Goodman School of Business: Recent submissions
Now showing items 21-26 of 26
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A counterfactual study of the Charge of the Light BrigadeWe use a mathematical model to perform a counterfactual study of the 1854 Charge of the Light Brigade. We first calibrate the model with historical data so that it reproduces the actual charge’s outcome. We then adjust the model to see how that outcome might have changed if the Heavy Brigade had joined the charge, and/or if the charge had targeted the Russian forces on the heights instead of those in the valley. The results suggest that all of the counterfactual attacks would have led to heavier British casualties. However, a charge by both brigades along the valley might plausibly have yielded a British victory.
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The salvo combat model with a sequential exchange of fireThis 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.
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A preliminary study of grade forecasting for studentsThis 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.
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A verification study of the stochastic salvo combat modelWhen 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.
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The salvo combat model with area fireThis 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.
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Modeling short-range ballistic missile defense and Israel's Iron Dome systemThis 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.
