Funding is available for a PhD position in operations research at Rutgers University, USA, to work on the topic "A Polyhedral Approach to some Infinite Sequencing Problems". (See the end of this message for description of the project.) Perspective students should have a strong mathematical background and an interest in game theory and discrete optimization.
Informal inquiries to Thomas Lidbetter at tlidbetter@business.rutgers.edu are welcome, but candidates will also need to apply to the Rutgers Business School's PhD program in Management, selecting the Operations Research concentration: see https://www.business.rutgers.edu/phd/admissions.
Abstract:
This project will focus on search problems for which a target is located in one of a finite number of possible locations but if a target is present in a given location, a search of that location does not necessarily guarantee that the target will be found - that is, there is some "overlook probability" which determines the likelihood that the target is not found.
This project will consider two related but distinct settings in this project. The first setting will be concerned with finding searches that minimize the time or expected time to find a hidden target. This could be appropriate if an attack (or cyberattack) is causing ongoing damage, and the objective is to stop it as soon as possible. The amount of damage being done may depend on the location of the target, and the time taken to search a location may vary with the location.
The second setting considers search problems for which the target may be a survivor of a natural disaster or a prisoner held by an adversary, and we assume there is a possibility that the search will be halted before the target has been found (for example if the searcher becomes trapped herself or captured by an adversary). In this case the objective is to maximize the probability of locating the target. It is assumed that at each location there is a given probability that the search will be terminated when that location is searched.
This project will take a geometric approach to understanding the structure of feasible searches in both settings, and will focus on leveraging this understanding to solve the problem of finding optimal worst-case searches.
Regards,
Thomas Lidbetter
Associate Professor
Department of Management Science and Information Systems
Rutgers University, NJ, USA
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