This Thursday I’ll be presenting the paper “Interdicting a Nuclear-Weapons Project,” by Brown, et al. (2009). [1] In a previous blog post, I gave an introduction to bilevel programming, which is a key component to understanding project interdiction models such as the one posed in this paper. In my presentation, I plan to spend the majority of my time talking about the model, algorithm, and computational results as reported by Brown, et al., so in my blog post this week I’d like to delve a little deeper into the background of the problem and to help you better visualize the problem setting so we can hit the ground running on Thursday.

In 1968, many nations of the worlds singed the*Treaty on the Non-proliferation of Nuclear Weapons. *In spite of this, some nations (even some that signed the treaty!) have continued to purse development of a nuclear-weapons arsenal. Of course, some nations are doing so covertly and the existence of their programs has not been confirmed (e.g., Iran and Syria). There is, therefore, international interest in stopping or slowing such programs. Since many world leaders are paying close attention to any nuclear-weapons development activity, if a new nation were to begin proliferation, it would likely do so covertly. Once confirmation of the project was received via intelligence capabilities and some information was gathered, a world leader would be interested in options to slow the proliferation efforts. Likely, the first acts would be diplomatic, escalating slowly and only if necessary to militaristic endeavors.

Even while diplomatic solutions are being sought, though, actions can be taken to hinder the nuclear-weapons project. Toward that end, the defender (*interdictor*) would attempt to lengthen the time required to perform project *tasks* (the discrete project units that must be completed before a nuclear weapon is available for use). The interdictor, then, wants to maximize the amount of time it takes to develop a nuclear weapon, whereas the *proliferator* is trying to minimize that amount of time. Both actors must expend large amounts of nonrenewable resources such as time, money, and highly enriched uranium ore, placing heavy constraints on both the interdictor and the proliferator. It is the complex interactions between resource allocation and project completion time on both sides that make this problem perfect for bilevel optimization. Specifically, the nuclear-weapons interdiction problem is an instance of the two-stage *Stackelberg game*. A Stackelberg game is a zero-sum game between an attacker and a defender. First, the defender guesses the attacker’s plan and acts to maximally inhibit that plan. Second, the attacker observes the moves made by the defender. Third and finally, the attacker adjusts his original plan to minimize the negative effects to himself. In reality, the nuclear-weapons interdiction problem is probably multi-stage, but we have a much better chance of solving a two-stage model than we do a multi-stage model. Thus, some modeling assumptions are made (I’ll discuss these more in my presentation) that might or might not be reasonable if a world leader actually wanted to implement this model. At the very least, the two-stage model gives a lower bound on how much the interdictor can delay the project.

I’ll get much more into the details of the model itself and how we might be able to solve it on Thursday, but I wanted to give you all a head-start in understanding the problem situation and how we’ll approach it from a modeling perspective.

~AGS

[1] Brown, Gerald G., et al. “Interdicting a nuclear-weapons project.” Operations Research 57.4 (2009): 866-877.

The variety of operations research work that is done in the area of nuclear weapons is amazing. I always enjoy how it manifests in different ways: network interdiction, project interdiction, infrastructure fortification, and so on.

I find that the assumptions present in many of these models are often too overreaching. In network interdiction, knowing exactly the probabilities of successful arc traversal is unlikely. In this model, assuming interdiction decisions are made prior to the project’s beginning (or even that the interdiction can be modeled as a bilevel program) is just as believable. Nonetheless, these assumptions are generally justifiable, if not to simplify the problem to a point where it can be solved with the current available tools.

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The uncontrollable nuclear weapon projects are really dangerous for all of us. To have a safe world and safe future it is really important to make sure that these systems are safe enough and under control. Studies on this subject are really necessary. However, I agree with the Eli’s idea about assumptions. I have another question about the computational part of the model. What is the number of total components in the model and how many of them interdicted? The point of the question is that are those number reasonable for real case? Is the data produced or real? Thanks for the presentation. That was really great to learn about this subject.

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