Assessing the Use of Technology and Using Technology to Assess

A Case Study

Alex Heidenberg
Michael Huber

Department of Mathematical Sciences
The United States Military Academy
West Point, New York

Appendix A      Sample Project

The following Problem Solving Lab is an in-class exercise that allows the students to model and solve a system of interacting Discrete Dynamical Systems.

Humanitarian Demining

Background

The country of Bosnia-Herzegovina has approximately 750,000 land mines that remain in the ground after their war ended in November 1995.  The United Nations (UN) has decided to establish a Mine Action Center (MAC) to coordinate efforts to remove the mines.  You are serving as a U.S. military liaison to the director of the UN-MAC.

The UN-MAC will initially have 1000 trained humanitarian deminers working in country.  Each of these trained personnel can remove 65 mines per week during normal operations.

Unfortunately, there is a rebel force of about 8,000 soldiers that opposes the UN-MAC's efforts to support the legitimate government of Bosnia-Herzegovina.  They conduct two major activities to oppose the UN-MAC:  killing the deminers and emplacing more mines.  They terrorize the deminers, killing 1 deminer for every 1,000 rebels each week.  However, due to poor training and funding, each of these soldiers can only emplace an average of 5 additional mines per week. 

Meanwhile, the accidental destruction of the mines maim and kill some of both the deminers and the rebel forces.  For every 1,000,000 mines, 1 deminer is permanently disabled or killed each week.  The mines have the exact same quantitative impact on the rebel forces.

Modeling and Analysis

Your current goal is to determine the outcome of the UN-MAC's efforts, given the current resources and operational environment.

 1.  Model the strength of the demining organization, the rebels, and the number of mines in the ground.  Ensure you define your variables and domain and state any initial conditions and assumptions.

2.  Write the system of equations in matrix form A(n+1) = R * A(n).

3.  If the interaction between the rebels and deminers as well as their respective efforts to affect the minefields remain constant, what happens during the first five years of operations?

4.  Graphically display your results.  Ensure you display your results for each of the three entities you model.

5.  What is the equilibrium vectors, D or Ae, for this system?  Is it realistic? 

6.  The General and Particular Solution for the new system of DDS's using eigenvalue and eigenvector decomposition.

We add a little more realism to the scenario by creating interaction between the model's components.  The following extension is the project that forces the students to adapt their model and prepare a written analysis. 

Humanitarian Demining

BETTER ESTIMATE ON CASUALTIES DUE TO MINES

We now have more accurate data on the casualties due to mines; it may (or may not) change part of your model.  Better estimates show that for every 100,000 mines, 2 deminers are permanently disabled or killed each week.  The mines have the exact same quantitative impact on the rebel forces.

OTHER MINEFIELD LOSSES

Other factors take their toll on the number of emplaced mines as well.  Weather and terrain cause some of the mines to self-destruct, and civilians occasionally detonate mines.  Approximately 1% of the mines are lost to these other factors each week.

NATURAL ATTRITION OF FORCES

Due to other medical problems, infighting, and desertion, the rebel forces lose 4% of their force from one week to the next.  The deminers have a higher attrition due to morale problems; they lose 5% of their personnel from one week to the next.

RECRUITING EFFORTS

Both the rebel forces and the deminers recruit others to help.  Each week, the rebels are able to recruit an additional 10 soldiers.  Meanwhile, the UN-MAC is less successful.  They only manage to recruit an additional 5 deminers each week.

For the project, your report should address the following at a minimum:

1.  Executive Summary in memo format that summarizes your research.

2.  The purpose of the report.

3.  Facts bearing on the problem.

4.  Assumptions made in your model, as well as the viability of these assumptions.

5.  An analysis detailing:

            a.   The equilibrium vector, D or Ae, for the system and discuss its relevance.

            b.   The General and Particular Solution for the new system of DDS's using eigenvalue and eigenvector decomposition.

            c.   A description of what is happening to each of the entities being modeled during the first five

            (5) years of operations. 

6.  The director of the UN-MAC also wants your recommendation on the following:

            a.   If the demining effort is going to be successful within the first five years, when will it succeed in eradicating all mines?  If the demining effort is not going to be successful, determine the minimum number of weekly demining recruits needed to remove all mines within five years of operations. 

            b.   Describe at least one other strategy the UN-MAC can employ to improve its efforts to eradicate all of the mines.  Quantify this strategy within a mathematical model and show the improvement (graphically, numerically, analytically, etc.).

7.  Discussion of the results.

            a.  Reflect on your assumptions and discuss what might happen if one or more of  the assumptions were not valid. 

            b.   Integrate graphs and tables into your report, discuss them, and be sure to label them correctly.

8.  Conclusion and Recommendations.