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     

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.     

A two product dynamic economic lot size production model with either-or production constraints

This paper considers the production of two products with known demands over a finite set of periods. The production and inventory carrying costs for each product are assumed to be concave. We seek the minimum cost production schedule meeting all demands, without backlogging, assuming that at most one of the two products can be produced in any period. The optimization problem is first stated as a nonlinear programming problem, which allows the proof of a result permitting the search for the optimal policy to be restricted to those which produce a product only when its inventory level is zero. A dynamic programming formulation is given and the model is then formulated as a shortest route problem in a specially constructed network.     

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.     

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.     

Three ways of obtaining the average cost expression in a problem related to joint replenishment inventory control

This paper does not present a new result, rather it is meant to illustrate the choice of modelling procedures available to an analyst in a typical inventory control problem. The same “average cost per unit time” expression is developed by three quite different procedures. This variety of approaches, as well as the recounting of the author's chronological efforts to solve the problem, should be of interest to the reader. The specific inventory problem studied is one where the controller of an item is faced with random opportunities for replenishment at a reduced setup cost; the problem is an integral component of the broader problem of inventory control of a group of items whose replenishments are coordinated to reduce the costs of production, procurement, and/or transportation.     

An explicit general solution in linear fractional programming

A complete analysis and explicit solution is presented for the problem of linear fractional programming with interval programming constraints whose matrix is of full row rank. The analysis proceeds by simple transformation to canonical form, exploitation of the Farkas-Minkowki lemma and the duality relationships which emerge from the Charnes-Cooper linear programming equivalent for general linear fractional programming. The formulations as well as the proofs and the transformations provided by our general linear fractional programming theory are here employed to provide a substantial simplification for this class of cases. The augmentation developing the explicit solution is presented, for clarity, in an algorithmic format.     

Sequential bid selection by stochastic approximation

Suppose that a contractor is faced with a sequence of “minimum bid wins contract” competitions. Assuming that a contractor knows his cost to fulfill the contract at each competition and that competitors are merely informed whether or not they have won, bids may be selected sequentially via a tailored stochastic approximation procedure. The efficacy of this approach in certain bidding environments is investigated.