On Monday we were given an introduction to the history of OR in the public sector and Laura gave us an insight into some of her own work. This involved learning about how OR was used in cities in America such as US during the 20th century in order to increase their efficiency under limited government funding. There was an interesting balance between the answers that were coming from the models of the time, and what the departments were willing to accept. An example of this was how staffing duties were found to be optimal by putting more staff at busier times, however, unions representing employees were often against this since it would inconvenience their daily schedules. Also since this was a new area there was scepticism as to how beneficial following the answers outputted would actually be, as opposed to experts who had worked in the industry for years.

Tuesday morning we were looking at how we can use integer programming to help us place ambulance stations on a map in order to give the best coverage to an area. This built up nicely on some of the work we had done last term with solving different kinds of optimisation problems. The aim was to try and build robustness into how we choose which station an ambulance is sent from in the case of an emergency. This is a simple problem if we are assuming all ambulances are available, but in reality we may have to send our second or even third choice. A problem particularly in America is working out how to provide acceptable service to rural areas whilst still having sufficient capacity in the city centres.

In the afternoon we took a different topic of how we can use OR to help in disasters like hurricanes or terrorism. In the aftermath it is important to work out how we can give aid as quickly as possible to those affected. Problems can include how we can divert resources when roads are blocked, or how we can rebuild the electricity network in order to reconnect key infrastructure in the optimal order.

In all it was an enjoyable two days and I feel like I learnt a lot about a new area that I had not really considered in the past. If you would like to read more about Laura she has her own blogs and

Queuing is something that all of us experience on a daily basis. It can be frustrating when we are faced with long queues that are not worth the wait and we may question why we bothered queuing up in the first place. This was first considered in the literature during the 1960s when thinking about how we could reduce queues in all walks of life such as at a cab stand or when hiring industrial equipment.

The method in which I will consider this is when we either have the option to assign an arrival into a queue, or to send them away when they first arrive into the system. This deviates slightly from traditional queuing theory where we consider how we can serve every single individual and this is an important distinction. There are two contrasting ways in which this can be thought of: selfish and social policies. With a selfish policy the individual is only concerned with maximizing their own expected profit, and does not take into account anybody else. This is in contrast to a social policy where there is some authority organizing the queue in order to maximize the expected profit of the entire population as a whole.

It is a relatively simple concept, but in fact it can spring surprising results. For example, what may not be instinctive is that in fact to increase the reward of the whole, we must shorten the length the queue can build up before turning new arrivals away. Thus the point of how one would go about implementing these in practice is not a simple task. One of the ideas first proposed in the literature is finding a toll that must be paid in order to join this queue. This has already been implemented in some systems such as for example when booking a taxi we have surge prices when demand is high, and cheaper prices when demand is low. Doing this helps to even out the arrival of customers in order to maximize the profit by the operator. For simple queues we can in fact mathematically calculate how we would go about doing this in order to push an individuals selfish policy to match up with the social policy for the system. However, this can lead into ethical complications when we are looking systems that represent a basic human need such as the distribution of aid or other essential supplies that are of immediate need for vulnerable people. This can lead into many different considerations and as such I did not go into this in my report but it is an interesting point and important to think about.

I instead was focused on the construction of the social and selfish policies for a general model of queuing. The methodology of this quickly becomes complicated due to the large number of scenarios we can find ourselves in. Thus I explained how we can come up with this directly for the most basic form of queue with one server at one facility and we can either choose to allow an arrival to join the back of the queue, or force them to leave with nothing (called balking). I then referred to methods that others have introduced in order to be able to solve more complicated and general methods with the help of computers. However, these quickly become infeasible when dealing with anything other than small toy problems and thus we must look at heuristics that can approximate the solution rather than solving it exactly.