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stochastic 0-1 linear programming under limited distributional information

OPERATIONS RESEARCH LETTERS 2008年第2期36卷 150-156页

作者： Wagner, Michael R. Calif State Univ Hayward Dept Management Hayward CA 94542 USA

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.

关键词： stochastic integer programming second order cone programming semidefinite programming

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Options analysis for long-term capacity design and operation of a lignocellulosic biomass refinery

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COMPUTERS & CHEMICAL ENGINEERING 2013年 58卷 178-202页

作者： Sharma, P. Romagnoli, J. A. Vlosky, R. Louisiana State Univ Dept Chem Engn Baton Rouge LA 70803 USA Louisiana State Univ Dept Renewable Nat Resources Baton Rouge LA 70803 USA

The growth of the lignocellulosic fuels has been hindered by technological and market uncertainty. This paper optimizes strategic investment decisions by prospective biobased fuel and chemical enterprises. A real options-based stochastic integer programming model is developed in this paper. We model a hypothetical, vertically integrated lignocellulosic enterprise that produces cellulosic ethanol and biosuccinic acid. Uncertainty is represented in bioproduct demands and prices. Strategic options including investment in research and development, investments in a flexible production platform and deferral of project investment are modeled. A hypothetical market model is also developed to correlate crude oil prices with the evolution of bioproduct markets. The discounted value of equity free cash flows is optimized. The optimal results include multiple capacity design plans based on the long term evolution of bioproduct markets. Monte Carlo simulations are also conducted to quantify the risk adjusted NPV's and returns on investment for the optimal capacity design trajectories. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Real options stochastic integer programming Multi-product biorefineries Uncertainty Lignocellulosic biomass

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A finite branch-and-bound algorithm for two-stage stochastic integer programs

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MATHEMATICAL programming 2004年第2期100卷 355-377页

作者： Ahmed, S Tawarmalani, M Sahinidis, NV Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA Purdue Univ Krannert Sch Management W Lafayette IN 47907 USA Univ Illinois Dept Chem & Biomol Engn Urbana IL 61801 USA

This paper addresses a general class of two-stage stochastic programs with integer recourse and discrete distributions. We exploit the structure of the value function of the second-stage integer problem to develop a novel global optimization algorithm. The proposed scheme departs from those in the current literature in that it avoids explicit enumeration of the search space while guaranteeing finite termination. Computational experiments on standard test problems indicate superior performance of the proposed algorithm in comparison to those in the existing literature.

关键词： stochastic integer programming branch-and-bound finite algorithms

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A cutting-plane approach to mixed 0-1 stochastic integer programs

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1997年第2期101卷 306-316页

作者： Caroe, CC Tind, J UNIV COPENHAGEN DEPT OPERAT RESUNIV PK 5DK-2100 COPENHAGEN ODENMARK

We consider a mixed 0-1 integer programming problem with dual block-angular structure arising in two-stage stochastic programming. A relaxation is proposed such that the problem is decomposed into subproblems each corresponding to the outcomes of the random variable. The convex hull of feasible solutions for the re laxation is characterized using results from disjunctive programming and it is shown how Lift-and-Project cuts can be generated for one subproblem and made valid far different outcomes. (C) 1997 Elsevier Science B.V.

关键词： stochastic integer programming mixed 0-1 integer programming cutting planes lift-and-project

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A two-stage stochastic programming model for electric energy producers

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COMPUTERS & OPERATIONS RESEARCH 2008年第10期35卷 3360-3370页

作者： Beraldi, Patrizia Conforti, Domenico Violi, Antonio Univ Calabria Dipartimento Elettron Informat & Sistemist I-87036 Arcavacata Di Rende CS Italy

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.

关键词： electricity markets power optimization stochastic integer programming

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Robust solutions and risk measures for a supply chain planning problem under uncertainty

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2008年第1期59卷 2-12页

作者： Poojari, C. A. Lucas, C. Mitra, G. Brunel Univ CARISMA Sch Informat Syst Comp & Math Uxbridge UB8 3PH Middx England

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.

关键词： supply chain planning stochastic integer programming Benders' decomposition generalized lambda distribution simulation genetic algorithm

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An exact algorithm for solving large-scale two-stage stochastic mixed-integer problems: Some theoretical and experimental aspects

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第1期204卷 105-116页

作者： Escudero, L. F. Garin, M. A. Merino, M. Perez, G. Univ Basque Country Dpto Econ Aplicada 3 Fac CC EE & Empresariales Bilbao 48015 Vizcaya Spain Univ Rey Juan Carlos Dpto Estadist & Invest Operat Madrid Spain Univ Basque Country Dpto Matemat Aplicada Estadist & Invest Operat Leioa Vizcaya Spain

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.

关键词： stochastic integer programming Nonanticipativity constraints Splitting variables Twin Node Family Branch-and-Fix Coordination

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Disjunctive Decomposition for Two-Stage stochastic Mixed-Binary Programs with Generalized Upper Bound Constraints

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INFORMS JOURNAL ON COMPUTING 2012年第1期24卷 172-186页

作者： Keller, Brian Bayraksan, Guezin Booz Allen Hamilton Annapolis Jct MD 20701 USA Univ Arizona Tucson AZ 85721 USA

The disjunctive decomposition (D-2) algorithm has emerged as a powerful tool to solve stochastic integer programs. In this paper, we consider two-stage stochastic integer programs with binary first-stage and mixedbinary second-stage decisions and present several computational enhancements to D-2. 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 problems with generalized upper bound constraints in the second stage and exploit this structure to generate cuts. We establish convergence of D-2 variants. We present computational results on a new stochastic scheduling problem with an uncertain number of jobs motivated by companies in industries such as consulting and defense contracting, where these companies bid on future contracts but may or may not win the bid. The enhancements reduced computation time on average by 45% on a set of test problems.

关键词： stochastic integer programming disjunctive decomposition generalized upper bound constraints stochastic scheduling

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Totally unimodular stochastic programs

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MATHEMATICAL programming 2013年第1-2期138卷 1-13页

作者： Kong, Nan Schaefer, Andrew J. Ahmed, Shabbir Purdue Univ Weldon Sch Biomed Engn W Lafayette IN 47907 USA Univ Pittsburgh Dept Ind Engn Pittsburgh PA 15261 USA Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA

We consider totally unimodular (TU) stochastic programs, that is, two-stage stochastic programs whose extensive-form constraint matrix is TU. We generalize the notion of total unimodularity to apply to sets of matrices and provide properties of such sets. We provide several sufficient conditions on stochastic programs to be TU. When solving TU stochastic problems using the L-shaped method, it is not clear whether the integrality restrictions should be imposed on the master problem. Such restrictions will make each master problem more difficult to solve. On the other hand, solving the linear relaxation of the master typically means sending fractional (and unlikely optimal) solutions to the subproblems, perhaps leading to more iterations. Our computational results investigate this trade-off and provide insight into which strategy is preferable.

关键词： stochastic integer programming Total unimodularity L-shaped method

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Mobility-Aware Relay Selection in 5G D2D Communication Using stochastic Model

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2019年第3期68卷 2837-2849页

作者： Singh, Durgesh Ghosh, Sasthi C. Indian Stat Inst Adv Comp & Microelect Unit Kolkata 700108 India

Challenges in relay selection for device-to-device (D2D) communication arise due to the mobility of nodes, which brings uncertainty in various network parameters. We first developed a network-assisted stochastic integer programming (SIP) model to incorporate uncertainty that predicts the network parameters for upcoming time instance based on information available at current time instance. We converted the SIP model to an equivalent deterministic mixed integer non-linear program (MINLP) model and proved its hardness result. By exploiting the constraints of MINLP, we developed a distributed greedy metric, termed as connectivity factor (CF), which is calculated locally at each node on per-hop basis. It captures the nodes mobility and, hence, takes care of link reliability that in turn controls packet loss and delay. It can be computed in O(n) time, where n is the number of transmitters interfering with the given link. Our approach is applicable to any mobility model with relevant distributions of mobility parameters known. We constructed perceived graph based on CF values to devise network-assisted and device-controlled relay selection algorithms for given source-destination pairs. Extensive simulation results show significant improvements in packet loss and average end-to-end delay by our approach over a recent implementation of an ad-hoc on-demand distance vector (AODV) based algorithm.

关键词： stochastic integer programming mobility of devices relay selection 5G D2D communication packet loss and end to end delay

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