profits when uncertainties are taken into account and when only average prices are used. The stochastic approach as formulated in this work generates solutions that were always feasible and better than the average solution, while the latter in many scenarios proved to be infeasible.
We introduce the bilevel knapsack problem with stochastic right-hand sides, and provide necessary and sufficient conditions for the existence of an optimal solution. When the leader's decisions can take only integ...
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We introduce the bilevel knapsack problem with stochastic right-hand sides, and provide necessary and sufficient conditions for the existence of an optimal solution. When the leader's decisions can take only integer values, we present an equivalent two-stage stochasticprogramming reformulation with binary recourse. We develop a branch-and-cut algorithm for solving this reformulation, and a branch-and-backtrack algorithm for solving the scenario subproblems. Computational experiments indicate that our approach can solve large instances in a reasonable amount of time. (C) 2010 Elsevier B.V. All rights reserved.
A two-stage stochasticinteger program to determine an optimal schedule for jobs requiring multiple classes of resources under uncertain processing times, due dates, resource consumption and availabilities is formulat...
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A two-stage stochasticinteger program to determine an optimal schedule for jobs requiring multiple classes of resources under uncertain processing times, due dates, resource consumption and availabilities is formulated. Temporary resource capacity expansion for a penalty is allowed. Potential applications of this model include team scheduling problems that arise in service industries such as engineering consulting and operating room scheduling. An exact solution method is developed based on Benders decomposition for problems with a moderate number of scenarios. Benders decomposition is then embedded within a sampling-based solution method for problems with a large number of scenarios. A sequential sampling procedure is modified to allow for approximate solution of integer programs and its asymptotic validity and finite stopping are proved under this modification. The solution methodologies are compared on a set of test problems. Several algorithmic enhancements are added to improve efficiency.
We study a stochastic scenario-based facility location problem arising in situations when facilities must first be located, then activated in a particular scenario before they can be used to satisfy scenario demands. ...
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We study a stochastic scenario-based facility location problem arising in situations when facilities must first be located, then activated in a particular scenario before they can be used to satisfy scenario demands. Unlike typical facility location problems, fixed charges arise in the initial location of the facilities, and then in the activation of located facilities. The first-stage variables in our problem are the traditional binary facility-location variables, whereas the second-stage variables involve a mix of binary facility-activation variables and continuous flow variables. Benders decomposition is not applicable for these problems due to the presence of the second-stage integer activation variables. Instead, we derive cutting planes tailored to the problem under investigation from recourse solution data. These cutting planes are derived by solving a series of specialized shortest path problems based on a modified residual graph from the recourse solution, and are tighter than the general cuts established by Laporte and Louveaux for two-stage binary programming problems. We demonstrate the computational efficacy of our approach on a variety of randomly generated test problems. (C) 2010 Wiley Periodicals, Inc. Naval Research Logistics 57: 391-402, 2010
We propose a multiobjective local search metaheuristic for a mean-risk multistage capacity investment problem with irreversibility, lumpiness and economies of scale in capacity costs. Conditional value-at-risk is cons...
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We propose a multiobjective local search metaheuristic for a mean-risk multistage capacity investment problem with irreversibility, lumpiness and economies of scale in capacity costs. Conditional value-at-risk is considered as a risk measure. Results of a computational study are presented and indicate that the approach is capable of producing high-quality approximations to the efficient sets with a modest computational effort. The best results are achieved with a new hybrid approach, combining Tabu Search and Variable Neighbourhood Search.
We present an algorithmic framework, so-called BFC-TSMIP, for solving two-stage stochastic mixed 0-1 problems. The constraints in the Deterministic Equivalent Model have 0-1 variables and continuous variables at any s...
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We present an algorithmic framework, so-called BFC-TSMIP, for solving two-stage stochastic mixed 0-1 problems. The constraints in the Deterministic Equivalent Model have 0-1 variables and continuous variables at any stage. The approach uses the Twin Node Family (TNF) concept within an adaptation of the algorithmic framework so-called Branch-and-Fix Coordination for satisfying the nonanticipativity constraints for the first stage 0-1 variables. jointly we solve the mixed 0-1 submodels defined at each TNF integer set for satisfying the nonanticipativity constraints for the first stage continuous variables. In these submodels the only integer variables are the second stage 0-1 variables. A numerical example and some theoretical and computational results are presented to show the performance of the proposed approach. (C) 2009 Elsevier B.V. All rights reserved.
We derive a cutting plane decomposition method for stochastic programs with first-order dominance constraints induced by linear recourse models with continuous variables in the second stage. (C) 2009 Elsevier B.V. All...
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We derive a cutting plane decomposition method for stochastic programs with first-order dominance constraints induced by linear recourse models with continuous variables in the second stage. (C) 2009 Elsevier B.V. All rights reserved.
A multiyear discrete stochasticprogramming model with uncertain water supplies and inter-year crop dynamics is developed to determine: (i) whether a multiyear drought's impact can be more than the sum of its part...
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A multiyear discrete stochasticprogramming model with uncertain water supplies and inter-year crop dynamics is developed to determine: (i) whether a multiyear drought's impact can be more than the sum of its parts, and (ii) whether optimal response to 1 year of drought can increase a producer's vulnerability in subsequent years of drought. A farm system that has inter-year crop dynamics, but lacks inter-annual water storage capabilities, is used as a case study to demonstrate that dynamics unrelated to large reservoirs or groundwater can necessitate a multiyear model to estimate drought's impact. Results demonstrate the importance of analysing individual years of drought in the context of previous and future years of drought.
This paper addresses integerprogramming problems under probabilistic constraints involving discrete distributions. Such problems can be reformulated as large scale integer problems with knapsack constraints. For thei...
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This paper addresses integerprogramming problems under probabilistic constraints involving discrete distributions. Such problems can be reformulated as large scale integer problems with knapsack constraints. For their solution we propose a specialized Branch and Bound approach where the feasible solutions of the knapsack constraint are used as partitioning rules of the feasible domain. The numerical experience carried out on a set covering problem with random covering matrix shows the validity of the solution approach and the efficiency of the implemented algorithm.
In this paper we generalize N-fold integer programs and two-stage integer programs with AT scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer program...
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ISBN:
(纸本)9783642130359
In this paper we generalize N-fold integer programs and two-stage integer programs with AT scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer programs are polynomial-time solvable for any linear objective. Moreover, we present a polynomial-time computable optimality certificate for the case of fixed blocks, variable N and any convex separable objective function. We conclude with two sample applications, stochasticinteger programs with second-order dominance constraints and stochasticinteger multi-commodity flows, which (for fixed blocks) can be solved in polynomial time in the number of scenarios and commodities and in the binary encoding length of the input data. In the proof of our main theorem we combine several non-trivial constructions from the theory of Graver bases. We are confident that our approach paves the way for further extensions.
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