Optimization of strategic defenses to provide specified post-attack production capacities

This paper presents a model for choosing a minimum-cost mix of strategic defenses to assure that specified production capacities for several economic sectors survive after a nuclear attack. The defender selects a mix of strategic defenses for each of several geographic regions. The attacker chooses an allocation of attacking weapons to geographic regions, within specified weapon inventories. The attack is optimized against any economic sector. This formulation allows the defense planner the capability to assess the results of the optimal defense structure for a “worst case” attack. The model is a mathematical program with nonlinear programming problems in the constraints; an example of its application is given and is solved using recently developed optimization techniques.     

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.     

Allocation of carrier-based attack aircraft using non-linear programming

The paper presents the formulation and several solutions of a model for allocating a fixed number of aircraft to carriers and to missions. The amount of damage that can be inflicted is maximized. A nonseparable concave nonlinear objective function expresses diminishing marginal damage. Linear constraints on aireraft, carrier space, and aircraft availability for missions are included. The model is solved using the sequential unconstrained minimization technique (SUMT). The model is presented in terms of a scenario. Several different exponential damage functions are treated, and S-shaped damage functions are discussed.     

Minimizing reductions in readiness caused by time-phased decreases in aircraft overhaul and repair activities

The Navy is often required to conduct personnel planning studies, A recent study on the assessment of effects of personnel reductions at the various aircraft Overhaul and Repair Activities (O & Rs) of the Bureau of Naval Weapons was carried out by one of the writers of the present paper. The methodology was systematic but relied on informal, judgmental decision procedures rather than on formal models incorporating optimization. Later study of the problem resulted in the approach described herein. The paper addresses this question: How can a personnel reduction in the Navy's aircraft O & Rs be distributed among activities with minimum reduction in readiness? A two-stage procedure involving linear programming models is developed. Solutions involve either extensions of aircraft overhaul cycles or a combination of such extensions with reductions in aircraft inventories.     

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.     

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