Application of the GLM technique to a production planning problem

Generalized Lagrange Multipliers (GLM) are used to develop an algorithm for a type of multiproduct single period production planning problem which involves discontinuities of the fixed charge variety. Several properties of the GLM technique are developed for this class of problems and from these properties an algorithm is obtained. The problem of resolving the gaps which are exposed by the GLM procedure is considered, and an example involving a quadratic cost function is explored in detail.     

Operations analysis during the underwater search for Scorpions

This paper discusses the operations analysis in the underwater search for the remains of the submarine Scorpion The a priori target location probability distribution for the search was obtained by monte-carlo procedures based upon nine different scenarios concerning the Scorpion loss and associated credibility weights. These scenarios and weights were postulated by others. Scorpion was found within 260 yards of the search grid cell having the largest a priori probability Frequent computations of local effectiveness probabilities (LEPs) were carried out on scene during the search and were used to determine an updated (a posteriori) target location distribution. This distribution formed the basis for recommendation of the current high probability areas for search The sum of LEPs weighted by the a priori target location probabilities is called search effectiveness probability (SEP) and was used as the overall measure of effectiveness for the operation. SEP and LEPs were used previously in the Mediterranean H-bomb search On-scene and stateside operations analysis are discussed and the progress of the search is indicated by values of SEP for various periods during the operation.     

Optimal control of multi-channel service systems

D. P. Heyman, M. Sobel, and M. J. Magazine among others have shown existence of an optimal policy for control of single server queuing systems. For queues under periodic review existence of an analogous rule is established for multi-server systems. Formulation as a dynamic programming problem is given and proofs for existence are presented for finite horizon, infinite horizon and average cost criteria.     

A note on adaptive boiler tube pulling

This paper develops an adaptive algorithm for determining boiler tube pulling strategies by postulating a Beta prior on the probability that an individual tube is defective. This prior is updated according to Bayes' Rule as a result of the sample obtained during the tube pulling process.     

A note on a comparison of confidence interval techniques in truncated life tests

Several approximate procedures are available in the literature for obtaining confidence intervals for the parameter A of an exponential distribution based on time truncated samples. This paper contains the results of an empirical study comparing three of these procedures.     

Differential game theoretic analysis of a problem of warfare

The present article considers a problem of missile warfare. It is formulated as a problem of economics and treated as a differential game. Some optimal strategies of targeting and firing of missiles are derived. Conditions under which such a war can be prevented are also developed.     

A test for the hypothesis that two extreme-value scale parameters are equal

A statistic is determined for testing the hypothesis of equality for scale parameters from two populations, each of which has the first asymptotic distribution of smallest (extreme) values. The probability distribution is derived for this statistic, and critical values are determined and given in tabular form for a one-sided or two-sided alternative, for censored samples of size n₁ and n₂, n₁ = 2, 3, …. 6, n₂ = 2, 3, …. 6. The power function of the test for certain alternatives is also calculated and listed in each case considered.     

On a new approach to the analysis of stationary inventory problems

The intent of this paper is to demonstrate that the theory of stationary point processes is a useful tool for the analysis of stationary inventory systems. In conventional inventory theory, the equilibrium distributions for a specified inventory policy are obtained, whenever possible, by recursive or limiting procedures, or both. A different and more direct approach, based on stationary point processes, is proposed here. The time instants at which stock delivery is effected are viewed as points of the stationary point process, which possesses uniform statistical properties on the entire real axis; hence the equilibrium statistics of the inventory process can be calculated directly. In order to best illustrate this approach, various examples are given, including some that constitute new results.     

A note on cycling in the simplex method

Although cycling in the simplex method has long been known, a number of theoretical questions concerning cycling have not been fully answered. One of these, stated in [3], is to find the smallest example of cycling, and Beale's example with three equations and seven variables is conjectured to be the smallest one. The exact bounds on dimensions of cycling examples are established in this paper. We show that Beale's example is the smallest one which cycles at a non-optimal solution, that a smaller one can cycle at the optimum, and that, in general (including the completely degenerate case), a cycling example must have at least two equations, at least six variables, and at least three non-basic variables. Examples and geometries are given for the extreme cases, showing that the bounds are sharp.     

Vessel allocation by linear programming

This paper presents a linear programming model of a fleet of vessels which is required to transport quantities of cargo, such as coal, iron ore, limestone, and salt from certain producing ports to specific destination ports. This model has been implemented and is currently being used both for planning purposes and as an aid in scheduling the trips to be made by each vessel.