Layered defense of deceptively based ICBMs

The basing of ICBMs is a fundamental problem of defense analysis. Deceptive basing and antiballistic missile defense are two of the methods available to attempt to insure that there are ICBMs surviving after undergoing an attack. This article treats tradeoffs among missiles, silos or shelters, exoatmospheric interceptors, and endoatmospheric interceptors. Most of the analysis deals with 200 missiles, the number of MX missiles which were recommended to be moved among the 4600 shelters of the Multiple Protective Shelter (MPS) deployment, though some variants in the number of missiles (from 115 to 400) are also treated here. The basic reference point of the analysis is the provision of 1000 ICBM warheads delivered in a second strike. The combination of exoatmospheric interceptors and endoatmospheric interceptors is referred to as “layered defense.” Warheads are destroyed by interceptors after the warheads separate from the missile which carries them. Exoatmospheric interceptors are assumed to achieve a non-nuclear kill, while endoatmospheric interceptors are assumed to achieve either a non-nuclear or nuclear kill, depending on the technology available to both sides. Exoatmospheric interceptors may be capable of protecting value targets against the warheads of a second strike. To the extent that this can be achieved, they facilitate a first strike with relative impunity and hence are destabilizing. This article explores various layered defense topics.     

Statistical decision analysis of stochastic linear programming problems

This paper presents a statistical decision analysis of a one-stage linear programming problem with deterministic constraints and stochastic criterion function. Procedures for obtaining numerical results are given which are applicable to any problem having this general form. We begin by stating the statistical decision problems to be considered, and then discuss the expected value of perfect information and the expected value of sample information. In obtaining these quantities, use is made of the distribution of the optimal value of the linear programming problem with stochastic criterion function, and so we discuss Monte Carlo and numerical integration procedures for estimating the mean of this distribution. The case in which the random criterion vector has a multivariate Normal distribution is discussed separately, and more detailed methods are offered. We discuss dual problems, including some relationships of this work with other work in probabilistic linear programming. An example is given in Appendix A showing application of the methods to a sample problem. In Appendix B we consider the accuracy of a procedure for approximating the expected value of information.     

Optimal staffing in nonstationary service centers with constraints

This paper considers optimal staffing in service centers. We construct models for profit and cost centers using dynamic rate queues. To allow for practical optimal controls, we approximate the queueing process using a Gaussian random variable with equal mean and variance. We then appeal to the Pontryagin's maximum principle to derive a closed form square root staffing (SRS) rule for optimal staffing. Unlike most traditional SRS formulas, the main parameter in our formula is not the probability of delay but rather a cost‐to‐benefit ratio that depends on the shadow price. We show that the delay experienced by customers can be interpreted in terms of this ratio. Throughout the article, we provide theoretical support of our analysis and conduct extensive numerical experiments to reinforce our findings. To this end, various scenarios are considered to evaluate the change in the staffing levels as the cost‐to‐benefit ratio changes. We also assess the change in the service grade and the effects of a service‐level agreement constraint. Our analysis indicates that the variation in the ratio of customer abandonment over service rate particularly influences staffing levels and can lead to drastically different policies between profit and cost service centers. Our main contribution is the introduction of new analysis and managerial insights into the nonstationary optimal staffing of service centers, especially when the objective is to maximize profitability. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 615–630, 2017     

The political command and control of nuclear forces

“Even more than in 1914, governments in our own day are likely to be ignorant of the technical detail of war and the tactical measures that can or cannot (or, more important, must or must not) be taken in various specialized situations. In peacetime the study and preparation of these measures will be relegated to military staffs as being narrow and technical. Today, .... it is almost impossible to get people interested in the tactics and strategy of thermonuclear war. It is now believed that only the prewar moves are of interest, and even those are not too important because deterrence is supposed to be so close to 'automatic'.” Herman Kahn (1960).