Minimum-cost mixtures of area and point defenses assuming simultaneous attack

It is desired to select numbers of area and point interceptors that minimize the cost of such defensive missiles under the condition that the maximum total expected damage produced by an unknown number of attacking missiles A be bounded above by a given function of A. Area coverages may overlap. The attacker is assumed to know the numbers of area and point interceptors and to launch a simultaneous attack (of arbitrary size A) against all targets, which is optimal against the given defenses. The defender is assumed to observe the attack and then allocate his area and point interceptors against attacking missiles so as to minimize the total expected damage. Upper and lower bounds on the minimal cost are obtained by solving integer programming problems.     

Algorithmic insights and a convergence analysis for a Karmarkar-type of algorithm for linear programming problems

This paper is concerned with a modification of a recently proposed variant of Karmarkar's algorithm for solving linear programming problems. In analyzing this variant, we exhibit interesting and useful relationships of these types of algorithms with barrier function methods, and subgradient optimization procedures involving space dilation techniques, which subsume the well-known ellipsoidal type of algorithms. Convergence of this variant is established under certain regularity conditions. We also provide remarks on how to obtain dual variables or Lagrange multipliers at optimality.     

Confidence coefficient of approximate two-sided confidence intervals for the binomial probability

The confidence coefficient of a two-sided confidence interval for the binomial parameter p is the infimum of the coverage probability of the interval as p ranges between 0 and 1. The confidence coefficients for five different approximate confidence intervals are computed and compared to the confidence coefficient for the two-sided Clopper-Pearson confidence interval. Pratt's approximation method [10] yields virtually the same confidence coefficients as the Clopper-Pearson interval, and is easily computed without resorting to interative methods.     

Estimating the probability of a diffusing target encountering a stationary sensor

The problem addressed is that of estimating the probability of a moving particle (called the target) avoiding detection by a stationary sensor to time t. The target follows a diffusion path and is constrained to remain within a square region R. The detecting sensor is fixed at the center of A. Two expressions for this probability are given. The first results from an approximation to the exact solution of the diffusion equation and the second from experimentation with a Monte Carlo simulation of the diffusion process.     

Algorithms and heuristics for variable-yield lot sizing

We consider the multiperiod lot-sizing problem in which the production yield (the proportion of usable goods) is variable according to a known probability distribution. We review two economic order quantity (EOQ) models for the stationary demand continuous-time problem and derive an EOQ model when the production yield follows a binomial distribution and backlogging of demand is permitted. A dynamic programming algorithm for an arbitrary sequence of demand requirements is presented. Heuristics based on both the EOQ model and appropriate modification of the underlying perfect-yield lot-sizing policies are discussed, and extensive computational evaluation of these heuristics is presented. Two of these heuristics are then modified to include the notion of supply safety stock. The modified heuristics consistently produce near-optimal lot-sizing policies for problems with stationary and time-varying demands.     

Waiting-time distributions for bulk arrival,bulk service queues with vehicle-holding and cancellation strategies

Procedures are developed for numerically calculating the waiting-time distribution for bulk arrival, bulk service queues operated under a vehicle-cancellation or a vehicle-holding strategy, as well as for queues where vehicles depart regardless of the length of the queue. Experiments indicate that the mean and variance of the calculated distribution agree very closely with analytical expressions obtained from transforms. The results can be used to study the service reliability of different dispatching strategies. Alternatively, the results may be used to evaluate simpler approximations for the higher moments.