• 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.