Asymptotic normality of the estimated optimal order quantity for one-period inventories with supply uncertainty

A one-period inventory situation where the supply is an NBUE random variable with mean proportional to the quantity ordered has been considered. The optimal exponential order quantity, which maximizes the minimum profit obtainable in the NBUE class of supply distributions, is a function of the demand distribution function. Here we show that an estimator of the maximin order quantity, which is already known to converge almost surely to its true value, converges also in distribution to an appropriate normal law with increasing sample size.     

The discrete evasion game with three-move lag

The discrete evasion game with three-move lag, formulated over 30 years ago, was one of the earliest games with time-lag complications. This game remains unsolved even though it is well known that the game has a value. In this article we obtain an upper bound for the value by constructing a strategy which consists of 400 conditional probabilities for the minimizing player. This is believed to be the best upper bound known.     

A new method to solve steady state queueing equations

There are a great number of queueing systems, including the M^X/M^Y/c, the Gl^X/M/c and the discrete Gl/G/1 queue in which the state probabilities are determined by repeated queue equations. This paper gives a simple, efficient and numerically stable algorithm to caiculate the state probabilities and measure of performance for such systems. The method avoids both complex arithmetric and matrix manipulations.     

A two-phase procedure for allotting geostationary orbital locations to communications satellites

We consider the problem of allotting locations in the geostationary orbit to communication satellites, subject to angle of elevation and electromagnetic interference constraints. An optimization framework is used as a means of finding feasible allotment plans. Specifically, we present a two-phase solution procedure for the satellite location problem (SLP). The objective in SLP is to allot geostationary orbital locations to satellites so as to minimize the sum of the absolute differences between the locations prescribed for the satellites and corresponding specified desired locations. We describe two heuristics, an ordering procedure and a k-permutation algorithm, that are used in tandem to find solutions to SLP. Solutions to a worldwide example problem with 183 satellites serving 208 service areas are summarized.