# Operations Research

Listed on this page are current research projects being offered for the Vacation Scholarship Program.

### The price of anarchy, the price of stability, and the price of communication in interacting intensive care units

The price of anarchy (PoA), the price of stability (PoS), and the price of communication (PoC) are measures of how inefficient the system is if interacting intensive care units (ICUs) do not communicate, communicate but do not cooperate, and communicate and cooperate, respectively. For this project we model the interaction between two ICUs as a continuous-time Markov chain and calculate the PoA, PoS, and PoC, and interpret the results. The model can be extended to incorporate more ICUs, or units and wards in the same hospital.

Contact: Mark Fackrell fackrell@unimelb.edu.au

### Floods, fires and explosions: how to design survivable networks in the modern age

Much of society’s critical infrastructure takes the form of large-scale networks. Think of examples such as the power grid, the NBN, gas and water pipelines, and transportation networks. All such networks are potentially vulnerable to natural disasters, or even terrorist attacks. Significant interruption to these networks can wreak havoc. So the question is: how do we design these networks to be robust against local, regional destruction, without blowing the national budget?

In this project we will use planar geometric graph models for this problem and analyse survivability when the destruction region is modelled as a circular disk. In particular, we would like to find algorithms for optimally designing networks that are survivable against failures of a given maximum radius. The project will use mathematical tools from graph theory, optimisation, computer science and just a little bit of Euclidean geometry.

Contact: Charl Ras cjras@unimelb.edu.au

### Charging coordination for plug-in electric vehicle fleets

With an increasing uptake of Plug-in Electric Vehicles (PEVs), it is becoming increasingly important for aggregate charging behaviour to be coordinated in way that does not place undue stress on electricity distribution infrastructure. On the other hand, PEV owners typically make charging decisions based on individual factors (such as minimising electricity costs) rather than factors affecting electricity distribution infrastructure as a whole. To reconcile these competing interests, this project will examine decentralised algorithms based on game theory for making coordinated optimal charging decisions in fleets of non-cooperation PEVs.

Contact: Matthew Tam matthew.tam@unimelb.edu.au

### Study of the relation between built environment and traffic congestion

This project proposes to identify related factors in the Built Environment as independent variables through an integrative model, and to investigate their effects on the dependent variables reflecting traffic capacity and congestion level using an inferential statistical model.  The established relationship between the variables will be utilised to support the development of congestion mitigation and optimal BE design strategies. Using spatial-temporal statistical analysis, we aim to investigate how congestion of one area can spatially interact with other area, and how dynamics of congestion temporally evolve.

Contact: Joyce Zhang lele.zhang@unimelb.edu.au, Tingjin Chu

### Design of a loading zone reservation system with travel and service times uncertainty

Couriers undertaking deliveries in Central Business Districts (CBDs) often have difficulty conducting efficient routes due to the uncertainty associated with the availability of loading zones. A booking system can better utilise the limited resource and improve the efficiency of the delivery system. This project will develop a reservation system for loading zones scattered in CBDs and takes into account the uncertainty in vehicle travel times and courier stay durations. The objective is to maximise the delivery efficiency and the service reliability.

Contact: Joyce Zhang lele.zhang@unimelb.edu.au