Armor configurations via dynamic programming

The problem of selecting materials, their thicknesses and order for armor designed for the defeat of shaped charge threats, has been formulated as a constrained optimization problem. The mathematical model provides an optimal order and thickness of each layer of material such that the resulting armor configuration will be of minimum mass per unit area subject to constraints on total thickness and shaped charge jet tip exit velocity.     

Minimal disconnecting sets in directed multi-commodity networks

The problem of finding minimal disconnecting sets for multi-commodity directed networks may be solved using an arc-path formulation and Gomory's all-integer integer programming algorithm. However, the number of network constraints may be astronomical for even moderately sized networks. This paper develops a finite algorithm similar to Gomory's, but requiring no more than m rows in the tableau, where m is the number of arcs in the network.     

Expectation of contract incentives

The application of statistical expectation to risk density functions and fee/incentive-element relationships is shown to be useful in structuring contract incentives. A mathematical procedure for calculating the expected value of fee for a given risk/incentive arrangement is described along with cost examples and related sensitivity analyses. The structuring of equivalent incentives is demonstrated by the use of the contracting procedure used for procuring the C-5A aircraft.     

Optimal multicommodity network flows with resource allocation

The problem of determining multicommodity flows over a capacitated network subject to resource constraints may be solved by linear programming; however, the number of potential vectors in most applications is such that the standard arc-chain formulation becomes impractical. This paper describes an approach—an extension of the column generation technique used in the multicommodity network flow problem—that simultaneously considers network chain selection and resource allocation, thus making the problem both manageable and optimal. The flow attained is constrained by resource availability and network capacity. A minimum-cost formulation is described and an extension to permit the substitution of resources is developed. Computational experience with the model is discussed.     

A combined approach to solve binary multicriteria problems

An implicit enumeration algorithm is developed to determine the set of efficient points in zero-one multiple criteria problems. The algorithm is specialized for the solution of a particular class of facility location problems. The procedure is complemented with the use of the utility function of the decision maker to identify a subset of efficient point candidates for the final selection. Computational results are provided and discussed.     

An alternative proof of the IFRA property of some shock models

Let , where A (t)/t is nondecreasing in t, {P(k)^1/k} is nonincreasing. It is known that H(t) = 1 — H (t) is an increasing failure rate on the average (IFRA) distribution. A proof based on the IFRA closure theorem is given. H(t) is the distribution of life for systems undergoing shocks occurring according to a Poisson process where P (k) is the probability that the system survives k shocks. The proof given herein shows there is an underlying connection between such models and monotone systems of independent components that explains the IFRA life distribution occurring in both models.     

On a search for a moving target

We consider the problem of searching for a target that moves in discrete time and space according to some Markovian process. At each time, a searcher attempts to detect the target. If the searcher's action at each time is such as to maximize his chances of immediate detection, we call his strategy “myopic.” We provide a computationally useful necessary condition for optimality, and use it to provide an example wherein the myopic strategy is not optimal.     

On the equivalence between the Node-ARC and ARC-Chain formulations for the multi-commodity maximal flow problem

The purpose of this article is to formulate the multi-commodity maximal flow problem into a node-arc form and to show that when decomposition is applied to this form the resulting master and subproblems become precisely those described by Ford & Fulkerson [3] using the arc-chain formulation. A generalization to the problem is then considered which can potentially speed its convergence.     

A linear programming model for minimum-cost procurement and operation of marine corps training aircraft

In military situations of sharply increasing combat activity the Marine Corps is faced with training problems in its expanding aviator corps. Additional training aircraft are required, and procurement decisions must be made. In view of the significant costs involved in procurement and operation of new high performance aircraft, it is very desirable to buy and operate an efficient mix of aircraft necessary for training the pilots to make the Marine Aircraft Wings essentially 100-percent tactically qualified. The mathematical model presented here enables computation of a least-cost mix of training aircraft which satisfies certain specified training requirements. The basic element allowing tradeoffs is the commonality of training available in the F4, RF4, A6, and EA6 types of aircraft. Both airframe oriented and mission oriented training are necessary, but the airframe oriented training can be conducted in either of the aircraft possessing the commonality. Training requirements over a five year period are considered, and the mix of training aircraft has the minimum five year procurement and operating cost.