Decision rules for attacking targets of opportunity

Frequently in warfare, a force is required to attack a perishable enemy target system - a target system where the targets are detected seemingly at random, and if not immediately attacked, will shortly escape from detection. A conflicting situation arises when an attack element detects a target of relatively low value and has to decide whether to expend his resources on that particular target or to wait for a more lucrative one, hoping one will be found. This paper provides a decision rule giving the least valued target that should be attacked as well as the resources that should be expended as a function of the attack element's remaining mission time.     

The conjugate gradient technique for certain quadratic network problems

We consider a class of network flow problems with pure quadratic costs and demonstrate that the conjugate gradient technique is highly effective for large-scale versions. It is shown that finding a saddle point for the Lagrangian of an m constraint, n variable network problem requires only the solution of an unconstrained quadratic programming problem with only m variables. It is demonstrated that the number of iterations for the conjugate gradient algorithm is substantially smaller than the number of variables or constraints in the (primal) network problem. Forty quadratic minimum-cost flow problems of various sizes up to 100 nodes are solved. Solution time for the largest problems (4,950 variables and 99 linear constraints) averaged 4 seconds on the CBC Cyber 70 Model 72 computer.     

Multichannel queueing systems with heterogeneous classes of arrivals

In an integrated telecommunications network, voice and data traffic compete for the same transmission facilities. Assuming Poisson arrivals and exponential service with different rates, analytic expressions are obtained for measures of performance such as blocking probability and average delay under the following operating rule: class 1 traffic behaves as a loss system while class 2 traffic is buffered when all channels are busy. In view of the inordinate amount of computational effort needed when the number of channels is large, simple approximations have been suggested.     

The performance of cannibalization policies in a maintenance system with spares,repair, and resource constraints

This article presents the results of comparing the performance of several cannibalization policies using a simulation model of a maintenance system with spares, repair, and resource constraints. Although the presence of cannibalization has been incorporated into a number of maintenance system models reported in the literature, the questions of whether cannibalization should be done and what factors affect canibalization have received little attention. Policies tested include both no cannibalization and unlimited cannibalization as well as other based on the number of maintenance personnel available, the short-term machine failure rate at the time of cannibalization, and the relationship between the mean cannibalization and repair rates. The best policies found are those that allow cannibalization only when it can be done quickly relative to repair or when it can be done without delaying part repair actions. The policy of complete cannibalization (always cannibalize when it is possible) is found to perform poorly except when either average maintenance personnel utilization is very low or when mean cannibalization times are very short relative to mean repair times. The latter result casts doubts on the appropriateness of the assumption of complete cannibalization in many models in the literature.     

A three-echelon,multi-item model for recoverable items

The main objective of this paper is to develop a mathematical model for a particular type of three-echelon inventory system. The proposed model is being used by the Air Force to evaluate inventory investment requirements for alternative logistic structures. The system we will model consists of a group of locations, called bases, and a central depot. The items of concern in our analysis are called recoverable items, that is, items that can be repaired when they fail. Furthermore, each item has a modular or hierarchical design. Briefly, the model is used to determine the stock levels at each location for each item so as to achieve optimum inventory-system performance for a given level of investment. An algorithm for the computation of stock levels for each item and location is developed and illustrated. Some of the ways the model can be used are illustrated with Air Force data.     

Approximation techniques in the solution of queueing problems

In the study of complex queueing systems, analysis techniques aimed al providing exact solutions become ineffective. Approximation techniques provide an attractive alternative in such cases. This paper gives an overview of different types of approximation techniques available in the literature and points out their relative merits. Also, the need for proper validation procedures of approximation techniques is emphasized.     

Nonstationary stochastic gold-mining: A time-sequential tactical-allocation problem

This paper presents an extension of gold-mining problems formulated in earlier work by R. Bellman and J. Kadane. Bellman assumes there are two gold mines labeled A and B, respectively, each with a known initial amount of gold. There is one delicate gold-mining machine which can be used to excavate one mine per day. Associated with mine A is a known constant return rate and a known constant probability of breakdown. There is also a return rate and probability of breakdown for mine B. Bellman solves the problem of finding a sequential decision procedure to maximize the expected amount of gold obtained before breakdown of the machine. Kadane extends the problem by assuming that there are several mines and that there are sequences of constants such that the jth constant for each mine represents the return rate for the jth excavation of that mine. He also assumes that the probability of breakdown during the jth excavation of a mine depends on j. We extend these results by assuming that the return rates are random variables with known joint distribution and by allowing the probability of breakdown to be a function of previous observations on the return rates. We show that under certain regularity conditions on the joint distributions of the random variables, the optimal policy is: at each stage always select a mine which has maximal conditional expected return per unit risk. This gold-mining problem is also a formulation of the problem of time-sequential tactical allocation of bombers to targets. Several examples illustrating these results are presented.     

The search for an intelligent evader: Strategies for searcher and evader in the two-region problem

This paper considers the search for an evader concealed in one of two regions, each of which is characterized by its detection probability. The single-sided problem, in which the searcher is told the probability of the evader being located in a particular region, has been examined previously. We shall be concerned with the double-sided problem in which the evader chooses this probability secretly, although he may not subsequently move: his optimal strategy consists of that probability distribution which maximizes the expected time to detection, while the searcher's optimal strategy is the sequence of searches which limits the evader to this expected time. It transpires for this problem that optimal strategies for both searcher and evader may generally be obtained to a surprisingly good degree of approximation by using the optimal strategies for the closely related (but far more easily solved) problem in which the evader is completely free to move between searches.     

A note on the limitations of goal programming as observed in resource allocation for marine environmental protection

After first formulating the problem of the Marine Environmental Protection program of the Coast Guard as a multiple-objective linear program, we investigate the applicability and limitations of goal programming. We point out how the preemptive goal-programming approach is incompatible with utility preferences. Then we observe the tendency of optimal solutions for standard linear goal programs to occur at extreme points. We also note problems of more general approaches, such as dealing with additively separable approximations to preferences.