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The Container Positioning Problem

by 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

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 Graphical User Interface (GUI) from which I have included a couple of screenshots below.

Problem generation.png
Our program can be used to create random data sets.

Solution process.png
The solution process.

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

3D visualization 1.png
3D visualization of the solution.

3D visualization 2.png
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).



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Part 4: Abel Tasman, Pancake Rocks and Greymouth

by on 24 December 2009, under Julekalender, New Zealand, Hiking

To try to make the text a bit more manageable for those who are in a hurry in these nice Christmas times I have introduced a footnote system – just look for the asterisks. Of course it would be nice if I remember to continue using this system in my later posts but I can guarantee nothing. For those who are in an extreme hurry are here some more alternatives:
1. Only look at the photos and maybe the belonging captions.
2. Read Skott’s version of the trip (often way shorter).
3. Don’t read blogs at all.

Marahau is placed by Abel Tasman National Park, New Zealand’s smallest national park covering an area of 225.3 square kilometers. The reason we had gone there was due to rumors about it being a fairly pretty area and I can indeed confirm these rumors now. You can enjoy the nature in Abel Tasman in different ways: Since the national park contains a fairly long stretch of coast it is very popular to sail around in kayaks. However, we chose to go on a small hike instead on the Abel Tasman Coast Track, one of New Zealand’s nine Great Walks*.

Luckily it was no problem for us to book room at a camp site on Abel Tasman Coastal Track and we could therefore start out on a hike which ended up taking seven hours (25 km). As the name of the track indicates the route took us along the coast which meant a nice view over the beautiful azure water most of the time. At some points the route did bend away from the coast which changed the landscape to a dense rain forest, similar to something taken directly from Jurassic Park. We had to cross specific points at certain times in order to avoid the high tide. The water levels could change with up to six meters at some points so we had to get to the tidal crossings at a proper time before high tide.

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Ready for seven hours of hiking.

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Our first tidal crossing. The bridge may give an idea about how high the water can be at high tide.

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A small example of our view most of the day – notice the many kayaks.

In general there are no dangerous animals in New Zealand. However, the country is infested with sandflies**. The camp ground in Abel Tasman was my first encounter with these beasts (but certainly not my last). Luckily I escaped with only a couple of bites on my feet – others in the group were not as lucky.

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This is unfortunately the best photo I have (so far on the trip) to illustrate what sandflies are capable of. You can see a couple of bites on Skott’s feet although I must admit that it doesn’t seem like much at this picture. What the photo further shows is what happens when Søren gets a camera in his hands – lots of photos of random stuff.

We did not plan on walking all of Abel Tasman Coast Track’s 51 km – it is described like a 3-5 day’s walk. Instead we had planned to tramp for two days, 35 km in total. The reason we had to go 25 the first day and only 10 the second was another tidal crossing. From where we stayed the first night we had a two hour walk to a part which needed to be crossed before 9 am unless we wanted to wait until late afternoon before the crossing was accessible again. Therefore we got up early and started walking in order to get there in time. When we arrived at the critical point it was a bit anti climatic since there was no water nearby at all. However, half an hour later it would have been impossible to pass. Our fairly short walk on this second day was rewarded by a couple of hours relaxation on the beach before we were picked up by a water taxi which brought us back to Marahau. On this trip back we saw a few sea lions playing around in the sun.

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Tidal crossing.

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Sea lion enjoying the sun on a rock.

Afterwards we went back to Nelson where we stayed in a funny hostel called The Palace***. We spent the night here and continued south the next day (now we have gotten to Saturday of the first week in the story which spans almost four weeks in total). We went along the west coast, a very sparsely populated area of New Zealand which was easily seen on the amount of cars we met on the road. We stopped shortly in Punakaiki where we took a quick look at The Pancake Rocks (see below) before we continued to the “big city”**** of the west coast, Greymouth.

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Skott shows what makes the Pancake Rocks so special – the taste! A lot of people mistakenly think it is due to their shape…

We spent a couple of days in Greymouth. After the first night, Borghild, kristian and I went horseback riding in Punakaiki while the other three went surfing. While the horseback riding was fine the surf trip was apparently more action packed. Not due to crazy waves or anything else like that but due to two visits to the hospital. At first Søren damaged a sinew (I think it is called) in one of his fingers while trying to correct his bathing shorts under his wetsuit. When he returned from the hospital (with some sort of splint on his finger which had to stay there for six weeks) he could pick up Skott who, after a couple of minutes of surfing, had managed to cut up his foot with his surfboard’s fins. Caroline was the only one who got to do a bit of surfing that day.

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Kristian, Borghild og me on the horses which we were let around on by a Swedish and a German girl (random info once again).

The second day we went kayaking, once again in Punakaiki. It was more fun than I had expected, especially because the river was a bit more aggressive than I thought in the beginning.

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The kayak rental place had some amazing 80-90’s cloth that we simply couldn’t resist putting on. In the confusion caused by my extreme enthusiasm I managed to throw away my watch which I miraculously managed to get back a couple of weeks later (now I at least have one loose thread to pick up on in a later post).

That’s it for this post (unless you haven’t read the footnotes yet and wish to do so. You should have done so as the references to them appeared in the text – maybe I should have mentioned that in the beginning but that is how I usually read footnotes so I didn’t think it would need an explanation). Notice how I have not spent four (fairly long) posts to almost get to the same point as Skott described in a single blog post about a month ago. But you have (among other things) seen a photo of a ninja in Wellington – Skott hasn’t been able to deliver anything like that on his blog!

For those who just can’t get enough are here the mentioned footnotes:
*About The Great Walks:
The Great Walks are routes through some of New Zealand’s most beautiful areas. As a lot of natural areas in New Zealand they are maintained by New Zealand Department of Conservation (DoC), who also runs the huts and camp grounds on the walks which often take 3-5 days to complete. If you are interested in a close encounter with New Zealand’s gorgeous nature these are the walks you should go on. Unfortunately they are so popular in the summer periods and the space in the huts and on the camp grounds so limited that you often need to book far in advance to be able to spend several days on the tracks. More than a month before our trip, Skott and I had talked about doing the Milford Track, which literally has gotten the nickname “The Finest Walk in the World”. All huts on the walk was booked far in advance, though, so it wasn’t possible for us to do that trip. Some may recall that I wrote about the Tongariro Alpine Crossing which I walked a while ago. That was actually my first encounter with one of The Great Walks since this one day trip is a subset of the four day Great Walk, Tongariro Northern Circuit.

**About sandflies:
Sandflies are small devils which made me miss the cute small Danish mosquitos which seem like the most lovable pets in comparison. Sandflies are the most annoying insects I have ever met: They attack in giant mobs, you can see and feel the after-effects of their bites for several weeks, more sandflies are attracted if you start scratching the bites and then they seem to especially enjoy Scandinavian blood for some reason. The Maori people believed that the sandflies were introduced in New Zealand by an angry god who was tired of looking at the lazy people stand around, enjoying the beautiful nature surrounding them. Sandflies behave in a peculiar way: If keep moving they won’t touch you but as soon as you stand still they attack you, 1000’s at a tie. They are therefore a very effective method to keep people moving.

***About hostels in New Zealand:
During our travels in New Zealand we did encounter a couple of peculiar hostels. A lot of them were “special” due to their shape, furniture, decoration and staff. The palace was for example a giant villa with enormous rooms and bath rooms which were shaped and decorated in typical Hundertwasser style (you do remember the famous public toilets, right?), changed into a hostel which was even fairly cheap to live in. Later on I might put up a post with photos from a couple of the hostels we visited during our travels.

****About calling Greymouth a “big city”:
“Big city” is here in quotes since an area with a population of about 14k wouldn’t be called that in many countries. Still, it is the sparsely populated west coast’s biggest city. In the middle of the 1800’s gold was found on NZ’s west coast which of course attracted a lot of people to the area. When the gold reserves had been emptied out most left again (a decision which was probably made easier by the awful weather – there is a reason the area is nicknamed “Wetland”). Greymouth is now one of the few proper cities left in the area. Less than 1% of NZ’s population lives on the West coast which covers an area of about 9% of the total area of New Zealand according to my Lonely Planet book. Don’t say that you do not learn anything from reading my blog!

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The Internet is slow in New Zealand

by on 14 September 2009, under New Zealand, Other blogs

I know a lot of people out there are just sitting and waiting for a new blog post from me – they’ll need to wait a bit longer. My two weeks of vacation from the university are about to end. During those two weeks I have been traveling around which of course have resulted in a lot of photos. Right now I’m trying to upload them to Flickr and I really don’t want to put my posts about my trips up before I have some photos online to make them just a bit more interesting to skip through. Of course I could just begin by uploading the couple of photos I intend to post directly on the blog, but that would be more cumbersome than just waiting for iPhoto to finish its uploads.

It will probably take a couple of days for all the photos to be uploaded since my internet is extremely slow. The Internet in New Zealand is extremely slow. I know it’s an extremely nerdy thing to say but having proper internet is actually one of the things I miss most about Denmark. I’m really looking forward to go back home and once again be able to download my video podcasts in HD without having to wait several days and be worried about some bizarre limit on data use.

And NO, it is not causing me to spend my time on something more sensible. On the contrary, the slow internet makes me so much more inefficient since it is not possible to quickly look something up and afterwards continue with something else. I have never spend so much time looking at a “Loading” message in the address bar of a browser as I have been doing down here.

I could continue complaining (e.g. Skype and Slingplayer are almost useless down here) but I think you’ve got my point: Exciting news about my mid-semester break will follow in a couple of days. And now you also know why the title of Josh’ blog is so perfect.

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Money problems

by on 25 August 2009, under New Zealand, PSV, Other blogs

The following is probably one of the most serious posts so far.

I am usually quite good at handling my finances if I may say so myself. For my stay here in New Zealand I had also drawn up a fine budget and I had planned that it should be financed by a bit of savings, a scholarship from the government paying the tuition fee and a couple of other scholarships. Before I left Denmark I had received a fine amount of money from scholarships from the following foundations, which I want to take the opportunity to send a kind thought to:

Otto Mønsteds Fond (12,000 DKK = 3,370 NZD)
Knud Højgaards Fond (9,000 DKK = 2,525 NZD)
Oticon Fonden (7,000 DKK = 1,960 NZD)

These scholarships was a contributing factor to a nice big plus on my bank account a couple of weeks ago. Therefore I was naturally a bit surprised when I logged into my bank account via the internet and saw that most of my money had suddenly disappeared. I do spend a bit of money down here but I still had trouble explaining a small hole of about 14,000 DKK (approx 4,000 NZD).

It turned out to be due to some weird transactions to (among other things) WWW.NIKESTORE.COM as it was nicely printed with capital letters in my account history. I told this to my bank which of course closed my Visa card – the only card I brought with me to New Zealand. So now I don’t have any way to get hold of what is left of my money, and I’ll have to borrow from friends which is not quite optimal, contrary to what some people might think. It doesn’t help that Skott and I decided to buy a car yesterday for which we’ll have to pay tomorrow. I was supposed to get the rest of my part of the cash payment today but the ATM declined it.

I have now opened a bank account here in New Zealand which I can transfer some money to, a new Visa card should be on the way from Denmark (although it will probably take some weeks to get it) and PBS (the company that handles credit cards transactions in Denmark) has been contacted so that I can hopefully get my money back soon. In other words: It’s all going to be OK, but I think I would rather not have had this particular experience.

To end on a positive note I want to continue referring to other blogs. This time it is my American friend, TJ, who has started a blog which can be found at http://tjsnewzealandadventure.wordpress.com/. TJ is yet another of The Village People (i.e. he also lives in Parnell Student Village – PSV) and his blog already contains extremely exciting posts about his shopping trips to the local supermarket, Foodtown. And if that is not positive enough I can mention that I tomorrow am going to watch Quentin Tarantino’s newest masterpiece, Inglorious Basterds, which I am really looking forward to. It is a well-known fact that the guy is a genius and I have only heard good things about the movie so I’m sure it is going to be a successful trip to the cinema.

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