Masters Thesis: "Continuous IED Supply Chain Model"
Tony Liu, 2nd Lt. USAF
Improvised Explosive Devices (IEDs) continue to be the main weapon used by terrorists against coalition forces overseas. Throughout the research led by the Joint IED Defeat Organization, the DoD defined 3 main strategies to fight IEDs: attack the network, defeat the device and equip military forces with counter-IED techniques. Our research intends to give U.S. forces a better perspective on how to attack the network. We begin by first developing a continuous model of the supply chain terrorists use to develop, emplace and detonate IEDs. Our model contains four states in which IEDs can exist: construction (C), emplaced (E), detonated (D) and found (F). Resources flow into the construction phase (at rate a0), while IEDs can flow from construction to emplaced (a1), emplaced to detonated (a2), construction to found (ß1) and emplaced to found (ß2). With this model, we have a total of nine parameters, four account for the number of IEDs in each state at our initial time and the other five account for the rates at which IEDs and resources flow from one state to the other.
Given this supply chain, we use a system of ordinary differential equations in order to derive equations for C, E, D and F as functions of time and our flow rate parameters. Over a given period of time, U.S. forces can collect data on the number of IEDs that they find (F) as well as the number of IEDs that detonate (D). From here, we apply a least squares method to attain the nine parameters that best fit the collected data for D and F. Minimizing our least squares equation allows us to estimate where the IEDs are located as well as how fast they are moving throughout the supply chain. Using this, we can better judge the impact of our past efforts in stopping IEDs and possibly determine how to best move forward. In our research we consider two different models. In the first model, we assume that our flow rates, ai and ßi, are constant. In the second model, we develop a more complicated insurgent strategy in which the rates IEDs flow from one state to another change as a result of how effective U.S forces are at finding IEDs.
Kevin Pond, Capt, USAF, PhD (advisor)
Benjamin F. Akers, PhD
William Baker, PhD