Background & Introduction

Ever-increasing globalization has significantly increased the number of cargo containers being transported internationally. Additionally, it is estimated that shipping containers account for approximately 95% of the world's international cargo in terms of value. While most contain food, equipment, raw materials or other commodities, some percentage of containers carry undesirable items, such as drugs, weapons, chemicals, and possibly even nuclear materials. As such, it is imperative to develop strategies for detecting contraband that can act as a viable deterrent against illegal shipping while leaving the fluidity of the shipping industry uncompromised; it would simply be infeasible to inspect even a statistically significant sample of the population of containers.

The previous work of the Port-of-Entry (POE) research group models the container inspection process as a set of n independent sensors, each with a corresponding threshold value T, that classify each container as "good" or "bad." Then, given a specified Boolean decision function, an overall decision of "clear" or "suspicious" (i.e. requiring manual inspection) is made for each inspected container. The POE group detailed a multi-objective optimization approach to determine the optimal sensor threshold levels and sensor sequence while incorporating inspection time, misclassification and measurement error.

For more detailed background information about the POE Project, check out my preliminary presentation below:

My Part

My part in the research project has been twofold thus far. Orginally, I was solely working on incorporating evasive tactics, particularly the shielding of nuclear materials, into our container inspection model. However, Tsvetan Asamov, a member of the POE research group and a talented PhD student at the Rutgers Center for Operations Research (RUTCOR), was trying to finalize some impressive work on optimal, randomized layered inspection policies. I was very interested in his work, and soon I began helping him complete the paper.

Optimal Randomized Layered Inspection

Tsvetan's work promised several improvements for the inspection process. First, by employing a randomized flow network through the various sensors, a given container could undergo a completely different inspection process upon reentering the sensor network. In this way, the intrinsic unpredicability of the inspection process acts as a deterrent to would-be attackers. Second, Tsvetan realized that, for a given set of thresholds Ti, the problem of finding the optimal randomized inspection policy can be formulated as a generalized linear programming network flow problem.

We found that it would be useful to present a comparison between Tsvetan's model and the previous model (which uses a Series Boolean decision function) in order to illustrate the new model's superiorty. To this end, I wrote a Matlab program to take the output of the Series model program from time vs. cost space into budget vs. expected prevented damage space. In the process of working out the formulas for the budget and expected preveted damage of the Series model, we had some exciting insights, and this was an invigorating first-encounter with real research. Now, we are in the process of finalizing the paper for submission.

Effects of Shielding Nuclear Materials

I am also working on incorporating the effects of the shielding of nuclear materials into the POE detection model.In contrast to the previous modeling done by the POE research group, the study of shielding effects requires not only mathematical analysis but also physical analysis of the problem. This has proven to be an arduous task, as the physical problem involves many complex parameters, such as type of radiation source (Uranium, Plutonium, Cesium, etc.), the source geometry (cylindrical, spherical, sheet, etc.), the type of shielding material (lead, poly-ethylene, etc.), the shielding geometry (spherical, rectangular, etc.), and the shielding thickness, all of which must, in general, be taken into account. For completeness, I include below my preliminary presentation on the matter, complete with questions and problems:

In an effort to make the problem tractable, I made several assumptions and simplifications to the problem. This is where my knowledge of the physics of the problem and other practical concerns played a criticl role. After considerable investigation of the literature, I found that the methods of nuclear detection were fairly universal, and hence we could split our model into the special cases based on the type of nuclear source material. Additionally, I found that the effects of the source and shielding geometry were small compared to the precision of our detection methods.

With these simplifications, I was able to construct a model of the detection process that views the shielding thickness and the source mass as parameters. Because the domain of the shielding thickness and the source mass are bounded, I was able to use a Beta distribution to approximate the density function for each parameter.

Then, because a Poisson process is memoryless (i.e. the sum of Poisson is the Poisson of the sum), I was able to use some straightforward statistical methods to combine the three distributions (Poisson for the observed radiation and Beta for both shielding thickness and source mass). In this way, I constructed the density function for the "bad" population of cargo containers (i.e. those containing SNMs or other nuclear materials), taking varying shielding and source mass into account.

With this improved model in hand, we can now use identical methods as before to choose the optimal threshold levels. In the final week of the DIMACS REU program, I will be generating some numerical results (including plots of Probability of False Accept vs. Threshold Level, Optimal Threshold Level vs. Budget, and Expected Prevented Damage vs. Budget) and writing up a technical report on my work.

In the future, I am interested in investigating new detection algorithms from a game theoretic perspective, both with respect to the detection of shielded nuclear materials and in the context of the general detection problem.

For a better explanation of my work this summer, check out my final presentation:

For a more technical explanation of my work on nuclear shielding, check out the technical report:


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