Analysis of a machine repair problem with an unreliable server and phase type repairs and services

In this paper we study a machine repair problem in which a single unreliable server maintains N identical machines. The breakdown times of the machines are assumed to follow an exponential distribution. The server is subject to failure and the failure times are exponentially distributed. The repair times of the machine and the service times of the repairman are assumed to be of phase type. Using matrix‐analytic methods, we perform steady state analysis of this model. The time spent by a failed machine in service and the total time in the repair facility are shown to be of phase type. Several performance measures are evaluated. An optimization problem to determine the number of machines to be assigned to the server that will maximize the expected total profit per unit time is discussed. An illustrative numerical example is presented. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 462–480, 2003     

Network reliability assessment in a random environment

In this paper we consider networks that consist of components operating under a randomly changing common environment. Our work is motivated by power system networks that are subject to fluctuating weather conditions over time that affect the performance of the network. We develop a general setup for any network that is subject to such environment and present results for network reliability assessment under two repair scenarios. We also present Bayesian analysis of network failure data and illustrate how reliability predictions can be obtained for the network. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 574–591, 2003     

Estimating a survival curve when new is better than used in expectation

Let X be a positive random variable. The distribution F of X is said to be “new better than used in expectation,” or “NBUE,” if E(X) ⩾ E(X – t|X > t) for all t ⩾ 0. Suppose X₁, …, X_n, is a random sample from an NBUE distribution F. The problem of estimating F by a distribution which is itself NBUE is considered. The estimator G_n, defined as the NBUE distribution supported on the sample which minimizes the (sup norm) distance between the NBUE class and the empirical distribution function, is studied. The strong uniform consistency of G_n, is proven, and a numerical algorithm for obtaining G_n, is given. Our approach is applied to provide an estimate of the distribution of lifetime following the diagnosis of chronic granulocytic leukemia based on data from a National Cancer Institute study.     

Some two-on-two homogeneous stochastic combats

In this article we consider two versions of two-on-two homogeneous stochastic combat and develop expressions, in each case, for the state probabilities. The models are natural generalizations of the exponential Lanchester square law model. In the first version, a marksman whose target is killed resumes afresh the killing process on a surviving target; in the second version, the marksman whose target is killed merely uses up his remaining time to a kill on a surviving target. Using the state probabilities we then compute such important combat measures as (1) the mean and variance of the number of survivors as they vary with time for each of the sides, (2) the win probabilities for each of the sides, and (3) the mean and variance of the battle duration time. As an application, computations were made for the specific case of a gamma (2) interfiring time random variable for each side and the above combat measures were compared with the appropriate exponential and deterministic Lanchester square law approximations. The latter two are shown to be very poor approximations in this case.     

A combined approach to solve binary multicriteria problems

An implicit enumeration algorithm is developed to determine the set of efficient points in zero-one multiple criteria problems. The algorithm is specialized for the solution of a particular class of facility location problems. The procedure is complemented with the use of the utility function of the decision maker to identify a subset of efficient point candidates for the final selection. Computational results are provided and discussed.     

Multilinear extensions and quotients of simple games

Studied here is the problem of evaluating the formation of coalitions in cooperative games by considering its internal and external effects. Our analysis is based upon a formal theory of the quotient game and the use of multilinear extensions to compute the Shapley value and the coalitional value. When it applies to simple games, a series of interesting results is obtained. © 1996 John Wiley & Sons, Inc.     

Bicriteria product design optimization: An efficient solution procedure using AND/OR trees

Competitive imperatives are causing manufacturing firms to consider multiple criteria when designing products. However, current methods to deal with multiple criteria in product design are ad hoc in nature. In this paper we present a systematic procedure to efficiently solve bicriteria product design optimization problems. We first present a modeling framework, the AND/OR tree, which permits a simplified representation of product design optimization problems. We then show how product design optimization problems on AND/OR trees can be framed as network design problems on a special graph—a directed series‐parallel graph. We develop an enumerative solution algorithm for the bicriteria problem that requires as a subroutine the solution of the parametric shortest path problem. Although this parametric problem is hard on general graphs, we show that it is polynomially solvable on the series‐parallel graph. As a result we develop an efficient solution algorithm for the product design optimization problem that does not require the use of complex and expensive linear/integer programming solvers. As a byproduct of the solution algorithm, sensitivity analysis for product design optimization is also efficiently performed under this framework. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 574–592, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10031     

Resourcing for defense: Solving the roles and missions puzzle

One of the most important issues facing the post‐Cold War U.S. defense establishment concerns the future allocation of combat tasks and responsibilities among different branches of the armed forces. The challenge is to reduce unnecessary redundancy across roles and missions when resources are highly constrained, without compromising military effectiveness. Defining the policy problem as one of resource allocation rather than operational effectiveness, we develop a methodology for allocating roles and missions. Our methodology focuses at the highest level of force aggregation and uses a mathematical programming model to produce cross‐service cross‐mission trade‐offs that will yield the best total force combat and non‐combat potential within resource consumption constraints.