The two-on-one stochastic duel

The one-on-one stochastic duel is extended to the general two-on-one duel for the first time. The state equations, win probabilities, mean value, and variance functions are derived. The case where one side has Erlang (2) firing times and the other is negative exponential is compared with the corresponding “Stochastic Lanchester” and Lanchester models to demonstrate their nonequivalence.     

An efficient heuristic for large set covering problems

A heuristic solution procedure for set covering is presented that works well for large, relatively dense problems. In addition, a confidence interval is established about the unknown global optimum. Results are presented for 30 large randomly generated problems.     

Simulation of nonhomogeneous poisson processes by thinning

A simple and relatively efficient method for simulating one-dimensional and two-dimensional nonhomogeneous Poisson processes is presented The method is applicable for any rate function and is based on controlled deletion of points in a Poisson process whose rate function dominates the given rate function In its simplest implementation, the method obviates the need for numerical integration of the rate function, for ordering of points, and for generation of Poisson variates.     

A single server queue with arrival rate dependent on server breakdowns

This paper considers a single server queueing system that alternates stochastically between two states: operational and failed. When operational, the system functions as an M/E_k/1 queue. When the system is failed, no service takes place but customers continue to arrive according to a Poisson process; however, the arrival rate is different from that when the system is operational. The durations of the operating and failed periods are exponential with mean 1/cβ and Erlang with mean 1/cβ, respectively. Generating functions are used to derive the steady-state quantities L and W, both of which, when viewed as functions of c, decrease at a rate inversely proportional to c². The paper includes an analysis of several special and extreme cases and an application to a production-storage system.     

Damage calculations for unreliable warheads

For large numbers of perfectly reliable, optimally targeted warheads the square-root law approximates the expected fraction damage achieved on an area target. In this paper a more exact expression is derived for this damage fraction which Holds for all numbers of warheads. This expression is shown to converge to the square-root law when a large number of warheads are fired. The more exact expression is used in a procedure to calculate expected damage when warheads are unreliable, and this procedure is shown to be superior to a modified square-root approximation which has been used previously.     

A note on eoq under fund constraints

An algorithm is developed to modify the Wilson Q to account for a short-term expenditure constraint over a catalog of items. Representative results are shown and generalizations made.     

The optimum design of multivariate acceptance sampling plans

A model is developed which may be used to determine the expected total cost of quality control per inspection lot under acceptance sampling by variables where several characteristics are to be simultaneously controlled. Optimization of the model is accomplished through the application of a conventional search procedure. The sensitivity of the model and the optimum solution to the shape of the underlying probability distributions is discussed and associated analyses are presented through an example.     

Optimal selection from a random sequence with observation errors

A form of sequential decision problem is introduced in which options are presented in sequence. with no recall of rejected options (as in the secretary problem), but in which the value of each option may only he inferred from experiments. Decisions have thus to be made concerning both the acceptance and rejection of each option and the degree of experimentation. General properties of the optimal policy are derived, and an algorithm is obtained for the solution in a special case. This special case suggests a heuristic rule for more general situations. the performance of which rule has been investigated by a Monte Carlo study.     

Bounds and elimination in generalized markov decisions

In discounted Markov decision processes bounds on the optimal value function can be computed and used to eliminate suboptimal actions. In this paper we extend these procedures to the generalized Markov decision process. In so doing we forfeit the contraction property and must base our analysis on other procedures. Duality theory and the Perron-Frobenius theorem are the main tools.     

Maximal nash subsets for bimatrix games

In this work maximal Nash subsets are studied in order to show that the set of equilibrium points of a bimatrix game is the finite union of all such subsets. In addition, the extreme points of maximal Nash subsets are characterized in terms of square submatrices of the payoff matrices and dimension relations are derived.