Differential-game examination of optimal time-sequential fire-support strategies

Optimal time-sequential fire-support strategies are studied through a two-person zero-sum deterministic differential game with closed-loop (or feedback) strategies. Lanchester-type equations of warfare are used in this work. In addition to the max-min principle, the theory of singular extremals is required to solve this prescribed-duration combat problem. The combat is between two heterogeneous forces, each composed of infantry and a supporting weapon system (artillery). In contrast to previous work reported in the literature, the attrition structure of the problem at hand leads to force-level-dependent optimal fire-support strategies with the attacker's optimal fire-support strategy requiring him to sometimes split his artillery fire between enemy infantry and artillery (counterbattery fire). A solution phenomnon not previously encountered in Lanchester-type differential games is that the adjoint variables may be discontinuous across a manifold of discontinuity for both players' strategies. This makes the synthesis of optimal strategies particularly difficult. Numerical examples are given.     

The optimum design of multivariate acceptance sampling plans

A model is developed which may be used to determine the expected total cost of quality control per inspection lot under acceptance sampling by variables where several characteristics are to be simultaneously controlled. Optimization of the model is accomplished through the application of a conventional search procedure. The sensitivity of the model and the optimum solution to the shape of the underlying probability distributions is discussed and associated analyses are presented through an example.     

Expedients for solving some specially structured mixed-integer programs

In this paper we consider dual angular and angular structured mixed integer programs which arise in some practical applications. For these problems we describe efficient methods for generating a desirable set of Benders' cuts with which one may initialize the partitioning scheme of Benders. Our research is motivated by the computational experience of McDaniel and Devine who have shown that the set of Benders' cuts which are binding at the optimum to the linear relaxation of the mixed integer program, play an important role in determining an optimal mixed integer solution. As incidental results in our development, we provide some useful remarks regarding Benders' and Dantzig-Wolfe's decomposition procedures. The computational experience reported seems to support the expedients recommended in this paper.     

Force-annihilation conditions for variable-coefficient lanchester-type equations of modern warfare

This paper develops a mathematical theory for predicting force annihilation from initial conditions without explicitly computing force-level trajectories for deterministic Lanchester-type “square-law” áttrition equations for combat between two homogeneous forces with temporal variations in fire effectivenesses (as expressed by the Lanchester attrition-rate coefficients). It introduces a canonical auxiliary parity-condition problem for the determination of a single parity-condition parameter (“the enemy force equivalent of a friendly force of unit strength”) and new exponential-like general Lanchester functions. Prediction of force annihilation within a fixed finite time would involve the use of tabulations of the quotient of two Lanchester functions. These force-annihilation results provide further information on the mathematical properties of hyperbolic-like general Lanchester functions: in particular, the parity-condition parameter is related to the range of the quotient of two such hyperbolic-like general Lanchester functions. Different parity-condition parameter results and different new exponential-like general Lanchester functions arise from different mathematical forms for the attrition-rate coefficients. This theory is applied to general power attrition-rate coefficients: exact force-annihilation results are obtained when the so-called offset parameter is equal to zero; while upper and lower bounds for the parity-condition parameter are obtained when the offset parameter is positive.     

The cyclic separation scheduling problem

This paper deals with the problem of scheduling items (tasks, employees, equipment, etc.) over a finite time horizon so as to minimize total cost expenditures while maintaining a predefined separation between certain items. The problem is cyclic, because the same schedule will be repeated over several consecutive time periods of equal length. Thus, requirements are present to maintain the separation of items not only within the individual time periods considered, but also between items in adjoining periods. A special purpose branch-and-bound algorithm is developed to solve this scheduling problem by taking advantage of its cyclic nature. Computational results are given.     

气动剥离液滴的附面层分析方法

本文根据附面层理论,对高速气流中的液滴,因气流和液滴表面相互作用而产生的气动剥离现象进行了分析,建立了气液两相附面层耦合问题的理论分析模型,得到了发生气动剥离时的最小气流速度的计算公式,为液体燃料在高速气流申雾化机理研究提供参考。     

Optimizing submarine berthing with a persistence incentive

Submarine berthing plans reserve mooring locations for inbound U.S. Navy nuclear submarines prior to their port entrance. Once in port, submarines may be shifted to different berthing locations to allow them to better receive services they require or to make way for other shifted vessels. However, submarine berth shifting is expensive, labor intensive, and potentially hazardous. This article presents an optimization model for submarine berth planning and demonstrates it with Naval Submarine Base, San Diego. After a berthing plan has been approved and published, changed requests for services, delays, and early arrival of inbound submarines are routine events, requiring frequent revisions. To encourage trust in the planning process, the effect on the solution of revisions in the input is kept small by incorporating a persistence incentive in the optimization model. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 301–318, 1997.     

Minimization of expected variance of completion times on single machine for stochastic jobs

This article deals with the problem of scheduling jobs with random processing times on single machine in order to minimize the expected variance of job completion times. Sufficient conditions for the existence of V-shaped optimal sequences are derived separately for general and ordered job processing times. It is shown that when coefficient of variation of random processing times are bounded by a certain value, an optimal sequence is V-shaped. © 1997 John Wiley & Sons, Inc.     

Compromise allocation in multivariate stratified sampling: An integer solution

The problem of determining the sample sizes in various strata when several characteristics are under study is formulated as a nonlinear multistage decision problem. Dynamic programming is used to obtain an integer solution to the problem. © 1997 John Wiley & Sons, Inc.     

Attrition models of the Ardennes campaign

This paper revisits the modeling by Bracken [3] of the Ardennes campaign of World War II using the Lanchester equations. It revises and extends that analysis in a number of ways: (1) It more accurately fits the model parameters using linear regression; (2) it considers the data from the entire campaign; and (3) it adds in air sortie data. In contrast to previous results, it concludes by showing that neither the Lanchester linear or Lanchester square laws fit the data. A new form of the Lanchester equations emerges with a physical interpretation. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 1–22, 1998