两阶段随机线性规划的费用型鲁棒模型

Vladmiron和Zenios曾引进了限制补偿的概念,给出了关于具有补偿的两阶段随机线性规划的鲁棒优化的新的表述。为适应决策者对补偿在技术操作上的稳定性与经费预算上的稳定性的需求,我们提出了费用型鲁棒模型以及混合型鲁棒模型,并转化为序列修正的线性规划的求解问题．     

A Linear Programming Model of Seasonality in Milk Production

Intra-year milk supply patterns depend largely on the distribution of cow calving dates which in turn are influenced by climatic factors. The most important and least costly input to milk production is grass and the fresh growth and high digestibility of grass in spring and early summer often gives rise to a highly seasonal distribution of calvings resulting in a seasonal milk supply pattern. However, milk for liquid consumption and production of certain perishable milk products must be produced to meet a constant consumer demand throughout the year, necessitating a considerable amount of production outside the least cost period. The solution to this linear programming model gives the distribution of calving dates which will ensure the demand constraints are satisfied while minimizing production costs, and the solution to the dual gives a set of seasonal prices which should be paid to producers, equitably compensating them for the costs they incur.     

A Linear Programming Model for an Integrated Crop and Intensive Beef Production Enterprise

In an integrated crop and intensive beef production enterprise, some of the feedstuffs used for cattle feeding are grown by the enterprise. In evaluating the performance of operations of this type, the interactions between the crop and beef production parts of the enterprise must be taken into account. A linear programming (L.P.) model of this type of enterprise is developed, with the coefficients of the animal feeding activities being derived from a dynamic programming (D.P.) model. This D.P. model is used to determine the least-cost method of feeding animals to produce a specified liveweight gain using rations formulated by L.P. from a given set of feedstuffs. This approach allows the interactions between crop and livestock production to be taken into account without the need to make assumptions about the source of feedstuffs or the rate of liveweight gain.     

A Stochastic Programming Model for Currency Option Hedging

In this paper we use a stochastic programming approach to develop currency option hedging models which can address problems with multiple random factors in an imperfect market. The portfolios considered in our model are rebalanced at the end of each time period, and reinvestments are allowed during the hedging process. These sequential decisions (reinvestments) are based on the evolution of random parameters such as exchange rates, interest rates, etc. We also allow the inclusion of a variety of instruments in the hedging portfolio, including short term derivative securities, short term options, and futures. These instruments help generate strategies that provide good liquidity and low trade intensity. One of the important features of the model is that it incorporates constraints on sensitivity measures such as Delta and Gamma. By ensuring that these hedge parameters track a desired trajectory (e.g., the parameters of a target option), the new model provides investment strategies that are robust with respect to the perturbations measured by Delta and Gamma. In order to manage the explosion of scenarios due to multiple random factors, we incorporate sampling within a scenario aggregation algorithm. We illustrate that when compared with other myopic hedging methods in imperfect markets, the new stochastic programming model can provide better performance. Our examples also illustrate stochastic programming as a practical computational tool for realistic hedging problems.     

多属性决策中的目标规划

针对只有部分权重信息的对方案有偏好的多属性决策问题,本文给出了一种简单的目标规划模型,通过对该模型的求解却可得到决策方案的排序。最后给出了一个算例。     

Bounds in Multistage Linear Stochastic Programming

Multistage stochastic programs, which involve sequences of decisions over time, are usually hard to solve in realistically sized problems. Providing bounds for optimal solution may help in evaluating whether it is worth the additional computations for the stochastic program vs. simplified approaches. In this paper we generalize measures from the two-stage case, based on different levels of available information, to the multistage stochastic programming problems. A set of theorems providing chains of inequalities among the new quantities are proved. Numerical results on a case study related to a simple transportation problem illustrate the described relationships.     

Robust Solutions in Stochastic Linear Programming

The recent developments in stochastic linear programming are reviewed here broadly in their applied aspects. They include 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.     

A Dynamic Programming Model for Pig Production

The feeding policy of a pig production unit affects both the cost of production and the weight and carcase composition of the pigs produced. Since the market value of the pigs produced is determined by the weight and composition of the carcase, feeding policy has a major influence on the economic performance of the unit. In order to evaluate possible feeding policies, the effect of feed intake on both the weight and the body composition of the growing pig must be known, and since an optimal policy will involve using least cost rations, it must be possible to determine the least cost rations to produce liveweight gains of specified body composition. A dynamic programming model to determine the optimal feeding policy to produce pigs of specified weight and carcase composition is developed using a published pig growth model which allows the formulation of the required least cost rations, and the use of this dynamic programming model is illustrated.     

A Partioning Technique for Leontief Type Linear Programming Production Models

This paper studies the application of linear programming to the class of production planning problems which maximise profit subject to constraints on interacting production processes which can be represented by a static Leontief model. The method partitions the matrices involved in the solution process which enables the matrices involved in the computational process to become smaller at each iteration. Preliminary computational results show that the partitioning technique is quite efficient in solving such problems and should prove to be very effective on large-scale problems.     

Deviation Measures in Linear Two-Stage Stochastic Programming

We consider a linear two-stage stochastic program. Whereas optimization in the traditional setting is based solely on expectation, we include risk measures reflecting dispersions of the random objective. Presenting the mean-risk models, we aim to extend existing results for the expectation-based model. In particular, we discuss structural properties such as continuity, differentiability and convexity and address stability issues. Furthermore, we propose algorithmic treatment with a slight variation of the L-shaped method     

Stochastic Optimal Control and Linear Programming Approach

We study a classical stochastic optimal control problem with constraints and discounted payoff in an infinite horizon setting. The main result of the present paper lies in the fact that this optimal control problem is shown to have the same value as a linear optimization problem stated on some appropriate space of probability measures. This enables one to derive a dual formulation that appears to be strongly connected to the notion of (viscosity sub) solution to a suitable Hamilton-Jacobi-Bellman equation. We also discuss relation with long-time average problems.     

Pointwise Efficiency in Multiobjective Stochastic Linear Programming

In most of the approaches to the Multiobjective Stochastic Linear Programming problem that have been proposed in the literature, the notion of quality of a solution is not adequately defined. We reconsider this problem from a decision point of view, in contexts where either the decision maker's preference structure cannot be described by a utility function, or where this structure is expressed by an unknown non-decreasing utility function and the probability distribution of the random parameters is unknown. We define a fundamental set of ‘pointwise admissible’ solutions, as well as several subsets of particular interest. We discuss the relevance of these various pointwise efficient sets, their interrelations, and their practical identification.     

带凹性生产成本运输问题的新随机规划模型及其求解

提出了一种新的能反映决策者满意度的随机变量序关系,并据此研究了随机不等式的确定性等价类,方法被称为满意度方法.最后将其应用于带凹性生产成本运输问题的求解中,并将方法与常用的机会约束方法进行比较,说明满意度法不仅合理可行,而且当决策者对约束条件的要求越高时,它所得最优值越优于机会约束法所得最优值.     

A Scalable Parallel Interior Point Algorithm for Stochastic Linear Programming and Robust Optimization

We present a computationally efficient implementation of an interior point algorithm for solving large-scale problems arising in stochastic linear programming and robust optimization. A matrix factorization procedure is employed that exploits the structure of the constraint matrix, and it is implemented on parallel computers. The implementation is perfectly scalable. Extensive computational results are reported for a library of standard test problems from stochastic linear programming, and also for robust optimization formulations.The results show that the codes are efficient and stable for problems with thousands of scenarios. Test problems with 130 thousand scenarios, and a deterministic equivalent linear programming formulation with 2.6 million constraints and 18.2 million variables, are solved successfully.     

一种可用于资金分配的线性规划模型

本运用DEA方法,给出了一种能够用来进行资金分配决策的线性规划模型,并证明了其最优解的存在性。     

A Linear Programming Salary Evaluation Model for High School Personnel

Journal of the Operational Research Society - In recent years, increased criticism has been directed at the present fixed step salary method used for compensating personnel in school districts in...     

基金最佳使用计划的线性规划模型

给出了基金存款策略的线性规划模型 .对基金 M使用 n年的情形 ,只需比较银行存款税后年利率 ,初步确定 n年内的一切可能有的基金存款方式及其到期本利率 ,通过基金流转分析 ,即可建立以最大奖金数为目标的线性规划模型 ( LP1 ) n;问题二则需先分析 n年内一切可行的存款和购国库卷的组合方式及其到期的最佳本利率 ,然后调整模型 ( LP1 ) .中有关的系数 ,即可得到模型 ( LP2 ) n,调整模型 ( LP1 ) n与 ( LP2 ) n中第三年的奖金 y的系数 ,即可得到问题三的线性规划模型 .本文用 SAS/OR软件求解上述模型 ,得到在 n=1 0 ,M=5 0 0 0的情形下 ,使每年奖金数为最大的各种问题的基金的最佳使用策略 .     

下层独立的一主多从双层随机线性规划问题研究

Herminia I.Calvete等研究了一主多从双层确定性线性规划问题,证明了这类问题等价于一类常规的双层线性规划问题.本文在此基础上,推广确定型的问题到随机型优化情况,考虑了一类下层优化相互独立的一主多从双层随机优化问题(SLBMFP).在特定的随机变量分布条件下,理论上证明了该类问题可以转化为一主一从双层确定性优化问题.本文的研究对于求解一主多从双层随机优化模型,解决此类模型在实际应用中的问题具有一定的意义.     

A Novel Mixed Integer Linear Programming Model for Clustering Relational Networks

Integer programming models for clustering have applications in diverse fields addressing many problems such as market segmentation and location of facilities. Integer programming models are flexible in expressing objectives subject to some special constraints of the clustering problem. They are also important for guiding clustering algorithms that are capable of handling high-dimensional data. Here, we present a novel mixed integer linear programming model especially for clustering relational networks, which have important applications in social sciences and bioinformatics. Our model is applied to several social network data sets to demonstrate its ability to detect natural network structures.     

Some Applications of Linear Programming Formulations in Stochastic Control

We present two applications of the linearization techniques in stochastic optimal control. In the first part, we show how the assumption of stability under concatenation for control processes can be dropped in the study of asymptotic stability domains. Generalizing Zubov??s method, the stability domain is then characterized as some level set of a semicontinuous generalized viscosity solution of the associated Hamilton?CJacobi?CBellman equation. In the second part, we extend our study to unbounded coefficients and apply the method to obtain a linear formulation for control problems whenever the state equation is a stochastic variational inequality.