Average-case analysis of the bin-packing problem with general cost structures

We consider a version of the famous bin-packing problem where the cost of a bin is a concave function of the number of items in the bin. We analyze the problem from an average-case point of view and develop techniques to determine the asymptotic optimal solution value for a variety of functions. We also describe heuristic techniques that are asymptotically optimal. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 673–686, 1997     

Northwest corner and banded matrix approximations to a Markov chain

In this paper, we consider approximations to discrete time Markov chains with countably infinite state spaces. We provide a simple, direct proof for the convergence of certain probabilistic quantities when one uses a northwest corner or a banded matrix approximation to the original probability transition matrix. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 187–197, 1999     

Planning accelerated life tests for censored two‐parameter exponential distributions

We consider optimal test plans involving life distributions with failure‐free life, i.e., where there is an unknown threshold parameter below which no failure will occur. These distributions do not satisfy the regularity conditions and thus the usual approach of using the Fisher information matrix to obtain an optimal accelerated life testing (ALT) plan cannot be applied. In this paper, we assume that lifetime follows a two‐parameter exponential distribution and the stress‐life relationship is given by the inverse power law model. Near‐optimal test plans for constant‐stress ALT under both failure‐censoring and time‐censoring are obtained. We first obtain unbiased estimates for the parameters and give the approximate variance of these estimates for both failure‐censored and time‐censored data. Using these results, the variance for the approximate unbiased estimate of a percentile at a design stress is computed and then minimized to produce the near‐optimal plan. Finally, a numerical example is presented together with simulation results to study the accuracy of the approximate variance given by the proposed plan and show that it outperforms the equal‐allocation plan. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 169–186, 1999     

A general model for accelerated life testing with time‐dependent covariates

This paper introduces a general or “distribution‐free” model to analyze the lifetime of components under accelerated life testing. Unlike the accelerated failure time (AFT) models, the proposed model shares the advantage of being “distribution‐free” with the proportional hazard (PH) model and overcomes the deficiency of the PH model not allowing survival curves corresponding to different values of a covariate to cross. In this research, we extend and modify the extended hazard regression (EHR) model using the partial likelihood function to analyze failure data with time‐dependent covariates. The new model can be easily adopted to create an accelerated life testing model with different types of stress loading. For example, stress loading in accelerated life testing can be a step function, cyclic, or linear function with time. These types of stress loadings reduce the testing time and increase the number of failures of components under test. The proposed EHR model with time‐dependent covariates which incorporates multiple stress loadings requires further verification. Therefore, we conduct an accelerated life test in the laboratory by subjecting components to time‐dependent stresses, and we compare the reliability estimation based on the developed model with that obtained from experimental results. The combination of the theoretical development of the accelerated life testing model verified by laboratory experiments offers a unique perspective to reliability model building and verification. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 303–321, 1999     

Probabilistic analysis of an asymptotically optimal solution for the completion time variance problem

Scheduling a set of n jobs on a single machine so as to minimize the completion time variance is a well‐known NP‐hard problem. In this paper, we propose a sequence, which can be constructed in O(n log n) time, as a solution for the problem. Our primary concern is to establish the asymptotical optimality of the sequence within the framework of probabilistic analysis. Our main result is that, when the processing times are randomly and independently drawn from the same uniform distribution, the sequence is asymptotically optimal in the sense that its relative error converges to zero in probability as n increases. Other theoretical results are also derived, including: (i) When the processing times follow a symmetric structure, the problem has 2^{⌊(n−1)/2⌋} optimal sequences, which include our proposed sequence and other heuristic sequences suggested in the literature; and (ii) when these 2^{⌊(n−1)/2⌋} sequences are used as approximate solutions for a general problem, our proposed sequence yields the best approximation (in an average sense) while another sequence, which is commonly believed to be a good approximation in the literature, is interestingly the worst. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 373–398, 1999     

A Cryptographic Escrow for Treaty Declarations and Step-by-Step Verification

The verification of arms-control and disarmament agreements requires states to provide declarations, including information on sensitive military sites and assets. There are important cases, however, in which negotiations of these agreements are impeded because states are reluctant to provide any such data, because of concerns about prematurely handing over militarily significant information. To address this challenge, we present a cryptographic escrow that allows a state to make a complete declaration of sites and assets at the outset and commit to its content, but only reveal the sensitive information therein sequentially. Combined with an inspection regime, our escrow allows for step-by-step verification of the correctness and completeness of the initial declaration so that the information release and inspections keep pace with parallel diplomatic and political processes. We apply this approach to the possible denuclearization of North Korea. Such approach can be applied, however, to any agreement requiring the sharing of sensitive information.     

Health Insurance,Health Conditions,and Veteran Health Care Utilization

Abstract

The utilization of health care services by veterans has received much attention in recent years. However, the impact of the large array of factors affecting the veterans’ demand for health care services remains understudied. These factors include individual socio-demographic and economic characteristics, the availability of various sources of health insurance, and the prevalence of medical conditions. We use public data to analyze how veterans’ utilization of health care services varies with these factors. We also analyze how the reliance on VA services varies when alternative sources of health insurance are available to veterans. Based on the estimated relationships, we use a micro-simulation model to forecast future health care utilization, both inside and outside of VA.     

Server scheduling on parallel dedicated machines with fixed job sequences

We consider server scheduling on parallel dedicated machines to minimize the makespan. Each job has a loading operation and a processing operation. The loading operation requires a server that serves all the jobs. Each machine has a given set of jobs to process, and the processing sequence is known and fixed. We design a polynomial‐time algorithm to solve the two‐machine case of the problem. When the number of machines is arbitrary, the problem becomes strongly NP‐hard even if all the jobs have the same processing length or all the loading operations require a unit time. We design two heuristic algorithms to treat the case where all the loading times are unit and analyze their performance.     

On the design of a tandem queue with blocking: Modeling,analysis, and gradient estimation

We demonstrate here how recent advances in the study of discrete-event stochastic systems provide fruitful results for the modeling, analysis, and design of manufacturing systems. We consider a multistage make-to-stock system where outputs from the final stage are used to satisfy customer demands. We address the problem of finding the appropriate trade-off between reduced order waiting time and increased process speeds. Using the idea of infinitesimal perturbation analysis (IPA), we establish a simple procedure where sample-path derivatives can be obtained along an arbitrary sample path. Under suitable conditions, we demonstrate that these derivative estimators are unbiased and strongly consistent and can be used in a classical stochastic optimization scheme to solve the problem. The role of continuity and convexity on the validity of the estimator is also addressed. Although the focus of this article is not to solve for the optimal solution, we provide a theoretical justification for such a pursuit. The approach is appealing as it is numerically stable, easy to implement, and can be extended to other system performance measures. © 1994 John Wiley & Sons, Inc.