A stochastic constrained optimal replacement model

In this paper a stochastically constrained replacement model is formulated. This model determines a sequence of replacement dates such that the total “current account” cost of all future costs and capital expenditures over an infinite time horizon for the n initial incumbent machines is minimized subject to the constraints that an expected number of machines are in a chosen utility class at any point in time. We then indicate one possible solution method for the model.     

Pursuit around a hole

The solution of isaacs¹ problem of optimal pursuit in a plane with a circular disk removed, given constant speeds, zero turning radius, and perfect visibility for both players is presented herein. The hole has three effects: the trivial effect that shortest paths are not straight, the trapping effect to turn the evader from running into the hole, and the screening effect causing an evader retreating behind the hole not to retreat across a line through its center.     

Programming the procurement of airlift and sealift forces: A linear programming model for analysis of the least-cost mix of strategic deployment systems

A linear programming model for analyzing the strategic deployment mix of airlift and sealift forces and prepositioning to accomplish the composite requirements of a set of possible contingencies is described in this paper. It solves for the least-cost mix of deployment means capable of meeting any one of a spectrum of contingencies, or meeting simultaneous contingencies. The model was developed by RAC as part of the U.S. Army's study program and has been used in analyses of deployment systems conducted in support of the U.S. Army, the Joint Chiefs of Staff and the Office of the Secretary of Defense. Results of analyses have influenced the preparation of long-range plans as well as the formulation of the FY67 Department of Defense budget. The paper gives the background and assumptions of the model, describes the model by means of a simple hypothetical example followed by a selected subset of a complete version, and discusses how the model is used.     

Attack and defense of ICBMs deceptively based in a number of identical areas

On-site verification of ICBMs in the context of an arms control agreement might involve a situation where an inspector would choose one or more of a number of identical areas to inspect and would have confidence that the other areas had the same characteristics. This article considers optimal attack and defense of missiles deceptively based in a number of identical areas. The attacker may allocate warheads across areas as he desires and uniformly within areas. The defender may allocate interceptors across areas as he desires and either uniformly or preferentially within areas. The effect of restricting the defender to uniform allocation across areas is explored for various assumptions. Robustness of surviving missiles with respect to the number of attacking warheads is studied. Results are presented for a wide range of cases.     

Additive utilities with finite sets: Applications in the management sciences

A theory of additive utilities is discussed for cases where the set X, on which an individual's preference-indifference relation is defined, is a subset of the Cartesian product of n finite sets. A number of potential applications of additive utilities in decision making are presented.