An Integer Programming Solution to a Capacity Planning Problem in an Armaments Factory

A production shop in Royal Ordnance contains machines which in many cases can be converted to manufacture any of the main products passing through the shop. The task of periodically reconfiguring the lines to match more nearly a given set of demands is a classic mathematical programming problem. A solution and some of its uses are presented as a case study.     

A Note on a Two-dimensional Dynamic Programming Problem

A two-dimensional dynamic programming problem is posed. By relaxing some of the restraints on the problem it is reduced to a standard dynamic programming problem. Results are quoted from a particular case study.     

On Analyses of the Solution to a Linear Programming Problem

Many complex problem situations in various contexts have been represented in recent years by the linear programming model. The simplex method can then be used to give the optimal values of the variables corresponding to a given set of values of the parameters. However, in many situations it is useful to have the solution to many other related problems which differ from the original problem only in the values of some of the parameters. This paper presents procedures by which the solutions to the changed problems can be derived from the simplex solution tableau corresponding to the original problem. The method will be illustrated by means of an example problem, and it will be shown how quantitative information obtained from such analyses can aid management in decision making.     

A Dynamic Programming Approach to the Three-machine Scheduling Problem

The three-machine scheduling problem, in which a number of jobsare to be sequenced for processing in the same order on eachof three machines so that the total elapsed time to completethe work is minimized, is formulated as a dynamic program. Aprocedure is developed which reduces the problem to one of evaluatinga subset of the total possible sequences. Some illustrativeexamples are given and the efficiency of the procedure discussedover a number of problems.     

区间数线性规划问题的解法

基于区间数与实数之间的关系,提出了区间数线性规划的激进最优解,保守最优解的定义.利用约束集之间以及目标函数值之间的关系,在原有区间数线性规划的基础之上,给出了两个求解激进最优解、保守最优解的方法.数值例子验证了该方法的有效性和可行性.     

投资组合问题的动态规划方法

关于投资组合问题,Markowitz的均值-方差模型奠定了理论基础。近年来出现了许多简化模型,多目标线性规划模型是其中之一,但是这种线性化方法不便于处理非线性的交易费,本文建立一种动态规划模型和递推算法。     

A Dynamic Programming Algorithm for the κ-Haplotyping Problem

The Minimum Fragments Removal （MFR） problem is one of the haplotyping problems： given a set of fragments, remove the minimum number of fragments so that the resulting fragments can be partitioned into k classes of non-conflicting subsets. In this paper, we formulate the κ-MFR problem as an integer linear programming problem, and develop a dynamic programming approach to solve the κ-MFR problem for both the gapless and gap eases.     

一类线性规划问题的快速解法

研究了在组合投资和多属性决策指标权重确定中有着重要应用的一类线性规划问题,得到了该类线性规划问题有可行解的充要条件,以及在有可行解的情况下寻求最优解的快速解法.     

一类最优指派问题的动态规划解法

考虑一类指派问题 :欲把 m项工作指派 n个人去完成 ( m≥ n) ,要求每项工作只能由一个人来做 ,第 i个人可以同时做 bi 项工作 ,其中 bi( bi≥ 1)是待求的未知数 ,i=1,2 ,… ,n,满足 ni=1bi =m,假定已知第 i人做第 j项工作所用的时间 cij≥ 0 ,i=1,2 ,… ,n;j=1,2 ,… ,m。文中给出了求解上述问题最优指派 (即使总耗用时间最小 )的动态规划解法。     

A Modeltheoretic Solution to a Problem of Tarski

Let 1 < n < ω and β > n. We show that the class Nr_nCA_β of n‐dimensional neat reducts of β‐dimensional cylindric algebras is not closed under forming elementary subalgebras. This solves a long‐standing open problem of Tarski and his co‐authors Andréka, Henkin, Monk and Németi. The proof uses genuine model‐theoretic arguments.     

最优炒股问题的动态规划模型

本文运用 Bellman的动态规划方法 ,给出了最优炒股问题的数学模型 ,并对其解进行了分析 .     

A Barrier Function Method for the Nonconvex Quadratic Programming Problem with Box Constraints

In this paper a barrier function method is proposed for approximating a solution of the nonconvex quadratic programming problem with box constraints. The method attempts to produce a solution of good quality by following a path as the barrier parameter decreases from a sufficiently large positive number. For a given value of the barrier parameter, the method searches for a minimum point of the barrier function in a descent direction, which has a desired property that the box constraints are always satisfied automatically if the step length is a number between zero and one. When all the diagonal entries of the objective function are negative, the method converges to at least a local minimum point of the problem if it yields a local minimum point of the barrier function for a sequence of decreasing values of the barrier parameter with zero limit. Numerical results show that the method always generates a global or near global minimum point as the barrier parameter decreases at a sufficiently slow pace.     

一类特殊二维0-1规划的广义指派模型求解

二维0-1整数规划模型应用广泛,对广义指派问题的研究,解决了一些二维0-1整数规划问题.但有些实际问题具有特殊上限约束,目前还没有对应的方法.针对该实际情形,本文建立了相应的数学模型,利用对指派模型的推广,求得问题最优解,从理论上解决了这一类特殊约束二维0-1整数规划的最优解求取问题.并通过算例说明了方法的使用.     

三人博弈问题的模型和一种解法的修正

简要叙述了三个擂台赛博弈问题,指出解法[1]的错误所在,其一是将无限延伸的博弈树以有限的形式看待,其二是概率计算过程与结果错误,提出一种新的解法,并比较了结果的大小。     

一类线性与框式约束凸规划问题的原始-对偶内点算法

本文对一类具有线性和框式约束的凸规划问题给出了一个原始-对偶内点算法, 该算法可在任一原始-对偶可行内点启动, 并且全局收敛,当初始点靠近中心路径时, 算法成为中心路径跟踪算法。 数值实验表明, 算法对求解大型的这类问题是有效的。     

A Geometrical Solution to a Tree Network Problem

A problem in tree networks, that of minimizing the cost of a pipeline tree connecting a source to a number of sinks, is discussed. A method of solution in which the optimal solution is synthesised from optimized subsystems is described. The method is built on the geometrical properties of the simplest subsystem; that with one source and two sinks. Experience with the method suggests that it is a practical alternative to numerical-iterative methods used hitherto.     

一个数学建模问题的简单解法

银行利率给出了一个简单计算方法 ,这种方法更符合中学生思维的习惯 .     

边界约束非凸二次规划问题的分枝定界方法

本文是研究带有边界约束非凸二次规划问题,我们把球约束二次规划问题和线性约束凸二次规划问题作为子问题,分明引用了它们的一个求整体最优解的有效算法,我们提出几种定界的紧、松驰策略,给出了求解原问题整体最优解的分枝定界算法,并证明了该算法的收敛性,不同的定界组合就可以产生不同的分枝定界算法,最后我们简单讨论了一般有界凸域上非凸二次规划问题求整体最优解的分枝与定界思想。