Monotone failure rates for multivariate distributions

It is shown that the monotone multivariate failure rates of Brindley and Thompson have no natural analog involving the multivariate failure rate function of Basu for absolutely continuous distributions. Quantities related to the multivariate failure rate function are used to define monotone failure rates. It is shown that these are equivalent to the monotone failure rates of Brindley and Thompson. Based on these quantities, the loss of memory property of Marshall and Olkin is characterized.     

Sequencing independent jobs with a single resource

This paper examines problems of sequencing n jobs for processing by a single resource to minimize a function of job completion times, when the availability of the resource varies over time. A number of well-known results for single-machine problems which can be applied with little or no modification to the corresponding variable-resource problems are given. However, it is shown that the problem of minimizing the weighted sum of completion times provides an exception.     

All-integer linear programming — a new approach via dynamic programming

An exact method for solving all-integer linear-programming problems is presented. Dynamic-programming methodology is used to search efficiently candidate hyperplanes for the optimal feasible integer solution. The explosive storage requirements for high-dimensional dynamic programming are avoided by the development of an analytic representation of the optimal allocation at each stage. Computational results for problems of small to moderate size are also presented.     

An integer programming algorithm for portfolio selection with fixed charges

A mean-variance portfolio selection model with limited diversification is formulated in which transaction and management costs are incorporated as the sum of a linear cost and a fixed cost. The problem is a fixed charge integer programming problem solved by hypersurface search using dynamic programming. Fathoming is performed in the forward pass of dynamic programming so that values of the state variable which correspond to infeasible solutions are eliminated from the tables. This logic permits the solution of problems with 20–30 possible investments.     

Cost analysis of pro rata and free-replacement warranties

This article examines the short run total costs and long run average costs of products under warranty. Formulae for both consumer cost under warranty and producer profit are derived. The results in the case of the pro rata warranty correct a mistake appearing in Blischke and Scheuer [5]. We also show that expected average cost to both the producer and the consumer of a product under warranty depends on both the mean of the product lifetime distribution and on its failure rate.     

Nonlinear integer programming for various forms of constraints

A theoretical and computational investigation is made of the performance of a dynamic-programming-based algorithm for nonlinear integer problems with various types of constraints. We include linear constraints, aggregated linear constraints, separable nonlinear constraints and constraints involving maxima and minima. Separability of the objective function is assumed. The new feature of the algorithm is that two types of fathoming or pruning are used to reduce the size of tables and number of computations: fathoming by bounds and fathoming by infeasibility.     

The logarithmic poisson gamma distribution: A model for leadtime demand

This paper considers an inventory system in which demand occurrences arise according to a stationary Poisson process, demand sizes at each occurrence follow a logarithmic distribution, and leadtimes are random variables with the gamma distribution. Both the exact and approximate distribution for leadtime demand are derived and computations are performed which compare the approximation to the exact distribution. The results have application to both repairable and consumable item inventory systems.     

一种制取缸内示功图的新方法

本文基于舰艇柴油机的推进工况,研究通过测试一组稳态参数,建立物理和数学模型,获取缸内示功图。分析认为:该方法简单实用、成本低,与实测示功图比较误差小,完全满足使用管理中性能分析、工况评判、故障诊断等方面的需要,是解决舰艇柴油机实测示功图困难的一种新的尝试。     

Sandwich approximation of univariate convex functions with an application to separable convex programming

In this article an algorithm for computing upper and lower ? approximations of a (implicitly or explicitly) given convex function h defined on an interval of length T is developed. The approximations can be obtained under weak assumptions on h (in particular, no differentiability), and the error decreases quadratically with the number of iterations. To reach an absolute accuracy of ? the number of iterations is bounded by