On some stocxastic tactical antisubmarine games

Mathematical models of tactical problems in Hntisubmarine Warfare (ASW) are developed. Specifically, a game of pursuit between a hunter-killer force. player 1, and a possible submarine, player 2 is considered. The game consists of a sequence of moves and terminates when player 2 is tcaught or evades player 1. When the players move they observe the actual tactical configuration of the forces (state) and each player choosa-s a tactical plan from a finite collection. This joint choice of tactical plans determines an immediate payoff and a transition probability distribution over the states. Hence an expected payoff function is defined, Formally this game is a Terminating Stochastic Game (TSG). Shapley demonstrated the existence of a value and optimal strategies (solution), An iterative technique to approximate the solution to within desired accuracy is proposed. Each iteration of the technique is obtained by solving a set of linear programs. To introduce more realism into the game several variations of the TSG are also considered. One variation is a finite TSG and linear programming techniques are employed to find the solution.     

Pseudo-monotonic interval programming

A pseudo-monotonic interval program is a problem of maximizing f(x) subject to x ε X = {x ε Rⁿ | a < Ax < b, a, b ε R^m} where f is a pseudomonotonic function on X, the set defined by the linear interval constraints. In this paper, an algorithm to solve the above program is proposed. The algorithm is based on solving a finite number of linear interval programs whose solutions techniques are well known. These optimal solutions then yield an optimal solution of the proposed pseudo-monotonic interval program.     

Refined prediction for linear regression models

Adequate prediction of a response variable using a multiple linear regression model is shown in this article to be related to the presence of multicollinearities among the predictor variables. If strong multicollinearities are present in the data, this information can be used to determine when prediction is likely to be accurate. A region of prediction, R, is proposed as a guide for prediction purposes. This region is related to a prediction interval when the matrix of predictor variables is of full column rank, but it can also be used when the sample is undersized. The Gorman-Toman ten-variable data is used to illustrate the effectiveness of the region R.     

Evaluation of force structures under uncertainty

A model, for assessing the effectiveness of alternative force structures in an uncertain future conflict, is presented and exemplified. The methodology is appropriate to forces (e.g., the attack submarine force) where alternative unit types may be employed, albeit at differing effectiveness, in the same set of missions. Procurement trade-offs, and in particular the desirability of special purpose units in place of some (presumably more expensive) general purpose units, can be addressed by this model. Example calculations indicate an increase in the effectiveness of a force composed of general purpose units, relative to various mixed forces, with increase in the uncertainty regarding future conflicts.     

Sequencing n jobs on two machines with setup,processing and removal times separated

The paper extends the machine flow-shop scheduling problem by separating processing time into setup, processing and removal times.