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

      Armstrong, Michael J. (Wiley, 2007)
      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.
    • The Effectiveness of Rocket Attacks and Defenses in Israel

      Armstrong, Michael J. (Oxford University Press, 2018-04-11)
      This empirical article studies rocket attacks and defenses in Israel during operations Protective Edge, Pillar of Defense, and Cast Lead, and also during the Second Lebanon War. It analyzes publicly available counts of rockets fired, fatalities, casualties, and property damage. The estimates suggest that interceptor deployment and civil defense improvements both reduced Israel’s losses slightly during Pillar of Defense and substantially during Protective Edge. They also imply that interceptor performance during Pillar of Defense may have been overstated. Ground offensives were the most expensive way to prevent rocket casualties. Interceptors were at least as cost-effective as military offensives, and their advantage improved over time.Without its countermeasures, Israel’s rocket casualties could have been more than fifty times higher during Operation Protective Edge. These results imply that Israel’s rocket concerns were more justified than critics admit, but its military operations were less worthwhile than intended.
    • Effects of lethality on naval combat models

      Armstrong, Michael J. (Wiley, 2004)
      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.
    • How gaps between target and midcourse grades impact undergraduates’ studying intentions and grade improvements

      MacKenzie, H.F. "Herb"; Armstrong, Michael (John Wiley & Sons, Inc, 2020-10-09)
      We examine how gaps between students’ chosen target grades and actual midcourse grades relate to their exam studying intentions and subsequent grade improvements. We further investigate whether those relationships are moderated by students’ academic ability (as measured by high school averages) and implicit theory of intelligence or mindset (as measured by questionnaire scores). Our study involved 250 undergraduate students in a first-year business course. The study used linear regression to analyze survey responses at the course’s beginning, survey responses near the course’s end, and actual course grades. The analysis showed students had greater studying intentions and grade improvements when midcourse grades were farther below initial target grades. Mindset moderated the relationship between grade gaps and studying intentions, whereas academic ability moderated the relationship between grade gaps and grade improvements. These results enhance our knowledge of how students respond to grade feedback and could help instructors assist students to make better decisions about their studying.
    • Influence of anticipated and actual grades on studying

      Armstrong, Michael J.; MacKenzie, H.F. (Herb) (Elsevier, 2017-03)
      This study explores two questions regarding differences between students’ anticipated and actual grades in university courses: what factors contribute to those differences arising, and which of those differences influence students’ subsequent studying? The research surveyed 278 students in a first-year undergraduate business course. Students with stronger academic abilities tended to have smaller (less negative) gaps between their grades and goals, while students with higher personal control scores tended to have wider (more negative) gaps. These gaps narrowed later in the course as students’ goals decreased to match their actual grades more closely. Students increased their studying if their actual grades were lower than their original goals, and/or lower than their updated goals. By contrast, the difference between students’ subjective grade goals and their objectively forecast final grades did not influence their studying intentions.
    • Inventory Flow in Canadian Candy Bar Supply Chains

      Armstrong, Michael J. (APICS, 2011)
      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.
    • Legal cannabis market shares during Canada’s first year of recreational legalisation

      Armstrong, Michael (Elsevier, 2020-11-19)
      Background: This study estimated legal products’ share of Canada’s total cannabis consumption during the first year of recreational legalisation, October 2018 to September 2019. Methods: Government data was used to estimate monthly recreational sales in dollars per capita, grams per user, and percentage share of kilograms or litres consumed. As explanatory factors, the analysis considered provincial differences in retail pricing (percentage mark-ups) and store density (stores per million users), as well as national monthly production of dry cannabis (kilograms) and cannabis oil (litres) finished products. Results: Legal recreational products’ share of Canada’s overall cannabis consumption began at 7.8% in October 2018 and grew to 23.7% by September 2019, with an average of 14.5% over the first 12 months. Sales growth was delayed by shortages of both dry cannabis products and licensed stores, but not cannabis oils. Across the 10 provinces, legal recreational shares in September 2019 varied from 13% to 70%; differences in store densities and retail prices partly explained the variation. Prince Edward Island’s large 70% share seemed due to it having minimal product shortages, high store densities, and low prices. Conclusions: Legal recreational products captured market share to the extent they were available, accessible, and low-priced. Problems with those factors slowed the initial expansion of legal product sales but also suggested ways to gradually increase their market share.
    • Modeling short-range ballistic missile defense and Israel's Iron Dome system

      Armstrong, Michael J. (Institute for Operations Research and Management Science (INFORMS), 2014-09)
      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.
    • A preliminary study of grade forecasting for students

      Armstrong, Michael J. (Wiley, 2013)
      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.
    • Refighting Pickett’s Charge: mathematical modeling of the Civil War battlefield

      Armstrong, Michael J.; Sodergren, Steven E. (Wiley, 2015)
      Objective. We model Pickett’s Charge at the Battle of Gettysburg to see whether the Confederates could have achieved victory by committing more infantry, executing a better barrage, or facing a weaker defense. Methods. Our mathematical modeling is based on Lanchester equations, calibrated using historical army strengths. We weight the Union artillery and infantry two different ways using two sources of data, and so have four versions of the model. Results. The models estimate that a successful Confederate charge would have required at least 1 to 3 additional brigades. An improved artillery barrage would have reduced these needs by about 1 brigade. A weaker Union defense could have allowed the charge to succeed as executed. Conclusions. The Confederates plausibly had enough troops to take the Union position and alter the battle’s outcome, but likely too few to further exploit such a success.
    • Relationships between increases in Canadian cannabis stores, sales, and prevalence

      Armstrong, Michael J. (Drug and Alcohol Dependence, 2021-09-22)
      Background: This study estimated the relationships between increases in legal cannabis stores, legal cannabis sales, and cannabis prevalence in Canadian provinces between 2018 and 2020. Method: Government data were used to calculate changes in licensed store numbers, retail sales dollars, and past-three-month users in 10 provinces across six time periods. The resulting N = 60 observations were standardized per million residents aged 15 and up, and then analyzed via linear regression. Results: Store growth explained 46.3% of the variation in provincial sales growth; each added store was associated with added quarterly sales of $305 (95% CI: $208 to $402) thousand. By contrast, store growth explained only 7.7% of the variation in provincial user growth; each added store was associated with 696 (95% CI: 58 to 1334) added users. Conclusion: From 2018 to 2020, Canada’s rapid cannabis retail expansion was strongly related to legal sales growth but only weakly related to prevalence growth. This implies prevalence growth during that period was related more to legalization’s other aspects and/or to the continuation of already-existing trends.
    • The salvo combat model with a sequential exchange of fire

      Armstrong, Michael J. (Palgrave, 2014)
      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.
    • The salvo combat model with area fire

      Armstrong, Michael J. (Wiley Periodicals, Inc., 2013-12)
      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.
    • A Stochastic Salvo Model Analysis of the Battle of the Coral Sea

      Armstrong, Michael J.; Powell, Michael B. (Military Operations Research Society (MORS), 2005)
      In this work we study the Battle of the Coral Sea using a stochastic version of the salvo combat model. We begin by estimating the range of probable alternative results for the battle, given the forces employed; i.e., if the battle were to be "re-fought", how likely are outcomes other than what historically transpired? Our analysis suggests that a wide range of results was indeed possible, even without any change in forces on either side. We then estimate the impact of hypothetical but plausible changes in the American forces employed. Our analysis suggests that a material advantage could have been obtained by committing extra aircraft carriers to the battle or by dispersing the carriers that were already deployed; on the other hand, equipping each carrier with more fighters but fewer bombers would have yielded a net disadvantage.
    • A stochastic salvo model for naval surface combat

      Armstrong, Michael J. (Institute For Operations Research and Management Science (INFORMS), 2005)
      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.
    • Students as clients: a professional services model for business education

      Armstrong, Michael (Academy of Management, 2003-12)
      My purpose in this article is to describe a professional services student-as-client model that I believe offers a more realistic guide for core business school operations than either the customer model or the partner model. I begin in the next section by noting the situations where the partner model is well suited, and show why I don't believe it is realistic for most programs. I then define the client analogy, illustrate how it offers a better fit, and describe some of the insights that it suggests.
    • A survey of the machine interference problem

      Haque, Lani; Armstrong, Michael J. (Elsevier, 2007)
      This paper surveys the research published on the machine interference problem since the 1985 review by Stecke & Aronson. After introducing the basic model, we discuss the literature along several dimensions. We then note how research has evolved since the 1985 review, including a trend towards the modelling of stochastic (rather than deterministic) systems and the corresponding use of more advanced queuing methods for analysis. We conclude with some suggestions for areas holding particular promise for future studies.
    • To repeat or not to repeat a course

      Armstrong, Michael J.; Biktimirov, Ernest N. (Taylor & Francis, 2013)
      The difficult transition from high school to university means that many students need to repeat (retake) one or more of their university courses. This paper examines the performance of students who were repeating first-year core courses in an undergraduate business program. It used data from university records for 116 students who took a total of 232 repeated courses across 6 subjects. The results show that the student’s original course grade and cumulative grade point average were positively associated with the new grade obtained in the repeated course. Conversely, the original course grade was negatively associated with the extent of improvement obtained by repeating.
    • A verification study of the stochastic salvo combat model

      Armstrong, Michael J. (Springer, 2011)
      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.