“simple-approximate” battle-outcome-prediction conditions for variable-coefficient lanchester-type equations of modern warfare

This article considers combat between two homogeneous forces modeled by variable- coefficient Lanchester-type equations of modern warfare and develops new “simple-approximate” battle-outcome-prediction conditions for military engagements terminated by two different types of prescribed conditions being met (fixed-force-level-breakpoint battles and fixed-force-ratio-breakpoint battles). These battle-outcome-prediction conditions are sufficient (but not necessary) to determine the outcome of battle without having to explicitly compute the force-level trajectories, and they are characterized by their simplicity, requiring no advanced mathematical knowledge or tabulations of “special functions” for their application. Integrability properties of the Lanchester attrition-rate coefficients figure prominently in their results, and involved in their development is a generalization of Lanchester's famous square law to variable-coefficient Lanchester-type combat and several other novel mathematical developments for the analysis of ordinary differential equations. Examples are given, with the attack of a mobile force against a static defensive position (both sides armed with weapons whose firepower is range dependent) being examined in detail.     

A new kind of fictitious play

Gass, Zafra, and Qiu (1996) introduce a modified version of fictitious play for matrix games where only the more successful player's strategy is retained. This paper introduces additional modifications that appear to converge faster. © 2001 John Wiley & Sons, Inc.* Naval Research Logistics 48: 270–280, 2001     

Attrition through a partially coordinated area defense

An area defense consists of several groups that act independently, i.e., do not communicate with each other. Each group has a fixed number of defenders and a controller that allocates these defenders optimally against the individual attackers comprising an attack. We analyze the effectiveness of this partially coordinated defense against a simultaneous attack of known size in which all attackers are considered to be equally lethal. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Weakest‐link attacker‐defender games with multiple attack technologies

In this article, we examine a model of terrorism that focuses on the tradeoffs facing a terrorist organization that has two qualitatively different attack modes at its disposal. The terrorist organization's objective is to successfully attack at least one target. Success for the target government is defined as defending all targets from any and all attacks. In this context, we examine how terrorist entities strategically utilize an efficient but discrete attack technology — e.g., suicide attacks — when a more conventional mode of attack is available, and the optimal anti‐terrorism measures.© 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

The multivariate Polya distribution in combat modeling

This paper investigates the multivariate Polya distribution (MPD) for application in combat models for which enemy targets must be randomly assigned to fighting units. Six sets of actual combat data motivate the allocation model. Scenarios include air‐to‐air combat, tank, and submarine warfare. Goodness of fit tests are derived which verify the validity of the MPD, and reinforce the notion that multinomial allocation is too simplistic for such combat models. Simulations to determine optimal allocations for minimal combat cost are applied in order to illustrate the role of the MPD in combat modeling. © 2001 John Wiley & Sons,Inc. Naval Research Logistics 48: 1–17, 2001     

An interactive procedure for selecting acceptable alternatives in the presence of multiple criteria

In this paper, we consider the multiple criteria decision‐making problem of partitioning alternatives into acceptable and unacceptable sets. We develop interactive procedures for the cases when the underlying utility function of the decision maker is linear, quasiconcave, and general monotone. We present an application of the procedures to the problem of admitting students to the master's degree program at the Industrial Engineering Department, Middle East Technical University. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 592–606, 2001.     

Attrition modeling in the presence of decoys: An operations-other-than-war motivation

Under various operational conditions, in particular in operations other than war (OOTW) or peacekeeping, an intervening force, here Blue, must occasionally engage in attrition warfare with an opposing force, here Red, that is intermingled with noncombatants. Desirably, Red armed actives are targeted, and not the unarmed noncombatants. This article describes some simple Lanchesterian attrition models that reflect a certain capacity of Blue to discriminate noncombatants from armed and active Red opponents. An explicit extension of the Lanchester square law results: Blue's abstinence concerning the indiscriminate shooting of civilians mixed with Red's is essentially reflected in a lower Blue rate of fire and less advantageous exchange rate. The model applies to other situations involving decoys, and reflects the value of a discrimination capability. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44 : 507–514, 1997     

导航对抗技术分析

从信息对抗的角度来看,导航战是指对立双方为争夺导航信息的控制权而展开的斗争。从进攻与防御两方面探讨了导航战对相关技术的需求。     

A chessboard model of the U‐boat war in the Atlantic with applications to signals intelligence

This paper uses a simple Monte Carlo model to analyze the influence of signals intelligence on the Second World War's Battle of the Atlantic. The principle measure of effectiveness is the number of U‐boat days of attack to which convoys were subjected. A secondary measure is the number of convoyed ships sunk. The model is validated against historical data and then used to explore the effectiveness of the two sides' signals intelligence. Allied use of signals intelligence is shown to have been capable of completely offsetting German use of signals intelligence, and then some. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Commitment decisions with partial information updating

In this paper, we extend the results of Ferguson M. Naval Research Logistics 8 . on an end‐product manufacturer's choice of when to commit to an order quantity from its parts supplier. During the supplier's lead‐time, information arrives about end‐product demand. This information reduces some of the forecast uncertainty. While the supplier must choose its production quantity of parts based on the original forecast, the manufacturer can wait to place its order from the supplier after observing the information update. We find that a manufacturer is sometimes better off with a contract requiring an early commitment to its order quantity, before the supplier commits resources. On the other hand, the supplier sometimes prefers a delayed commitment. The preferences depend upon the amount of demand uncertainty resolved by the information as well as which member of the supply chain sets the exchange price. We also show conditions where demand information updating is detrimental to both the manufacturer and the supplier. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

An engagement model to optimize defense against a multiple attack assuming perfect kill assessment

We present an air-defense engagement model to counter an attack by multiple antiship missiles, assuming perfect kill assessment. In this model, the probability of shooting down all incoming missiles is maximized. A generating function is employed to produce an algorithm which is used to evaluate the outcomes. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 687–697, 1997     

When is model complexity too much? Illustrating the benefits of simple models with Hughes' salvo equations

The simulations that many defense analysts rely upon in their studies continue to grow in size and complexity. This paper contrasts the guidance that the authors have received—from some of the giants of military operations research—with the current practice. In particular, the analytic utility of Hughes' simple salvo equations is compared with that of the complex Joint Warfighting System (JWARS), with respect to JWARS' key performance parameters. The comparison suggests that a family of analytic tools supports the best analyses. It follows that smaller, more agile, and transparent models, such as Hughes' salvo equations, are underutilized in defense analyses. We believe that these models should receive more attention, use, and funding. To illustrate this point, this paper uses two very simple models (by modern standards) to rapidly generate insights on the value of information relative to force strength. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

A generalized Johnson's rule for stochastic assembly systems

Johnson's rule gives the optimal order to schedule a set of jobs through a two-machine flow shop with deterministic processing times. We extend Johnson's rule to fork-join systems with random processing times. Most of the system may be an arbitrary network. We give conditions under which Johnson's rule is optimal in the stochastic sense, in the increasing convex sense, and in expected value. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 211–220, 1997     

A sequential attribute sampling inspection game for item facilities

The routine inspection of facilities storing large numbers of identical items is modeled as a two‐person, sequential game. Timely detection of illegal activity is parameterized in terms of a critical time to detection, and equilibria are derived which provide inspection strategies. Necessary conditions for deterrence of illegal behavior are discussed. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 496–505, 2001     

Suppression of enemy air defenses (SEAD) as an information duel

Blue strike aircraft enter region ? to attack Red targets. In Case 1, Blue conducts (preplanned) SEAD to establish air superiority. In the (reactive) SEAD scenario, which is Case 2, such superiority is already in place, but is jeopardized by prohibitive interference from Red, which threatens Blue's ability to conduct missions. We utilize both deterministic and stochastic models to explore optimal tactics for Red in such engagements. Policies are developed which will guide both Red's determination of the modes of operation of his engagement radar, and his choice of Blue opponent to target next. An index in the form of a simple transaction kill ratio plays a major role throughout. Published 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 723–742, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10046     

Approximation of multiclass queueing networks with highly variable arrivals under deterministic routing

In this paper, we present the heavy‐traffic bottleneck phenomenon under multiclass deterministic routing and discuss how it can be addressed by decomposition approximation. Examples show that Bitran and Tirupati's method and Whitt's enhancements for deterministic routing may not properly account for this phenomenon. We propose refinements to these methods based on Whitt's variability functions. Results of numerical experiments on simple networks and semiconductor manufacturing process show significant improvement in the approximation of expected waiting time at bottleneck stations. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

‘Immediate redress’: USS Potomac and the pirates of Quallah Batoo

Maritime interests in the twenty-first century are not immune to the growing number of irregular challenges and hybrid threats that have come to dominate land warfare. In order to better understand these challenges a study of naval history can help provide a vital foundation. In the early 1830s the United States Navy dispatched the frigate USS Potomac to Sumatra to investigate a pirate attack on the spice trader Friendship. Potomac's crew of sailors and Marines conducted a landing at the village Quallah Batoo and fought a pitched battle. As the navies of the world approach naval irregular warfare in the new century, studying past examples like Potomac's mission can help illuminate the principles of successful naval irregular warfare.     

Effective attacks in the salvo combat model: Salvo sizes and quantities of targets

This article considers two related questions of tactics in the context of the salvo model for naval missile combat. For a given set of targets, how many missiles should be fired to produce an effective attack? For a given available salvo size, how many enemy targets should be fired at? In the deterministic version of the model I derive a simple optimality relationship between the number of missiles to fire and the number of targets to engage. In the stochastic model I employ the expected loss inflicted and the probability of enemy elimination as the main performance measures and use these to derive salvo sizes that are in some sense “optimal.” I find that the offensive firepower needed for an effective attack depends not only on a target's total strength but also on the relative balance between its active defensive power and passive staying power. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Rendezvous search when marks are left at the starting points

Leaving marks at the starting points in a rendezvous search problem may provide the players with important information. Many of the standard rendezvous search problems are investigated under this new framework which we call markstart rendezvous search. Somewhat surprisingly, the relative difficulties of analysing problems in the two scenarios differ from problem to problem. Symmetric rendezvous on the line seems to be more tractable in the new setting whereas asymmetric rendezvous on the line when the initial distance is chosen by means of a convex distribution appears easier to analyse in the original setting. Results are also obtained for markstart rendezvous on complete graphs and on the line when the players' initial distance is given by an unknown probability distribution. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 722–731, 2001     

On the inspection game

The Inspection Game is a multistage game between a customs inspector and a smuggler, first studied by Melvin Dresher and Michael Maschler in the 1960s. An extension allowing the smuggler to act more than once, treated by Sakaguchi in a special case, is solved. Also, a more natural version of Sakaguchi's problem is solved in the special case where the smuggler may act at each stage. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 327–334, 1998