Limiting survival functions of self‐similar structures

We show the existence of a unique analytic single parameter limiting survival function arising from the repeated composition of a coherent structure as the number of components tends to infinity. Examples include the repeated composition process of the bridge structure. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Exact likelihood inference for the exponential distribution under generalized Type‐I and Type‐II hybrid censoring

Chen and Bhattacharyya [Exact confidence bounds for an exponential parameter under hybrid censoring, Commun Statist Theory Methods 17 (1988), 1857–1870] considered a hybrid censoring scheme and obtained the exact distribution of the maximum likelihood estimator of the mean of an exponential distribution along with an exact lower confidence bound. Childs et al. [Exact likelihood inference based on Type‐I and Type‐II hybrid censored samples from the exponential distribution, Ann Inst Statist Math 55 (2003), 319–330] recently derived an alternative simpler expression for the distribution of the MLE. These authors also proposed a new hybrid censoring scheme and derived similar results for the exponential model. In this paper, we propose two generalized hybrid censoring schemes which have some advantages over the hybrid censoring schemes already discussed in the literature. We then derive the exact distribution of the maximum likelihood estimator as well as exact confidence intervals for the mean of the exponential distribution under these generalized hybrid censoring schemes. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

On the uncapacitated K‐commodity network design problem with zero flow‐costs

Extending Sastry's result on the uncapacitated two‐commodity network design problem, we completely characterize the optimal solution of the uncapacitated K‐commodity network design problem with zero flow costs for the case when K = 3. By solving a set of shortest‐path problems on related graphs, we show that the optimal solutions can be found in O(n³) time when K = 3, where n is the number of nodes in the network. The algorithm depends on identifying a list of “basic patterns”; the number of basic patterns grows exponentially with K. We also show that the uncapacitated K‐commodity network design problem can be solved in O(n³) time for general K if K is fixed; otherwise, the time for solving the problem is exponential. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Dual sourcing: Responsive hedging against correlated supply and demand uncertainty

This article analyzes dual sourcing decisions under stochastically dependent supply and demand uncertainty. A manufacturer faces the trade‐off between investing in unreliable but high‐margin offshore supply and in reliable but low‐margin local supply, where the latter allows for production that is responsively contingent on the actual demand and offshore supply conditions. Cost thresholds for both types of supply determine the optimal resource allocation: single offshore sourcing, single responsive sourcing, or dual sourcing. Relying on the concept of concordance orders, we study the effects of correlation between supply and demand uncertainty. Adding offshore supply to the sourcing portfolio becomes more favorable under positive correlation, since offshore supply is likely to satisfy demand when needed. Selecting responsive capacity under correlated supply and demand uncertainty is not as straightforward, yet we establish the managerially relevant conditions under which responsive capacity either gains or loses in importance. Our key results are extended to the broad class of endogenous supply uncertainty developed by Dada et al. [Manufact Serv Operat Mange 9 (2007), 9–32].© 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Coalitions & the Legitimisation of UK Security Policy

Abstract

David Moore analyses the role of the Treasury in detemining and controlling defence policy and expenditure, and the place of the MoD within this function.     

Large deviations of the winsorized mean of an exponential distribution

An asymptotic representation for large deviation probabilities of the Winsorized mean of a sequence of independent, identically distributed exponential random variables is derived. The Winsorized mean, a linear combination of exponential order statistics, is first transformed into a weighted sum of exponential random variables, and then a large deviation theorem for weighted sums can be applied. The representation obtained is then compared with results already known for the mean and the median, the two extreme cases of the Winsorized mean.     

Covariance of weibull order statistics

Let X₁ < X₂ <… < X_n denote an ordered sample of size n from a Weibull population with cdf F(x) = 1 - exp (?x^p), x > 0. Formulae for computing Cov (X_i, X_j) are well known, but they are difficult to use in practice. A simple approximation to Cov(X_i, X_j) is presented here, and its accuracy is discussed.     

Computerized scheduling of seagoing tankers

Computerized Scheduling of Seagoing Tankers The tanker scheduling problem considered in this paper is that of the Defense Fuel Supply Center (DFSC) and the Military Sealift Command (MSC) in the worldwide distribution of bulk petroleum products. Routes and cargoes which meet delivery schedule dates for a multiplicity of product requirements at minimum cost are to be determined for a fleet of tankers. A general mathematical programming model is presented, and then a mixed integer model is developed which attempts to reflect the true scheduling task of DFSC and MSC as closely as possible. The problem is kept to within a workable size by the systematic construction of a set of tanker routes which does not contain many possible routes that can be judged unacceptable from practical considerations alone.     

Variations on a cutting plane method for solving concave minimization problems with linear constraints

A cutting plane method for solving concave minimization problems with linear constraints has been advanced by Tui. The principle behind this cutting plane has been applied to integer programming by Balas, Young, Glover, and others under the name of convexity cuts. This paper relates the question of finiteness of Tui's method to the so-called generalized lattice point problem of mathematical programming and gives a sufficient condition for terminating Tui's method. The paper then presents several branch-and-bound algorithms for solving concave minimization problems with linear constraints with the Tui cut as the basis for the algorithm. Finally, some computational experience is reported for the fixed-charge transportation problem.     

Generalized programming by linear approximation of the dual gradient: Equality constraints

A modified generalized programming procedure is presented for solving concave programming problems with equality constraints. The procedure constructs convenient linear approximations of the gradient of the dual and finds points where the approximating functions vanish. In the quadratic programming case, the procedure is finitely convergent. Global convergence is established for the non-quadratic case. Illustrative numerical examples are included.