New inequalities for finite and infinite group problems from approximate lifting

In this paper, we derive new families of facet‐defining inequalities for the finite group problem and extreme inequalities for the infinite group problem using approximate lifting. The new valid inequalities for the finite group problem include two‐ and three‐slope facet‐defining inequalities as well as the first family of four‐slope facet‐defining inequalities. The new valid inequalities for the infinite group problem include families of two‐ and three‐slope extreme inequalities. These new inequalities not only illustrate the diversity of strong inequalities for the finite and infinite group problems, but also provide a large variety of new cutting planes for solving integer and mixed‐integer programming problems. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

A discounted machine-replacement model with an expected future technological breakthrough

A machine-replacement problem is analyzed in a technological-development environment, in which a new-type machine (built by a new technology) may appear in the future. The solution of the replacement problem depends on purchasing, operating, and resale costs, and on the probability distribution of the market debut of the new technology, and it indicates whether to replace the existing machine now with an available similar type of machine, or to continue to operate the existing machine for at least one more period. A dynamic discounted cost model is presented, and a method is suggested for finding the optimal age for replacement of an existing machine (under rather general conditions of a technological environment). A solution procedure and a numerical example are given.     

A general age replacement model with minimal repair

A general age replacement is introduced which incorporates minimal repair, planned and unplanned replacements, and costs which depend on time. Finite and infinite horizon results are obtained. Various special cases are considered. Furthermore, a shock model with general cost structure is considered.     

Clinical Characterization of Insomnia among Veterans with PTSD: Identifying Risk Factors for Diagnosis and Treatment with Sedative-Hypnotics

Abstract

Insomnia is prevalent among Veterans with post-traumatic stress disorder (PTSD), it exacerbates PTSD symptoms, and it contributes to impaired functioning and quality of life. To improve treatment outcomes, it is important to identify risk factors for insomnia and sedative-hypnotic use. Classification and regression trees and logistic regression models were used to identify variables associated with insomnia or sedative-hypnotic use. Key findings include low insomnia diagnosis rates (3.5–5.6%) and high rates of sedative-hypnotics (44.2–49.0%). Younger Veterans and those without a breathing-related sleep disorder (BRSD) were more likely to receive an insomnia diagnosis. Veterans with greater service connection and those with an alcohol/substance use disorder were more likely to be prescribed sedative-hypnotics. Interaction terms may have identified potential groups at risk of being under-diagnosed with insomnia (i.e. non-black Veterans with psychiatric co-morbidity, black Veterans without psychiatric co-morbidity) as well as groups at risk for sedative-hypnotic use (i.e. younger Veterans without BRSD). In sum, Veterans with PTSD have high rates of sedative-hypnotic use despite minimal evidence they are effective. This is counter to recommendations indicating behavioral interventions are the first-line treatment. Policy changes are needed to reduce use of sedative-hypnotics and increase access to behavioral insomnia interventions.     

Mean residual life of coherent systems consisting of multiple types of dependent components

Mean residual life is a useful dynamic characteristic to study reliability of a system. It has been widely considered in the literature not only for single unit systems but also for coherent systems. This article is concerned with the study of mean residual life for a coherent system that consists of multiple types of dependent components. In particular, the survival signature based generalized mixture representation is obtained for the survival function of a coherent system and it is used to evaluate the mean residual life function. Furthermore, two mean residual life functions under different conditional events on components’ lifetimes are also defined and studied.     

Adjacency‐based local top‐down search method for finding maximal efficient faces in multiple objective linear programming

It is well‐known that the efficient set of a multiobjective linear programming (MOLP) problem can be represented as a union of the maximal efficient faces of the feasible region. In this paper, we propose a method for finding all maximal efficient faces for an MOLP. The new method is based on a condition that all efficient vertices (short for the efficient extreme points and rays) for the MOLP have been found and it relies on the adjacency, affine independence and convexity results of efficient sets. The method uses a local top‐down search strategy to determine maximal efficient faces incident to every efficient vertex for finding maximal efficient faces of an MOLP problem. To our knowledge, the proposed method is the first top‐down search method that uses the adjacency property of the efficient set to find all maximal efficient faces. We discuss this and other advantages and disadvantages of the algorithm. We also discuss some computational experience we have had with our computer code for implementing the algorithm. This computational experience involved solving several MOLP problems with the code.     

Properties of a mean residual life function arising from renewal theory

The present article discusses the properties of the mean residual life function in a renewal process. We examine the relationship this function has with the failure rate function and the conventional mean, variance and coefficient of variation of residual life. We also discuss some monotonicity properties of the mean residual life function. A partial order based on the renewal mean residual function is introduced along with its interrelationship with some existing stochastic orders. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

On labeling the vertices of products of complete graphs with distance constraints

Variations of Hale's channel assignment problem, the L(j, k)‐labeling problem and the radio labeling problem require the assignment of integers to the vertices of a graph G subject to various distance constraints. The λ_j,k‐number of G and the radio number of G are respectively the minimum span among all L(j, k)‐labelings, and the minimum span plus 1 of all radio labelings of G (defined in the Introduction). In this paper, we establish the λ_j,k‐number of ∏ K for pairwise relatively prime integers t₁ < t₂ < … < t_q, t₁ ≥ 2. We also show the existence of an infinite class of graphs G with radio number |V(G)| for any diameter d(G). © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Optimal sample size allocation for tests with multiple levels of stress with extreme value regression

In this article, we discuss the optimal allocation problem in a multiple stress levels life‐testing experiment when an extreme value regression model is used for statistical analysis. We derive the maximum likelihood estimators, the Fisher information, and the asymptotic variance–covariance matrix of the maximum likelihood estimators. Three optimality criteria are defined and the optimal allocation of units for two‐ and k‐stress level situations are determined. We demonstrate the efficiency of the optimal allocation of units in a multiple stress levels life‐testing experiment by using real experimental situations discussed earlier by McCool and Nelson and Meeker. Monte Carlo simulations are used to show that the optimality results hold for small sample sizes as well. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007