## UoA

## The Container Positioning Problem

by Jonas Ahmt on 27 June 2010, under DTU, New Zealand, UoA

**What this post is about**

I think I have promised a couple of times that this post would appear on my blog at some point. Apparently “at some point” is exactly this very moment (or rather, probably some seconds/minutes/hours/days/weeks/years/decades/centuries ago, depending on when you have decided to read it compared to the time I wrote this). If you didn’t really care for last semester’s post about my studies (which I of course assume that you, avid reader of my blog, has read long ago), there is a good chance that you will find this post pretty boring as well. I will assume it will become quite nerdy. On the other hand, I don’t expect that anyone would ever choose to visit this blog unless they can handle a bit of nerdiness.

**What I study**

It seems like a good idea to start from scratch, so that’s what I’ll do, even though I would assume that most people who have somehow ended up at this site already have a vague idea about what it is I study. I am currently trying hard to finish my master’s degree at The Technical University of Denmark (DTU), called MMC Master, an acronym for Mathematical Modelling and Computation Master. The name reveals a good deal about what most of my courses are about: Formulating mathematical models and using them to compute exciting numbers. A mathematical model is not some geeky guy or girl going on catwalks. Neither is it a bunch of clay shaped into numbers, symbols or multiplication signs. They can, however, be (partly) responsible for the bad sense of humor demonstrated in the last two sentences as I have spent almost five years studying them by now. No, mathematical models are a series of formulas set up to represent some kind of real life problem. When all of Europe (and especially the UK) got yet another reason for hating Iceland, this time due to the eruption of Eyjafjallajökull which prevented almost every airplane around Europe from flying, mathematical models were used to estimate the risks of flying through the ash spewed up by the volcano. Likewise, models were created to compute how long the eruption would last and the probabilities that other, larger volcanos in the area, would erupt.

The type of mathematical models I usually deal with are of a bit different kind, however. During my studies, I have chosen to focus on Operations Research (OR). OR uses a combination of statistics, mathematical modeling and mathematical optimization to calculate optimal or near-optimal solutions or proposals to solutions for different decision-making problems. It is heavily used to create production plans and work schedules while it also plays an essential role in route planning and almost any logistic problem you can come up with.

**What my thesis is about**

My thesis deals with what has been named *The Container Positioning Problem*. I am writing it with my study buddy, Skott, who was also in Auckland last semester, taking the exact same courses as me. Skott’s description of the project can be read on his blog- it is all in Danish, though, since he’s too lazy to translate it into English. Either that, or he is clever enough to know that it is a waste of time to do the translation since nobody would want to read these kinds of blogs anyway, except for a few family members, perhaps. Many of the people I meet down here seem to be surprised that we are working two people on the same project. I am glad that we do have that opportunity at my university as I’m sure the final result will be more than the sum of its parts. It is extremely helpful to have someone to discuss with on a daily basis about the progress of the thesis, without having to schedule meetings with supervisors who (understandably) don’t know all the exact details of what we have been doing with the project since the last meeting. We have two supervisors, one in Denmark and one in New Zealand who have both been quite unavailable for long periods of time. In those situations it has been even more helpful to be two people on the same project.

The project is about something as exciting as moving containers. When a container ship arrives at a harbor, the containers it brings with it are often paced in a terminal where they will be located for storage for a while, until they need to depart again, either via trucks further into the country, or continue with another ship. In the meantime (between arrival and departure of the containers) it is important to have a plan for how the containers should be moved around at the terminal: A container which is about to leave must not be buried underneath a lot of other containers since the crane can only pick up the ones placed at the top of a stack. It is important to spend as little time as possible to move the containers around; the cranes are expensive to use, especially if they have to be controlled manually, which is still the case at many terminals.

*Containers at Auckland Harbor – can you imagine anything more exciting?*

The last couple of years research has been done to try to solve the problem using OR methods. In 2008, Louise K. Sibbesen, a Danish Ph.D. student from DTU, wrote her doctoral thesis about the problem. Her approach was to use a so-called metaheuristic, a method in mathematical optimization which often results in “good” solutions without guaranteeing that the found solutions are also optimal. It is often acceptable to find just “good” solutions (measured in e.g. profit) to many of the problems which occur in real life. These solutions can still easily be better than what a human being would be able to find manually. Even if the solution is “only” on par with the ones that can be found manually there is often a certain value in having a computer program being able to compute these solutions automatically. Often it can be done much faster and the labor cost can be saved. In my bachelor thesis I (and two other people) developed a heuristic to help plan which teachers should be assigned which class to teach during a school year in the high schools around Denmark. Already before the thesis had been handed in, the heuristic had been implemented in the commercial product Lectio, used by the majority of Danish high schools. Later we were awarded the prize for best bachelor thesis at DTU by McKinsey & Co as I also mentioned on this blog last semester.

Optimal solutions are of course always attractive. Therefore, a student from The University of Auckland, Antony Phillips, decided last semester to look at the problem once again but from a different point of view. He wanted to prove that there was another approach to solving the problem which, possibly, could lead to optimal solutions in the future, without using heuristics. Using heuristics is in some circles seen as “cheating” since they don’t necessarily lead to pure, perfect solutions. He wrote about the subject in his Fourth Year Project which is kind of similar to a Danish bachelor thesis. Here he found a number of different mistakes and deficiencies in the original doctoral thesis by Sibbesen.

Skott and I are now trying to carry on the torch with our project. Our goal is to get closer to be able to solve real life sized problems to optimality. We spent the first month on going through the two previous theses about the subject and did find some more mistakes and deficiencies we found it necessary to take into consideration in the mathematical model. The ideal for a mathematical model for problems such as the one we are dealing with, is for it to follow a specific structure which makes the problem linear. Basically this means that there exist certain rules for how the mathematical formulas describing the problem can be set up. The special thing about linear programming (LP), as it is called if the formulation follows this structure, is that there exists certain solution methods (The Simplex method), which can be exploited. These are methods which run extremely fast and have been perfected through many years. Therefore it pays off to comply with these restrictions, even though it also means that a certain amount of thought is required to formulate these models. A mathematical model which describes an LP problem consists of two parts: An *objective function* plus a number of *constraints*. The objective function describes the goal for the optimization, which in our case is to minimize the use of the crane at the terminal. The constraints define what is meant by a feasible solution. For instance, our mathematical model contains constraints such as “a container can only be picked up if it is on top of a stack”, “a container needs to be at either exactly one position or be moving at any given time” and “a container needs to arrive to/depart from the terminal at the times specified by the given data”.

After we had spent some time looking into the previous theses we created our own model which corrected the mistakes we found in the original ones. At the same time the model is now more realistic since it captures more details of the problem as it exists in real life. For example the model now constraints how fast the crane can move, not only when it carries a container (which was the case in the original models) but also when it doesn’t carry anything at all. We have also implemented a solution technique which uses a “rolling time window”. Instead of trying to take **all** containers into consideration which might arrive or depart within the planning horizon, we cut down the focus to be a subset of the full period. In container shipping there often exists great uncertainty about the precise arrival and departure times for the containers. Often precise information doesn’t arrive until fairly close to the actual arrival or departure of the containers themselves. Therefore it doesn’t make sense to make big, detailed plans for every single container since there might very well arrive new information later which can completely ruin the meticulously laid plan. What we do instead is to focus on containers which are about to depart or arrive in a given period. The placement of a container which doesn’t depart until much later is fairly irrelevant as long as it doesn’t create conflicts with a container that is actually about to depart which need to get to the top of a stack so the crane can pick them up. The solution technique we use thereby focuses on the containers which are about to depart within a foreseeable future (a day or two). It is a continuously running solution process which moves the time window focused on as time goes by. Not only does this solution technique represent the reality much better than an assumption about all information being known from the very beginning; working with smaller time periods also makes the problem significantly easier to solve, resulting in faster solution times.

With this method (and a number of other clever techniques) we have accomplished some pretty good results so far. A problem which took 3000 seconds to solve previously, after Philips’ modifications to the original model, now takes about 50 seconds to solve. That is a fairly good improvement. Our program cannot yet solve problems so big that they could represent real life cases, though. Especially Skott has also spent a good deal of time on implementing a **G**raphical **U**ser **I**nterface (GUI) from which I have included a couple of screenshots below.

*Our program can be used to create random data sets.*

*The solution process.*

*A Gantt-diagram which shows the solution computed by our program.*

*3D visualization of the solution.*

*Example of a container being moved.*

And that is pretty much our project. We are supposed to hand it in in the beginning of August and present it a couple of weeks after. We will be using the last available time to test our program, discuss the results and make some conclusions on our formidable work.

**What these headlines are doing in this blog post**

Pass… Maybe it is a weak attempt to make this text, full of technical terms and container talk, seem more clear and less boring. I think I failed (but at least the container pictures are colorful).

*:*Containers, DTU, Post with pictures, Skott, Studies, Thesis, UoA, Wikipedia, Other blogs more...

## Part 1: Conclusion on studies

by Jonas Ahmt on 20 December 2009, under Julekalender, New Zealand, UoA

I did not only go to New Zealand for the sole purpose of experiencing the country. I also went there to study. I will use the first part of the “julekalender” to wrap up my studies in New Zealand so we can move on to something more interesting afterwards. Therefore this post will be fairly short.

I think I did mention that my exams had gone OK and my grades seem to confirm that. As far as I know (once again wonderful Wikipedia has been an immense help) you can pass a course with nine different grades (the letters A, B, and C with +/- variations) and fail it with either two or six different grades: D and E – I’m not sure whether or not they use +’s and -’s for the failing grades. It seems like a lot to have six different ways to fail but I must admit that I have never really thought much about the grades in that end of the scale.

I ended receiving three A’s and one A+. I got the A+ in my only undergraduate course which corresponds pretty well with the fact that I’m regarded as a post graduate student in New Zealand since I’m on my fifth year of my studies. I think I’m supposed to be pretty happy about those grades, especially since I don’t feel like the workload during the semester has been very large (no books to read for any of the courses and not that many assignments to hand in). Only in the last weeks of the semester did I have to focus intensely on the studies.

Now that I am writing about my studies I want to mention that my bachelor thesis which I wrote two fellow students (Johan Musaeus Brrun and Martin Lundberg-Jensen) in the (Danish) spring of 2008 has been awarded the best bachelor thesis in 2009 of the big consultancy company McKinsey & Company. We couldn’t participate in the 2008 competition since we didn’t defend the thesis until late August 2008 which meant the thesis was considered as finished in the school year 08/09. Only theses students themselves had chosen to submit to the competition were considered but I still think it is a pretty nice award to receive. Besides the honor we also received 15,000 DKK (about 4000 NZD) to split between us. Unfortunately it was only Martin who could be present at the award ceremony since both Johan and I was studying abroad (Johan in Sydney, Australia, and I in Auckland, New Zealand, as some of you may have noticed at this point).

I promise that this will be the last I write about my studies for a while (unless people protest and demand more about that particular subject). Next post will be about my travels in New Zealand (finally!).

*:*Money, Studies, UoA, Wikipedia more...

## Exams

by Jonas Ahmt on 12 November 2009, under New Zealand, UoA, Hiking

It has been a while since I last wrote on my blog. It is not because nothing is going on down here, though. The culprits are my exams which I have needed to focus on for the last couple of weeks.

Last time I wrote was the day (or night) before my birthday which went well. Not only did I receive some gifts, we also had a small party to celebrate my great accomplishment of having survived 23 years of life. The weather was terrible the most of the day but I guess that is because everything is acting the opposite way down here (the water in the toilet spins the wrong way when flushing, people drive in the wrong side of the road, it gets colder when you go south etc.). With that in mind, the bad weather on my birthday must mean that I have been behaving quite well this past year (this is one of the few cases where I can definitely agree with the weather). Now that we are talking about the weather (or rather, now that I am boring people with it) I can mention that it definitely starts to feel like summer now. We still have the occasional days with bad weather which makes me even more sad than normally since it can sometimes completely kill my beloved Internet. It seems so weird to have Internet which depends on the weather but that is at least my theory on how the speed can go from “modem like” (on the good days!) to “non-existing”.

*I got flowers from the two Americans Josh and TJ*

Most days the weather has been pretty nice, though, and we have utilized that to have a few barbecues. The most recent of these was last weekend where David Ryan, the professor who has previously had us for dinner, had invited us for a late lunch barbecue at Waiheke Island, one of the small islands close to Auckland. Here Ryan owns a small summer cottage (or “badge” as I learned it is called in New Zealand) which is soon to be demolished in order for a proper house to be build on the ground. The idea is that he and his wife will move there when the new house has been constructed. That is quite understandable; the island was a lovely place with easy access to the beach and great views. Not a bad place to settle! Unfortunately I had forgotten my camera so you will have to take my word for it.

My biggest “adventure” took place a couple of weeks ago. Skott and a couple of my other friends down here have taken up surfing and had planned to go on a surf trip for a couple of days to celebrate the end of lectures. I have never managed to become excited about the prospect of surfing so I could instead look forward to some days all alone and sad (since no one wanted to go with me to Fiji or Tonga). At least that’s how it seemed until the night before Saturday (same day as my lectures ended) where I was offered to go on a trip to Tongariro the following day. The plan was to go down there Saturday and spend Sunday on the Tongariro Alpine Crossing which is known to be one of the very best one day hikes New Zealand has to offer. I can easily see how it has achieved this reputation: It was an amazing trip which went up active volcanoes, snow covered mountain tops, hot springs, beautiful lakes and ending in “rain forest” style surroundings. The highest point was Mt Tongariro at 1900 m above sea level and needless to say the view was fantastic from there. It was a long hike (approximately 9 hours, 23 km) but luckily I did not twist my ankle until after the steepest ascents. However, I did have to walk the last three hours with a somewhat sore ankle after having twisted it on my way down but that’s (my) life. I can also mention that Mt Tongariro along with e.g. Mt Ngauruhoe (an optional side trip of about three hours you can do if you think you have the time – we didn’t) were used as settings for Mount Doom in the Lord of the Rings movies.

As I mentioned in the beginning I do spend most of my time studying for my exams at the moment. Today I have had my second one out of a total of three. I have done OK in both of them although I don’t think I have answered everything 100% correctly in any of them. My last exam is this Saturday which I am of course looking forward to. Afterwards I am going to the South Island for some weeks until I leave the country the 13th of December. I’ll spend a couple of days in New York and then return to the cold and dark Denmark.

*:*Ankles, Birthday, Exams, Internet, Me complaining, Mountains, New Zealand, Snow, Studies more...

## Nothing new

by Jonas Ahmt on 15 October 2009, under New Zealand, PSV, UoA, Hiking

It has been awfully quiet on my blog recently and I know a lot of people must fear that something has happened to me. I can understand that, I mean, we have had a couple of tsunamis here. In this connection I would like to thank everybody for not sending me a single concerned message. It is nice to know that you are loved… I hope you, my dear reader, catches the double sarcasm used in the remark above but down here I have learned that not everybody gets my humor which probably does not give the right image of me as the fantastic guy that I really am.

But what has happened these last couple of weeks since I have been so busy that I haven’t been able to look after my exciting blog? Not much, actually. After the break there has been a bit more focus on the school work but it is not too bad. I have already completed one course by giving a single presentation about an article that proved to be completely wrong (I did suspect that when I read it but might not have been too clear about this in my presentation). In my other courses it is going pretty well also (thanks for asking), at least I have gotten full marks in all my assignments (although I have received no extra marks for the new ones as I did in my first assignment), except for one where marks were deducted since I hadn’t been able to fit an introduction and conclusion into an assignment which was limited to three pages.

To illustrate how little is going on down here at the moment I will now tell you about me and cleaning (I could also call it “me and the encounter with other cultures” but that would make it sound much more thrilling than it actually is). I do have a couple of places where I don’t represent the typical Danish man. Some might call me a nerd; others call me “special” which I have chosen to take as a compliment (you only get the compliments you claim yourself – at least in my experience). One of the things that makes me “special” is apparently my attitude towards cleaning or at least washing-up. Apparently it is quite unreasonable to ask your flatmates to clean their pots, pans, dishes etc. after they have used it. Instead, this is a task that rests on the next person who wants to cook something (i.e. me). I make it sound worse than it is but after a couple of discussions with my flatmates about this matter I have concluded that I must be wrong – although I have still not realized why (this might be one of the drawbacks of living with three girls, I suppose). I guess I will learn why at some point.

A couple of weeks ago the flats in PSV were inspected. They were going to check if we kept our flat in a nice condition. This was a good excuse to do some proper cleaning which was definitely needed. I will let the picture of the area behind the oven speak for itself, although I can mention that the top of the shelves didn’t look much better.

It is funny that the only one who seems to agree somewhat with me down here when it comes to cleaning is the other Dane in PSV, Skott (or, I think another Dane also lives here but I never meet her). When I was studying in the US I encountered the same phenomenon. The kitchen was extremely gross and useless. One of the first things us four Danes did when we moved in was to clean the disgusting fridges. When we spoke with the international office about the matter later on they mentioned that it was weird that it was always Danes who complained about the lack of cleaning – as if they had encountered that exact problem before without doing much about it. Cleanliness is apparently a very Danish thing which I haven’t valued enough so far.

That must be enough complaining for now. To continue on a more positive note I can mention that I once again have become quite good at twisting my ankle. My left foot seems particularly happy to place itself at wrong angles at the moment, which is usually followed by delightful pain. One of the times I twisted my left ankle was on a new trip to Waitakere Ranges, which I also visited one of my first days down here. This time we went on another hike which wasn’t as impressive as the first one to Karekare. This was probably because of the fog which made it impossible to enjoy the nice views from the hilltops we climbed. The most exciting part about the hike was probably the last half hour where we almost got lost. The path we were supposed to follow was marked off pretty badly. Or to be more precise, the markers were put in one direction, the path was continuing in another. We chose to follow the path even though it kept going upwards and it started getting pretty windy. It was at this point that my left ankle decided that it would be perfect timing to twist. And so it did, just as we had reached the top and had started to climb down, still not knowing if we were on the right path. Very exciting last part of the hike indeed.

The other times I have twisted my ankle have been while playing squash. When you live in one of the student accommodations provided by the university you get free access to the university’s recreation centre which includes two squash courts. I often play against my American friend, Josh, whom I beat regularly – it is always fun. A tip for pros: Don’t step on the walls since this is when you can most easily twist your ankles. I am sure that it takes professional squash players much longer to learn this lesson than the week it took me to realize it. Of course it can be debated whether or not I have learned it yet, seeing as I today, many weeks after the first incident, chose to step on a wall again…

I hope that the above is enough about “everyday life in NZ” as was requested by my readers (or at least one) – I can’t really come up with much more ordinary things to bore people with.

I will try to improve my segues for my later blog posts so the paragraphs will not be connected by me complaining and talk about my bad ankles.

But now it is my birthday! And with that, I will end this post (yeah, I should try to improve the way I end my blog posts also).

*:*Ankles, Birthday, Cleaning, Me complaining, New Zealand, Segues, Squash, Studies, USA more...

## My studies

by Jonas Ahmt on 28 September 2009, under New Zealand, UoA

I will try to see if I can’t make my blog posts a bit more manageable in the future, i.e. shorter, not necessarily less filled with boring nonsense, as this post is probably a good example of. Except that this post is also way too long, which means its actually the opposite of what I want to achieve. Well, next time, maybe…

So far my blog might have given the (wrong) impression that the only things I do down here is climb through caves, go on hiking trips, go to the beach, make horrible attempts at climbing, go to quiz nights and go to the movies. While I certainly have done that stuff a lot, I actually also study down here which is lucky since it is one of the primary reasons for my trip to New Zealand.

As I have mentioned earlier, I have been so lucky/good/studious (the last word my dictionary just taught me) that I have received scholarships from Otte Mønsteds Fond, Knud Højgaards Fond and Oticon Fonden which I am certainly very grateful for. Most of that money has already been spend on accommodation, the trip down here and the usual costs of living. Therefore I was certainly not sad when I a couple of times the past weeks was told that I had received yet another couple of scholarships:

Frk. Marie Månssons Legat (10,000 DKK = 2,750 NZD)

Civilingeniør Frants Allings Legat (10,000 DKK = 2,750 NZD)

Of course I also want to thank these foundations (although nobody associated with those read my blog – especially not in English) since they make my stay and my studies so much easier down here. As I said, I *do* study also, and therefore I thought it would be a good idea to give a small description of my classes down here. This way, people might get a better idea of what I am actually studying.

**Applied Modelling in Simulation and Optimization**

This class (or “paper” as they for some reason call them here) is actually an undergraduate course but we (Skott and I – we are taking all the same classes down here) chose to take it anyway since it among other subjects contained an introduction to simulation which we thought sounded pretty interesting. The focus is put on *application* and we therefore only have one hour of lecture week, while we spend three hours in labs doing exercises and assignments.

The course started out with some basic mathematical modelling on computers which Skott and I both have a good deal of experience with. It is basically concerned about taking some kind of problem which needs optimization after some performance measure and constrained by some parameters, put it into a computer and get the optimal solution. In the project we are going to hand in at the end of the semester, we are supposed to formulate a model which can set up a network using hubs and switches so that each component can send the correct amount of data to another component in the network. The task is to create this network at the lowest cost, i.e. using the cheapest possible cables, and fewest number of hubs and switches which can still support the required data flow. It has actually proven to be a bit harder problem than we first thought but in the end we did create a model which seems to take everything into account and also seems to work.

As mentioned, the course also contains an introduction to simulation which was our main reason for taking it. Simulation can be used to, yeah, simulate situations which do not necessarily have a specific, deterministic outcome but is instead dependent on stochasticity (randomness). In our project, for example, we are going to test our created network by simulating computers which send random amounts of data to each other in random time intervals in order to see if our network can actually support this.

**Advanced Simulation and Stochastic Modelling**
This class is actually the successor to the class mentioned above since it contains advanced simulation. In the beginning it didn’t seem like the smartest idea to have chosen to jump directly to the “advanced” class but now that it is over and we have had the short introduction to simulation in the other course, most of it actually makes a lot of sense. A lot of the first part of the course have been about how to generate random numbers on a computer which can be done in a lot of different ways depending on the “type” of randomness is connected to the number. It is actually not as easy to create a random number as one could be fooled to think.

We have handed in a single assignment in the class where we were supposed to calculate the probability of being dealt a full hand in computer. This was done by simulating the dealing of cards a lot of times and then seeing how many times the first person was dealt a full house. We were also asked to explain how to create a random number with a certain probability distribution. The last part of the assignment was to explain how one could estimate how much water there would be in an entire region if it was known that tests in small areas showed that there on average could be found two water tables with depth and size connected. While the first two questions seemed straightforward, the last part was a bit tricky since it was very vaguely formulated. We were also told that it did not have a specific “right” answer. I did give a suggestion for a solution so now I’ll just have to wait and see how it is received.

The second part of the course is about stochastic modelling. It is mathematical modelling where you work with probability distributions instead of fixed numbers. The classical example is the Newsvendor problem where a newsvendor can buy newspapers early in the morning for a certain price, sell them with a profit during the day and sell the leftovers (if any) at a loss in the end of the day. The problem is to find out how many newspapers the newsvendor should invest in in the beginning of the day in order to maximize the expected profit. It is not easy, though, since the profit depends on how many newspapers can be sold (i.e. the demand) which is not known for certain – it is instead a “random” number with a certain probability distribution. This should be taken into consideration during the solution process.

**Research Topics in Operations Research 1**
This class is divided into three parts. The first part was about non-linear optimization, mostly without any constraints. This means that the most of this part of the course was about how to find out where a complex mathematical function has its maximum or minimum value. I have had a couple of courses like that at DTU but the approach here was a bit more theoretic than what I have been used to. I must have understood some of it anyway, though – at least if you are going to take the assignment in that part of the course as any kind of indication. I received 25 out of 20 marks for the assignment! The lecturer sent out an e-mail where he told us that some students had made an outstanding report and he wanted to reward that with some bonus points. I was apparently one of those students.

The second part of the course, which we have just finished this week, was about advanced linear optimization. A lot of the optimization problems you encounter in the real world can be formulated linearly and therefore there have been done a lot of research on how to solve this problems to optimality as fast as possible. This part of the course introduced a lot of different methods which can be used to solve those problems. Some of them I knew already, others were completely new to me. I feel I have really learned a lot in this part of the course.

The last part of the course will be about game theory (among other things). It does not have anything to do with video games, however but is instead concerned with finding solutions to problems with several interest groups. A classical game theoretical problem (Prisoner’s Dilemma) goes like this: Two suspects are taken in for questions by the police. The two suspects are put in separate interrogation rooms and offered a deal by the police: If one cooperates while the other remains silent, the former will be released while the other has to serve the full sentence, 10 years. If both of them talks they will each get 5 years. Do they both remain silent they will receive a sentence of six months.

Clearly the two suspects will get the least amount of time behind bars (collectively) if both remain silent – this will result in a total of one year in prison compared to the 10 years in total for any other solution. The dilemma is that if each prisoner is only concerned about himself, he will co-operate with the police: No matter what the other guy chooses to do, this tactic will result in less jail time for the first person – either from 10 years to 5 (if the other talks), or from six months to no time at all (if the other remains silent). Both prisoners will however think like this, and thereby end up in the so called Nash equilibrium (it is John Forbes Nash who is portrayed in the movie, A Beautiful Mind – he had a big influence on the development of game theory) where they will each be put behind bars for five years.

This is one kind of the problems game theory deals with. As far as I know it is mainly used in economics but can also be used in other fields.

**Research Topics in Operations Research 2**

This class was originally supposed to be cancelled but “unfortunately” they didn’t get to take it down before people had already signed up for it (including Skott and me). Since so students had signed up (six in total) the course was changed to function more like a seminar type course. The first part of the semester we didn’t have any lectures and we were just given a paper each. They are all about multi objective linear programming – optimization of problems where you try to look at several (conflicting) goals at once, e.g. a factory which wants to minimize cost and maximize CO2 emissions. We were told that we would get an introduction to the subject after the mid-semester break so we didn’t really think much about it before last week where we had our first lecture. Here we got a bit of a shock when we told to begin the presentation of our paper the next week. It so happened that I was the first to get the honor to hold a 40-minute presentation about 16 pages of hardcore math which I had had for several weeks and not understood much of. Luckily it was postponed for a week the day after so this weekend has been spend on trying to understand the article so I can make a presentation for the rest of the class and be prepared for questions which the lecturer has promised there will be lots of.

That is basically all my courses but I would also like to make some general notes about studying here. There are a few points where it is completely different from DTU. For instance are all my classes pretty small, from 6 to approximately 25 students but of course I have also encountered a few classes like that at DTU, especially the last couple of years when I have taken more specialized courses. I am, however, not used to having all my courses in the same two small class rooms instead of lecture halls.

Things seem a bit less structured here than what I am used to from DTU. We were pretty surprised the first day when one of our lectures was suddenly moved to another time slot without warning and that almost all our lectures tried to reschedule the classes in the first days. We had spend lots of time trying to figure out which courses we could take which would not have any time clashes. We had even had to ignore some really interesting courses since they clashed with others. Therefore it was pretty frustrating that it was suggested that the times were changed already from day one. It all worked out in the end, though.

I am not used to the idea about changing lecturers during a course but almost all my courses are split into smaller sections with different lecturers. I don’t really know what I prefer; on one hand it seems like you can get through more stuff in this way but on the other hand we don’t really get to go into as much depth with a single subject as we do at DTU.

I also know the days of my exams now: 9th, 11th and 14th of November. It is going to be interesting since none of them allows any books or other types of aid. I don’t think I have ever had an examination like that at DTU but I have gotten the impression that this just makes the exams a bit easier since they cannot ask us questions about stuff we are not supposed to be able to memorize. But of course that is impossible to say until the exams are over. The lectures end the October 23 which gives us about two weeks of study period before the exams. There is a possibility that one of those weeks will be spend on Fiji for instance – but I don’t know that for sure yet :)

And that’s it for now. As usual it ended up being way too long but I’ll try make it shorter next time.

*:*Exams, Fiji, Mathematical Modelling, New Zealand, Operations Research, Studies, Scholarships more...