Optimal control for entry of many classes of customers to an M/M/1 queue

A method is developed for determining the optimal policy for entry of customers from many independent classes of Poisson arrivals to a first-come, first-serve (for customers admitted to the queue) single-server queue with exponential service times. The solution technique utilizes a semi-Markov formulation or the decision problem.     

Production planning for multi-resource network systems

Production planning for large-scale production systems requiring the allocation of numerous resources is considered. It is demonstrated how the dynamic activity analysis developed by Shephard leads to linear programming solutions of production planning problems. Three types of planning problems are formulated: maximization of output levels for a given time horizon; minimization of production duration for given output histories; and minimization of production costs for given output histories.     

Missile Strategy in a Post-Nuclear Age

While the arrival of nuclear weapons coincided roughly with the development of short, medium, intermediate, and eventually intercontinental missiles, the contribution of missile technology to the deterrence equation is often lost. If nuclear weapons were eliminated, even new generation missiles with conventional payloads could struggle to render effective deterrence. But some of the physical and psychological effects commonly ascribed to nuclear weapons could still be in play. And in a world without nuclear weapons, thinking about the use and control of force from the nuclear age would also deserve renewed attention.     

Covariance of weibull order statistics

Let X₁ < X₂ <… < X_n denote an ordered sample of size n from a Weibull population with cdf F(x) = 1 - exp (?x^p), x > 0. Formulae for computing Cov (X_i, X_j) are well known, but they are difficult to use in practice. A simple approximation to Cov(X_i, X_j) is presented here, and its accuracy is discussed.     

A computation procedure for the exact solution of location-allocation problems with rectangular distances

A method is presented to locate and allocate p new facilities in relation to n existing facilities. Each of the n existing facilities has a requirement flow which must be supplied by the new facilities. Rectangular distances are assumed to exist between all facilities. The algorithm proceeds in two stages. In the first stage a set of all possible optimal new facility locations is determined by a set reduction algorithm. The resultant problem is shown to be equivalent to finding the p-median of a weighted connected graph. In the second stage the optimal locations and allocations are obtained by using a technique for solving the p-median problem.     

Sequential bid selection by stochastic approximation

Suppose that a contractor is faced with a sequence of “minimum bid wins contract” competitions. Assuming that a contractor knows his cost to fulfill the contract at each competition and that competitors are merely informed whether or not they have won, bids may be selected sequentially via a tailored stochastic approximation procedure. The efficacy of this approach in certain bidding environments is investigated.