# Stephen Ford's Homepage

# About Me

I'm currently a PhD student at STOR-i. Before coming to Lancaster, I did a MSc in Scientific Computation and Industrial Mathematics at the University of Nottingham, and before that did a BA in Mathematics at the University of Cambridge.

# My Research

The title of my PhD is 'Dynamic Allocation of Assets Subject to Failure and Replenishment'. To explain, allocation of assets is a common real-life problem, and a much-studied one. The simple expedient of allowing the assets to fail and require repair renders simple allocation problems difficult, and complex allocation problems nearly unsolvable.

As such, my PhD aims to look at heuristic methods effective for such problems, in circumstances where the size and complexity of the problem renders exact methods impractical. I will be initially looking at myopic and index policies, as they are inherently computationally efficient.

# My PhD

The project concerns the analysis of generic models for dynamic resource allocation in situations where the assets available for deployment are subject to failure or depletion. Suppose that N assets are available for allocation to K tasks. Once deployed, each asset has a useful life of limited duration, at the end of which it is sent for repair/replenishment. Once repaired/ replenished, the asset is again available for redeployment. The central question for analysis concerns how newly replenished assets should be allocated to the K tasks which require them.

The tasks will be linked in many applications. Consider our assets to be UAVs searching for targets in a communication degraded environment. Some UAVs search for targets (task 1 is search, say) while other UAVs form a line-of-sight communication network (tasks 2,…,K are communication at distinct network locations, say) back to the centre of operations (base). A target is only detected if its sighting is reported back to base successfully. In order for this system to function effectively, we need some UAVs searching, with enough UAVs also deployed to form a fully connected communication network from the search region to base. UAVs have a limited endurance and must periodically return to refuel. After refuelling, a UAV is sent back to the area of operation as either a searcher (task 1) or a communicator (one of tasks 2,…,K). The goal is to determine effective approaches to UAV deployment

We aim to develop optimal or near-optimal heuristic policies for UAV assignment to maximise objectives such as the long-run target detection rate. Contributions may include: (i) formulation of a Markov decision process model to determine optimal assignment policies, to be solved for small instances; (ii) development of heuristic assignment policies that are fast to compute and which perform well in a variety of circumstances; (iii) extensions to build in more realism.

Initially we will assume failure times and replenishment times follow exponential distributions. However, in many situations this is not realistic, so we may investigate better ways to model these times to balance realism and tractability. Another possible extension is that rather than always assigning an asset to a task immediately after replenishment, it may be better to keep some assets in reserve, ready to be assigned when other assets fail.

Contact me at s.ford1@lancaster.ac.uk