Landmarks in defense literature

The Cavalry Goes Through. By Bernard Newman. Henry Holt, New York (1930)     

An (s,S) inventory system with rest periods to the server

We study the (s,S) inventory system in which the server takes a rest when the level of the inventory is zero. The demands are assumed to occur for one unit at a time. The interoccurrence times between successive demands, the lead times, and the rest times are assumed to follow general distributions which are mutually independent. Using renewal and convolution techniques we obtain the state transition probabilities.     

A parallel sequencing algorithm for minimizing total cost

The problem of sequencing jobs on parallel processors when jobs have different available times, due dates, penalty costs and waiting costs is considered. The processors are identical and are available when the earliest job becomes available and continuously thereafter. There is a processor cost during the period when the processor is available for processing jobs. The proposed algorithm finds the sequence (or sequences) with minimum total cost (sum of waiting, penalty and processor costs.). A proof of the algorithm and numerical results are given.     

Optimal investment,pricing and replacement of computer resources

The problem of multiple-resource capacity planning under an infinite time horizon is analyzed using a nonlinear programming model. The analysis generalizes to the long term the short-run pricing model for computer networks developed in Kriebel and Mikhail [5]. The environment assumes heterogeneous resource capacities by age (vingate), which service a heterogeneous and relatively captive market of users with known demand functions in each time period. Total variable operating costs are given by a continuous psuedoconcave function of system load, capacity, and resource age. Optimal investment, pricing, and replacement decision rules are derived in the presence of economies of scale and exogenous technological progress. Myopic properties of the decision rules which define natural (finite) planning subhorizons are discussed.     

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.     

An optimum t-test for the scale parameter of an extreme-value distribution

A Student's t-test proposed by Ogawa is considered for the hypothesis Ho: σ=σo against the alternative hypothesis H₁: σ ≠ σo, where σ is the scale parameter of the Extremevalue distribution of smallest values with known location parameter μ. The test is based on a few sample quantiles chosen from a large sample so as to give asymptotically maximum power to the test when the number of sample quantiles is fixed. A table which facilitates the computation of the test statistic is given. Several schemes for determining the ranks of the sample quantiles by the optimal spacings are compared and the effect of the bias of the estimate of σ on the test is investigated through a Monte Carlo study.     

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.     

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.