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.     

An algorithm for the solution of a location problem with metric constraints

In many location problems, the solution is constrained to lie within a closed set. In this paper, optimal solutions to a special type of constrained location problem are characterized. In particular, the location problem with the solution constrained to be within a maximum distance of each demand point is considered, and an algorithm for its solution is developed and discussed.     

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.     

A special case of the 3 × n flow shop problem

Johnson [2] in 1954 solved the two machine flow shop problem by giving an argument for a sufficient condition of optimality and by stating an efficient algorithm which produces a solution via satisfaction of the sufficient condition. Moreover, Johnson solved two special cases of the corresponding three machine flow shop problem. Since that time, six other special cases have been solved, two contributed by Arthanari and Mukhopadhyay [1], two by Smith, Panwalkar, and Dudek [3], and two of a different nature by Szwarc [5]. This paper contributes an extension to one of the classes described by Szwarc.     

Optimal ordering policies for a product that perishes in two periods subject to stochastic demand

This paper considers the problem of computing optimal ordering policies for a product that has a life of exactly two periods when demand is random. Initially costs are charged against runouts (stockouts) and outdating (perishing). By charging outdating costs according to the expected amount of outdating one period into the future, a feasible one period model is constructed. The central theorem deals with the n-stage dynamic problem and demonstrates the appropriate cost functions are convex in the decision variable and also provides bounds on certain derivatives. The model is then generalized to include ordering and holding costs. The paper is concluded with a discussion of the infinite horizon problem.     

Optimal location of a single service center of certain types

Hakimi has considered the problem of finding an optimal location for a single service center, such as a hospital or a police station. He used a graph theoretic model to represent the region being serviced. The communities are represented by the nodes while the road network is represented by the ares of the graph. In his work, the objective is one of minimizing the maximum of the shortest distances between the vertices and the service center. In the present work, the region being serviced is represented by a convex polygon and communities are spread over the entire region. The objective is to minimize the maximum of Euclidian distances between the service center and any point in the polygon. Two methods of solution presented are (i) a geometric method, and (ii) a quadratic programming formulation. Of these, the geometric method is simpler and more efficient. It is seen that for a class of problems, the geometric method is well suited and very efficient while the graph theoretic method, in general, will give only approximate solutions in spite of the increased efforts involved. But, for a different class of problems, the graph theoretic approach will be more appropriate while the geometric method will provide only approximate solutions though with ease. Finally, some feasible applications of importance are outlined and a few meaningful extensions are indicated.     

A branch and bound algorithm for the minimum storage‐time sequencing problem

The minimum storage‐time sequencing problem generalizes many well‐known problems in combinatorial optimization, such as the directed linear arrangement and the problem of minimizing the weighted sum of completion times, subject to precedence constraints on a single processor. In this paper we propose a new lower bound, based on a Lagrangian relaxation, which can be computed very efficiently. To improve upon this lower bound, we employ a bundle optimization algorithm. We also show that the best bound obtainable by this approach equals the one obtainable from the linear relaxation computed on a formulation whose first Chvàtal closure equals the convex hull of all the integer solutions of the problem. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 313–331, 2001     

The residual life of the renewal process: A simple algorithm

We develop a simple algorithm, which does not require convolutions, for computing the distribution of the residual life when the renewal process is discrete. We also analyze the algorithm for the particular case of lattice distributions, and we show how it can apply to an inventory problem. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 435–443, 1999