A measure of effectiveness for sensors and strategies

This paper discusses a possible measure of effectiveness for information sensing equipment, such as radar or sonar, based on its ability to provide information. It is shown that such a measure is particularly appropriate for situations where a sequence of similar limited engagements may occur, as on antisubmarine patrol, for example. In this case the measure expresses the expected rate of gain per engagement of the relative resources of the participants. Rates are calculated for the optimal and certain simpler, but suboptimal, strategies. The measure is illustrated by an exact analysis of a gambling problem and a qualitative treatment of an anti-missile missile allocation problem.     

Product moments of order statistics from the doubly truncated exponential distribution

Recurrence relations for the product moments of order statistics from a doubly truncated exponential distribution are obtained. These relations allow us to evaluate the product moments for all sample sizes.     

A generalization of the entropy model for brand purchase behavior

Hemiter's entropy model for brand purchase behavior has been generalized for Renyi's measure of entropy which is a more general concept than Shannon's measure of entropy used by Herniter and which includes Shannon's measure as a limiting case. The generalized model considered here is more flexible than Herniter's model since it can give different marketing statistics for different products and it can give these statistics even when only some of the brands are considered.     

An attack-defense game with matrix strategies

This paper presents the results and the method of analysis for an attack-defense game involving allocation of resources. Each player is assumed to have several different types of resources to be divided in optimal fashion among a fixed set of targets. The payoff function of the game is convex. The “No Soft-Spot” principle of M. Dresher, and the concept of the generalized inverse of a matrix are used to determine optimal strategies for each player and the value of the game.     

Reliability of a single unit with k spares in case of the hyper-exponential and the erlang failure distribution

In this paper formulas are derived for the reliability of a single unit to which identical spares in standby are allocated, with all of these units having a hyper-exponential or Erlang distributed lifetime. Two advantages are obtained by using these distributions. First, the general procedure for calculating the effect of redundancy is applicable, in contrast with most of the common life distributions, such as Weibull. Moreover, both distributions are suitable for matching to observed curves and practical data by varying the values of the parameters, covering together most of the cases of practical interest.     

Challenges of measuring progress in Afghanistan using violence trends: the effects of aggregation,military operations,seasonality, weather,and other causal factors

Measuring nationwide progress of counterinsurgency operations in Afghanistan using violence trends is difficult due to several factors: aggregation of data to the national level may obfuscate disparate local trends; the observed seasonality in violence makes comparisons difficult and may obscure progress; and short-term spikes or troughs – attributable to weather, military operations and tempo, or holiday periods – heavily influence simple averaging schemes. Despite these challenges, proper understanding of violence statistics is critical to estimating the effectiveness of military forces added during a surge or redeployed as part of transition. This article explores methods for analyzing observed violence trends to identify causal factors, to provide a comparable baseline, and to inform assessments at appropriate levels of aggregation. One methodology for seasonal adjustment of violence data is discussed and shown to provide a logical baseline for examining trends. An ordinary least squares regression model is developed and implemented using time-series violence data.     

Modeling and analysis of vessel casualties resulting from tanker traffic through narrow waterways

In this paper, we present a physics-based stochastic model to investigate vessel casualties resulting from tanker traffic through a narrow waterway. A state-space model is developed to represent the waterway and the location of vessels at a given time. We first determine the distribution of surface current at a given location of the waterway depending on channel geometry, bottom topography, boundary conditions, and the distribution of wind. Then we determine the distribution of the angular drift for a given vessel travelling at a given location of a waterway. Finally, we incorporate the drift probabilities and random arrival of vessels into a Markov chain model. By analyzing the time-dependent and the steady-state probabilities of the Markov chain, we obtain risk measures such as the probability of casualty at a given location and also the expected number of casualties for a given number of vessels arriving per unit time. Analysis of the Markovian model also yields an analytical result that shows that the expected number of casualties is proportional to square of the tanker arrival rate. We present our methodology on an experimental model of a hypothetical narrow waterway. © 1999 John Wiley & Sons, Inc. Naval Reseach Logistics 46: 871–892, 1999     

A set-processing algorithm for scheduling staff on 4-day or 3-day work weeks

This paper presents an efficient algorithm for scheduling a single-category work force on 4-day or 3-day work weeks. Employees work 4 or 3 days each week, have A out of every B weekends off, and work no more than 5 consecutive days in a work stretch on 4-day work weeks and no more than 4 days in a work stretch on 3-day work weeks. Such conditions often prevail in 7-day-a-week organizations such as hospitals, manufacturing plants, and retail stores. We determine the minimum number of workers required to satisfy the scheduling constraints under any pattern of daily requirements. Then we present the algorithm for assigning days off for each worker, thereby determining the work schedules. We show that the algorithm, by construction, will necessarily satisfy the scheduling constraints. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 839–853, 1998     

Using multiple searchers in constrained-path,moving-target search problems

The search theory open literature has paid little, if any, attention to the multiple-searcher, moving-target search problem. We develop an optimal branch-and-bound procedure and six heuristics for solving constrained-path problems with multiple searchers. Our optimal procedure outperforms existing approaches when used with only a single searcher. For more than one searcher, the time needed to guarantee an optimal solution is prohibitive. Our heuristics represent a wide variety of approaches: One solves partial problems optimally, two use paths based on maximizing the expected number of detections, two are genetic algorithm implementations, and one is local search with random restarts. A heuristic based on the expected number of detections obtains solutions within 2% of the best known for each one-, two-, and three-searcher test problem considered. For one- and two-searcher problems, the same heuristic's solution time is less than that of other heuristics. For three-searcher problems, a genetic algorithm implementation obtains the best-known solution in as little as 20% of other heuristic solution times. © 1996 John Wiley & Sons, Inc.