Postoptimality analysis in integer programming by implicit enumeration: The mixed integer case

This paper develops a method for doing postoptimality analysis on the mixed integer programming problem. The proposed procedures form a natural adjunct to enumerative I.P. algorithms that are linear programming based, and they are designed, in effect, to capitalize on insights generated as the problem is initially solved to do subsequent analysis upon it. In particular, limited ranging analysis is possible on selected parameters, as is the efficient resolving of the problem following parameter changes.     

An approach to postoptimality and sensitivity analysis of zero-one goal programs

In this article we present a methodology for postoptimality and sensitivity analysis of zero-one goal programs based on the set of k-best solutions. A method for generating the set of k-best solutions using a branch and bound algorithm and an implicit enumeration scheme for multiple objective problem are discussed. Rules for determining the range of parameter changes that still allows a member of the k-best set to be optimal are developed. An investigation of a sufficient condition for postoptimality analysis is also presented.     

Determining restrictive goals in linear goal programs

Goal programming is a method for solving problems having multiple, conflicting objectives. Information on the characteristics of the goals can help in setting goal weights and levels, determining priority levels, and in conducting postoptimality analysis. One characteristic affecting the outcome of a goal program is the restrictiveness of a goal. A restrictive goal is one whose inclusion in the goal set most degrades the value of the total objective function, or the attainment of the remaining goals. An algorithm is presented that determines restrictive goals.     

Postoptimality analysis in nonlinear integer programming: The right-hand side case

An algorithm is presented to gain postoptimality data about the family of nonlinear pure integer programming problems in which the objective function and constraints remain the same except for changes in the right-hand side of the constraints. It is possible to solve such families of problems simultaneously to give a global optimum for each problem in the family, with additional problems solved in under 2 CPU seconds. This represents a small fraction of the time necessary to solve each problem individually.     

一种新的装备配置优化模型

传统的装备配置优化问题一般采用确定性的数学规划方法解决,难以满足高技术条件下现代战争中需要对大量随机现象和模糊现象进行精确定量分析的实际要求。在分析了高技术条件下装备配置问题一般特性的基础上,根据机会约束规划和模糊机会约束规划的思想,提出了一种新的建立装备配置优化模型的思路和方法,并给出了基于随机模拟的遗传算法的实值算例,算例结果与实际情况基本相符,反映了模型的科学性与实用性。     

An easy solution for a special class of fixed charge problems

The fixed charge problem is a mixed integer mathematical programming problem which has proved difficult to solve in the past. In this paper we look at a special case of that problem and show that this case can be solved by formulating it as a set-covering problem. We then use a branch-and-bound integer programming code to solve test fixed charge problems using the setcovering formulation. Even without a special purpose set-covering algorithm, the results from this solution procedure are dramatically better than those obtained using other solution procedures.     

Statistical decision analysis of stochastic linear programming problems

This paper presents a statistical decision analysis of a one-stage linear programming problem with deterministic constraints and stochastic criterion function. Procedures for obtaining numerical results are given which are applicable to any problem having this general form. We begin by stating the statistical decision problems to be considered, and then discuss the expected value of perfect information and the expected value of sample information. In obtaining these quantities, use is made of the distribution of the optimal value of the linear programming problem with stochastic criterion function, and so we discuss Monte Carlo and numerical integration procedures for estimating the mean of this distribution. The case in which the random criterion vector has a multivariate Normal distribution is discussed separately, and more detailed methods are offered. We discuss dual problems, including some relationships of this work with other work in probabilistic linear programming. An example is given in Appendix A showing application of the methods to a sample problem. In Appendix B we consider the accuracy of a procedure for approximating the expected value of information.     

Turbo C与Microsoft FORTRAN混合编程的实现

本文通过研究Borland公司的Turbo C与Microsoft公司的FORTRAN混合编程时出现的问题,提出了修改初始化模块及函数库的原理与方法,并利用TLINK的动态连接功能,实现了这两种语言在源程序级的混合编程,最后说明了实现过程与注意事项。     

Entropy-based selection with multiple objectives

In this article we present an approach to determine the initially unspecified weights in an additive measurable multiattribute value function. We formulate and solve a series of nonlinear programming problems which (1) incorporate whatever partial information concerning the attribute weights or overall relative value of alternatives the decision maker chooses to provide, yet (2) yield a specific set of weights as a result. Although each formulation is rather easily solved using the nonlinear programming software GINO (general interactive optimizer), solutions in closed form dependent on a single parameter are also provided for a number of these problems.     

Parametric inference for component distributions from lifetimes of systems with dependent components

In system reliability analysis, for an n ‐component system, the estimation of the performance of the components in the system is not straightforward in practice, especially when the components are dependent. Here, by assuming the n components in the system to be identically distributed with a common distribution belonging to a scale‐family and the dependence structure between the components being known, we discuss the estimation of the lifetime distributions of the components in the system based on the lifetimes of systems with the same structure. We develop a general framework for inference on the scale parameter of the component lifetime distribution. Specifically, the method of moments estimator (MME) and the maximum likelihood estimator (MLE) are derived for the scale parameter, and the conditions for the existence of the MLE are also discussed. The asymptotic confidence intervals for the scale parameter are also developed based on the MME and the MLE. General simulation procedures for the system lifetime under this model are described. Finally, some examples of two‐ and three‐component systems are presented to illustrate all the inferential procedures developed here. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

战役优势参数及其应用研究

数学分析方法在军事行动计划中扮演着越来越显著的角色。对以兰彻斯特作战模型为基础的描述诸兵种合成作战的矩阵微分方程，以及由方程的控制矩阵和状态变量初值，在不解方程的情况下导出的战役优势参数进行了研究；以空战为例讨论了预测战役结局、辅助军事决策、优化兵力部署和规划火力分配等战役优势参数的主要应用；给出了对战役优势参数和数学模型的评价。     

Nonadjacent extreme point methods for solving linear programs

In this article we present some advanced basis or block-pivoting, relaxation, and feasible direction methods for solving linear programming problems. Preliminary computational results appear to indicate that the former two types of simplex-based procedures may hold promise for solving linear programming problems, unlike the third type of scheme which is shown to be computationally unattractive.     

Implicit enumeration based algorithms for postoptimizing zero-one programs

It has been shown by G. Roodman that useful postoptimization capabilities for the 0-1 integer programming problem can be obtained from an implicit enumeration algorithm modified to classify and collect all fathomed partial solutions. This paper extends the the approach as follows: 1) Improved parameter ranging formulas are obtained by higher resolution classification criteria. 2) Parameters may be changed so as to tighten the original problem, in addition to relaxing it. 3) An efficient storage structure is presented to cope with difficult data collection task implicit in this approach. 4) Finally, computer implementation is facilitated by the elaboration of a unified set of algorithms.     

A note on a comparison of confidence interval techniques in truncated life tests

Several approximate procedures are available in the literature for obtaining confidence intervals for the parameter A of an exponential distribution based on time truncated samples. This paper contains the results of an empirical study comparing three of these procedures.     

Parametric analysis of linear programs with upper bounded variables

Linear programming problems with upper bounded variables can be solved by regular simplex method by considering upper bounding constraints as explicit constraints of the problem. However, more efficient methods exist which consider these upper bound constraints implicitly. When parametric analysis for problems with upper bounds is to be carried out, one can use the regular parameter analysis by considering the upper bound constraints explicitly. This paper develops formulas for parametric analysis where upper bound constraints are used implicitly, thus reducing the size of the basic matrix.     

Cyclic scheduling in flow lines: Modeling observations,effective heuristics and a cycle time minimization procedure

In this paper we address the cyclic scheduling problem in flow lines. We develop a modeling framework and an integer programming formulation of the problem. We subsequently present exact and approximate solution procedures. The exact solution procedure is a branch-and-bound algorithm which uses Lagrangian and station-based relaxations of the integer programming formulation of the problem as the lower bounding method. Our heuristic procedures show a performance superior to the available ones in the literature. Finally, we address the stability issue in cyclic scheduling, demonstrate its relationship to the work-in-progress inventory control of a flow line, and present a very simple procedure to generate stable schedules in flow lines. © 1996 John Wiley & Sons, Inc.     

Convex/stochastic programming and multilocation inventory problems

This paper examines a convex programming problem that arises in several contexts. In particular, the formulation was motivated by a generalization of the stochastic multilocation problem of inventory theory. The formulation also subsumes some “active” models of stochastic programming. A qualititative analysis of the problem is presented and it is shown that optimal policies have a certain geometric form. Properties of the optimal policy and of the optimal value function are described.     

基于Simulink的复杂可修系统的建模与仿真方法

利用排队论、有限状态机理论与面向对象编程思想,提出了建立基于Simulink复杂可修系统模型的思路、分析步骤、难点问题的解决以及参数统计模型。利用Simulink对一种复杂呵修系统进行了具体的建模与仿真。结果表明：基于Simulink的模型与仿真能够有效地评估复杂可修系统的可靠性参数,并具有可视化、流程化和层次化的特点。     

Maximizing the ratio of two convex functions over a convex set

The purpose of this article is to present an algorithm for globally maximizing the ratio of two convex functions f and g over a convex set X. To our knowledge, this is the first algorithm to be proposed for globally solving this problem. The algorithm uses a branch and bound search to guarantee that a global optimal solution is found. While it does not require the functions f and g to be differentiable, it does require that subgradients of g can be calculated efficiently. The main computational effort of the algorithm involves solving a sequence of subproblems that can be solved by convex programming methods. When X is polyhedral, these subproblems can be solved by linear programming procedures. Because of these properties, the algorithm offers a potentially attractive means for globally maximizing ratios of convex functions over convex sets. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

An explicit general solution in linear fractional programming

A complete analysis and explicit solution is presented for the problem of linear fractional programming with interval programming constraints whose matrix is of full row rank. The analysis proceeds by simple transformation to canonical form, exploitation of the Farkas-Minkowki lemma and the duality relationships which emerge from the Charnes-Cooper linear programming equivalent for general linear fractional programming. The formulations as well as the proofs and the transformations provided by our general linear fractional programming theory are here employed to provide a substantial simplification for this class of cases. The augmentation developing the explicit solution is presented, for clarity, in an algorithmic format.