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A stochastic linear-programming MODEL FOR CORN RESIDUE PRODUCTION

JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 1992年第9期43卷 843-857页

作者： BOUZAHER, A OFFUTT, S OFF MANAGEMENT & BUDGET WASHINGTONDC

This paper presents the results of a stochastic linear program for estimating the supply of corn residue for use as raw material in an ethanol plant. The model is based on the production capacity of an average Illinois farm, and considers the feasibility of three mutually exclusive residue harvesting alternatives-own baling, custom baling, and cob collection. Since the potential for residue use in animal feed may be even more promising, these results are directly useful for the feed industry. They also indicate the profitability of investing in residue harvesting equipment. From a methodological point of view, the paper contrasts the results of three OR approaches, a deterministic LP approach, a stochastic LP approach, and a chance-constrained approach. Because of the stochastic nature of the problem both Monte Carlo simulation and chance-constrained programming are found to be computationally viable, even though they differ in the way they incorporate risk information.

关键词： CORN RESIDUE ETHANOL PRODUCTION stochastic linear programming MONTE-CARLO SIMULATION CHANCE-CONSTRAINED programming

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stochastic linear programming for Reservoir Operation with Constraints on Reliability and Vulnerability

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WATER 2018年第2期10卷 175-175页

作者： Chen, Cheng Kang, Chuanxiong Wang, Jinwen Huazhong Univ Sci & Technol Sch Hydropower & Informat Engn Wuhan 430074 Hubei Peoples R China

Reliability and vulnerability (RV) are two very important performance measures but, due to their stage-inseparable nature, they cannot be explicitly incorporated in stochastic dynamic programming (SDP), which is extensively used in reservoir operation. With inflows described as a Markov chain, a stochastic linear programming (SLP) model is formulated in this paper to explicitly incorporate the RV constraints in the reservoir operation, aimed at maximizing the expected power generation by determining the optimal scheduling decisions and their probabilities. Simulation results of the SLP and SDP models indicate the equivalence of the proposed SLP and SDP models without considering the RV constraints, as well as the strength of the SLP in explicitly incorporating the RV constraints. A simulated scheduling solution also reveals a reduction of power generation fluctuation, with the reservoir capacity emptied in advance to meet given reliability and vulnerability.

关键词： stochastic linear programming Markov chain reliability vulnerability reservoir operation stochastic dynamic programming

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A stochastic linear programming approach to hierarchical production planning

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 1997年第2期48卷 207-211页

作者： Kira, D Kusy, M Rakita, I CONCORDIA UNIV MONTREALPQCANADA

This paper examines production planning decisions. The process is formulated as a hierarchical production planning (HPP) model under uncertain demand. A review of HPP articles indicates that while current models do consider uncertainty as a part of their solution methods, a deficiency persists since these models fail to incorporate the uncertain demand explicitly in the formulation of the problem. A stochastic linear programming model (SLP) is proposed to better reflect reality and to provide a superior solution. The model remains computationally tractable despite the precise incorporation of uncertainty and the imposition of penalties when constraints are violated. A problem is introduced which illustrates the superiority of the proposed model over those currently being applied.

关键词： hierarchical stochastic linear programming simple recourse production planning

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Computation of some stochastic linear programming problems with Cauchy and extreme value distributions

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2005年第6期82卷 685-698页

作者： Sahoo, NP Biswal, MP Indian Inst Technol Dept Math Kharagpur 721302 W Bengal India

stochastic programming is concerned with optimization problems in which some or all parameters are treated as random variables in order to capture the uncertainty which is almost always an inherent feature of the system being modelled. It is a methodology for allocating today's resources to meet tomorrow's unknown demands. A general approach to deal with uncertainty is to assign a probability distribution to the unknown parameters. The basic idea used in stochastic optimization is to convert the probabilistic model to an equivalent deterministic model. The resulting model is then solved by standard linear or non-linear programming methods. In this paper two probability distributions, the Cauchy distribution and the extreme value distribution, are introduced for stochastic programming. Two different approaches are applied to transform the probabilistic multi-objective linear programming problem into deterministic models. The computational procedures of the models are discussed.

关键词： stochastic linear programming multi-objective programming goal programming Cauchy distribution extreme value distribution computation

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A stochastic linear programming model for maximizing generation and firm output at a reliability in long-term hydropower reservoir operation

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JOURNAL OF HYDROLOGY 2023年第1期618卷

作者： Chen, Cheng Feng, Suzhen Liu, Shuangquan Zheng, Hao Zhang, Hong Wang, Jinwen Huazhong Univ Sci & Technol Sch Civil & Hydraul Engn Wuhan 430074 Peoples R China Huazhong Univ Sci & Technol Inst Water Resources & Hydropower Wuhan 430074 Peoples R China Yunnan Elect Power Dispatch & Control Ctr Kunming 650011 Yunnan Peoples R China Griffith Univ Sch Engn & Built Environm Gold Coast Campus Gold Coast Qld 4222 Australia

The firm output, usually determined in the design stage of a hydroplant to serve as a threshold to measure system reliability, can be regarded as an unknown parameter to be explored to its maximum in long-term hydropower reservoir operation (LHRO). An unknown firm output to be ensured at certain reliability, however, will make the problem much more nonlinear and then complicate the modeling. This work presents a stochastic linear pro-gramming (SLP-1) model that can explicitly incorporate reliability in ensuring an unknown firm output to be maximized by using a probability variable to represent a decision at a state and introducing binary variables to decide whether the decision will ensure the unknown firm output. The present SLP-1 is improved on 1) another previous SLP model (SLP-0) that must have a firm output prespecified at certain reliability, and compared with 2) the stochastic dynamic programming (SDP) model that can only manage to estimate the firm output at a reli-ability with trial and error. Case studies show the superiority of the present SLP to the SDP that can hardly make the reliability any closer to what the SLP can achieve, especially in ensuring a high firm output, with gaps to desired reliability ranging up to 42.33% for Xiaowan and 31.8% for Nuozhadu. Indeed, the SLP-1 will encounter the dimensional difficulty that needs further efforts to overcome when applied to cascaded reservoirs.

关键词： Long -term hydropower operation stochastic linear programming Firm output Reliability

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ROBUST SOLUTIONS IN stochastic linear-programming

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 1991年第10期42卷 857-870页

作者： SENGUPTA, JK UNIV CALIF SANTA BARBARA DEPT ECON SANTA BARBARA CA 93106 USA

The recent developments in stochastic linear programming are reviewed here broadly in their applied aspects. They included non-parametric methods which are applicable in situations of incomplete knowledge and partial uncertainty. This framework is shown to be most suitable for developing robust optimal solutions. For instance, a class of non-parametric methods based on the minimax principle and the criteria of stochastic dominance is developed here to illustrate its wide scope of application. It is shown that this class of methods provides a measure of robustness through the adoption of a cautious policy. Some examples are discussed using the recent field of data envelopment analysis.

关键词： stochastic linear programming MINIMAX SOLUTIONS DATA ENVELOPMENT ANALYSIS

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Optimal structural design under stochastic uncertainty by stochastic linear programming methods

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RELIABILITY ENGINEERING & SYSTEM SAFETY 2001年第2期72卷 165-177页

作者： Marti, K Fed Armed Forces Univ Munich D-85577 Neubiberg Munchen Germany

In the optimal plastic design of mechanical structures one has to minimize a certain cost function under the equilibrium equation, the yield condition and some additional simple constraints, like box constraints. A basic problem is that the model parameters and the external loads are random variables with a certain probability distribution. In order to get reliable/robust optimal designs with respect to random parameter variations, by using stochastic optimization methods, the original random structural optimization problem must be replaced by an appropriate deterministic substitute problem. Starting from the equilibrium equation and the yield condition, the problem can be described in the framework of stochastic (linear) programming problems with 'complete fixed recourse'. The main properties of this class of substitute problems are discussed, especially the 'dual decomposition' data structure which enables the use of very efficient special purpose LP-solvers. (C) 2001 Elsevier Science Ltd. All rights reserved.

关键词： optimal structural design random structural parameters stochastic linear programming

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Estimating the Optimal Probability of a Candidate Basic Solution in stochastic linear programming 60

Estimating the Optimal Probability of a Candidate Basic Solu...

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60th Annual Conference of the Society-of-Instrument-and-Control-Engineers-of-Japan (SICE)

作者： Gao, Zhenzhong Inuiguchi, Masahiro Osaka Univ Grad Sch Engn Sci Toyonaka Osaka 5608531 Japan

ISBN: (纸本)9784907764739

In this paper, we study the linear programming problem with random objective coefficients that have specific probability distributions. Since a candidate basic solution is hard to maintain optimal in all conditions, it is essential to estimate its probability of being optimal. To accomplish the goal, we assume one can get the probability distribution of coefficients, which forms the corresponding stochastic problem. Aided by the optimality's characteristics of a feasible basic solution in linear programming, we propose the probability estimation approach by utilising the probability density functions of coefficients. Furthermore, we show that the approach can estimate multiple candidate basic solutions, enabling a decision-maker to choose the one with the most significant probability. For generality, we test the approach with coefficients in uniform distribution and normal distribution, where we also simulate the process and make a verification. Moreover, since one can regard the uniform distribution as equivalent to the interval one, we compare both results and show that our estimation is more convincible.

关键词： stochastic linear programming Optimality Candidate Basic Solution Random Coefficients Probability Density Function (p.d.f.)

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Application of stochastic linear programming in managerial accounting Scenario analysis approach

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INTERNATIONAL JOURNAL OF ACCOUNTING AND INFORMATION MANAGEMENT 2020年第1期28卷 184-204页

作者： Wu, Di Choi, Yong Li, Ji Calif State Univ Bakersfield Dept Accounting & Finance Bakersfield CA 93311 USA

Purpose This paper aims to focus on applications of stochastic linear programming (SLP) to managerial accounting issues by providing a theoretical foundation and practical examples. SLP models may have more implications - and broader ones - in industry practice than deterministic linear programming (DLP) models do. Design/methodology/approach This paper introduces both DLP and SLP methods. In addition, continuous and discrete SLP models are explained. Applications are demonstrated using practical examples and simulations. Findings This research work extends the current knowledge of SLP, especially concerning managerial accounting issues. Through numerical examples, SLP demonstrates its great ability of hedging against all scenarios. Originality/value This study serves as an addition to building a cumulative tradition of research on SLP in managerial accounting. Only a few SLP studies in managerial accounting have focused on the development of such an instrument. Thus, the measurement scales in this research can be used as the starting point for further refining the instrument of optimization in managerial accounting.

关键词： Scenario analysis Data analytics Deterministic linear programming stochastic linear programming

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Mitigating Uncertainty via Compromise Decisions in Two-Stage stochastic linear programming: Variance Reduction

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OPERATIONS RESEARCH 2016年第6期64卷 1422-1437页

作者： Sen, Suvrajeet Liu, Yifan Univ Southern Calif Daniel J Epstein Dept Ind & Syst Engn Los Angeles CA 90089 USA

stochastic programming (SP) has long been considered a well-justified yet computationally challenging paradigm for practical applications. Computational studies in the literature often involve approximating a large number of scenarios by using a small number of scenarios to be processed via deterministic solvers, or running Sample Average Approximation on some genre of high performance machines so that statistically acceptable bounds can be obtained. In this paper we show that for a class of stochastic linear programming problems, an alternative approach known as stochastic Decomposition (SD) can provide solutions of similar quality in far less computational time using ordinary desktop or laptop machines of today. In addition to these compelling computational results, we provide a stronger convergence result for SD, and introduce a new solution concept that we call the compromise decision. This new concept is attractive for algorithms that call for multiple replications in sampling-based convex optimization algorithms. For such replicated optimization, we show that the difference between an average solution and a compromise decision provides a natural stopping rule. We discuss three stopping criteria that enhance the reliability of the compromise decision, reducing bias and variance associated with the result. Finally our computational results cover a variety of instances from the literature, including a detailed study of SONET Switched Network (SSN), a network planning instance known to be more challenging than other test instances in the literature.

关键词： stochastic linear programming stochastic decomposition computational experiments

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