Effects of lethality on naval combat models

In the context of both discrete time salvo models and continuous time Lanchester models we examine the effect on naval combat of lethality: that is, the relative balance between the offensive and defensive attributes of the units involved. We define three distinct levels of lethality and describe the distinguishing features of combat for each level. We discuss the implications of these characteristics for naval decision-makers; in particular, we show that the usefulness of the intuitive concept "more is better" varies greatly depending on the lethality level.Natural Sciences & Engineering Research Council (NSERC) Discovery Gran

Modeling short-range ballistic missile defense and Israel's Iron Dome system

This paper develops a model of short-range ballistic missile defense and uses it to study the performance of Israel’s Iron Dome system. The deterministic base model allows for inaccurate missiles, unsuccessful interceptions, and civil defense. Model enhancements consider the trade-offs in attacking the interception system, the difficulties faced by militants in assembling large salvos, and the effects of imperfect missile classification by the defender. A stochastic model is also developed. Analysis shows that system performance can be highly sensitive to the missile salvo size, and that systems with higher interception rates are more “fragile” when overloaded. The model is calibrated using publically available data about Iron Dome’s use during Operation Pillar of Defense in November 2012. If the systems performed as claimed, they saved Israel an estimated 1778 casualties and $80 million in property damage, and thereby made preemptive strikes on Gaza about 8 times less valuable to Israel. Gaza militants could have inflicted far more damage by grouping their rockets into large salvos, but this may have been difficult given Israel’s suppression efforts. Counter-battery fire by the militants is unlikely to be worthwhile unless they can obtain much more accurate missiles.Fulbright Canada, Norwich Universit

A preliminary study of grade forecasting for students

This experiment enabled undergraduate business students to better assess their progress in a course by quantitatively forecasting their own end-of-course grades. This innovation provided them with predictive feedback in addition to the outcome feedback they were already receiving. A total of 144 students forecast their grades using an instructor-prepared spreadsheet, and then responded to a brief survey. Of these participants, 29% said the forecast grades were lower than expected, while 6% said they were higher. Subsequent to the forecast, 47% of the respondents said they were studying more than planned, while 3% said they were studying less. The relative difference between the students’ forecast grades and their prior expectations showed no direct influence on subsequent motivation or studying effort. Instead, increased studying was reported by students who had experienced increased anxiety, increased motivation, or positive impressions subsequent to the forecasting experience, as well as by students who had received low absolute grade forecasts

The salvo combat model with area fire

This paper analyzes versions of the salvo model of missile combat where area fire is used by one or both sides in a battle. While these models share some properties with the area fire Lanchester model and the aimed fire salvo model, they also display some interesting differences, especially over the course of several salvos. Whereas the relative size of each force is important with aimed fire, with area fire it is the absolute size that matters. Similarly, while aimed fire exhibits square law behavior, area fire shows approximately linear behavior. When one side uses area and the other uses aimed fire, the model displays a mix of square and linear law behavior

The salvo combat model with a sequential exchange of fire

This paper develops a version of the stochastic salvo combat model in which the exchange of fire is sequential, rather than simultaneous. This sequential-fire version is built by modifying the equations in the original simultaneous-fire version. The performance of the sequential model is tested by comparing its outputs to those of a Monte Carlo simulation. The fit between the model and the simulation is very close, especially for the mean and standard deviation of losses. The model is then applied to the Battle of the Coral Sea. The results suggest that attacking first would have given the American force a larger advantage than that provided by an extra aircraft carrier

A verification study of the stochastic salvo combat model

When the stochastic version of the salvo combat model was designed, several assumptions and approximations were made to keep its mathematical structure relatively simple. This paper examines the impact of those simplifications by comparing the outputs of the stochastic model to those from a Monte Carlo simulation across 486 scenarios. The model generally performed very well, even where the battle size was relatively small or the damage inflicted by each missile was not normally distributed. The model’s accuracy did decrease where missiles were positively correlated instead of independent

Inventory Flow in Canadian Candy Bar Supply Chains

This study examined the ages of candy bars to measure the inventory flow in their supply chains. It sampled 6888 candy bars at 8 retail chains made by 4 manufacturers over a 4 year period. The first objective of the study was exploratory: were there any significant differences in inventory turnover across retailers, manufacturers, or time periods? The second objective was explanatory: could those differences be explained by business events, factory location, market share, or pricing? The analysis showed that there were substantial differences in inventory turnover, especially among the retailers. Unlike in previous research, these differences seemed independent of the particular retail sector. The analysis also found that significant changes in inventory ages coincided with major events at one manufacturer. Interestingly, locating factories close to their markets did not necessarily lead to faster flows. These findings have implications for firms operating in the increasingly integrated North American marketplace

A stochastic salvo model for naval surface combat

In this work we propose a stochastic version of the salvo model for modern naval surface combat. We derive expressions for the mean and variance of surviving force strengths and for the probabilities of the possible salvo outcomes in forms simple enough to be implemented in spreadsheet software. Numerical comparisons of the deterministic and stochastic models suggest that while the two models tend to provide similar estimates of the average number of ships surviving a salvo, this average by itself can be highly misleading with respect to the likely outcomes of the battle. Our results also suggest that a navy's preferences for risk (variability) and armament (offensive versus defensive) will depend on not only its mission objectives but also on whether it expects to fight from a position of strength or of weakness.National Science & Engineering Research Council (NSERC) Discovery Gran

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.Natural Science & Engineering Research Council (NSERC) Discovery Gran

Role-playing Game Based Learning, EFL Curriculum

The following is a proposed curriculum design for an intensive English theme-based immersion program designed for use in Korean post-secondary education. It is designed to address three deficits within the EFL classroom; lack of significant increase in English ability, self-efficacy and motivation to study English. This curriculum has a foundation in five main parts; Korean culture and social identity; Types of possible second language acquisition programs, Collaborative and Task Based learning; Bronfrenbrenner’s Ecological Systems Theory; and Gamification and Role Playing Game Based Learning. First I will discuss relevant literature, second I will present a proposed approach to learning based on the theories discussed in part I. Next I will present a curriculum based on the learning approach described in part II. In part III, I will demonstrate a sample curriculum for a proposed camp that addresses the three deficits listed above