A Better Way to Solve Problems – with Computers

I used to be, and I probably still am, a little naïve about what it is possible for a person to achieve in this world. So I dreamt that I might be able to help the world when I entered the work force. I first tried this helping in the scientific world (at Culham Laboratory). But I soon found out that, as a mathematician, I was very limited in the degree to which I could help. So then I tried to give industry the great blessing of my help.

Much of the work I had done in my PhD was oriented towards Operation Research. So I was well qualified to work in this field. I joined Caltex Oil and, within a year, I was the manager of a small team of four people with me as the leader. So that was OK.
            But I found out was that all that the management really wanted me to do was to add some fine looking mathematics to the decisions they already wanted to make themselves. I, as quietly as possible, avoided doing this dubious task. Instead I found out that Caltex ran a large terminal at Banksmeadow, where several complex scheduling jobs were carried out. These jobs were too complex for management to interfere with. So I could try to solve these problems.
            The three main tasks were:

            Scheduling the pipelines
There were four pipelines that took the various products from the Caltex’s Refinery across the bay to this Banksmeadow terminal. These pipelines needed to be scheduled between the various products so that the cleaning costs were minimised, and the terminal didn’t run out of any product.

            Scheduling the Rail Tank Cars
About twenty rail-tank cars (owned by the company) arrived at the terminal over-night. These rail-tank cars needed to be scheduled out in the morning to the various country terminals, so that these terminals didn’t run out of product.

            Scheduling the tank-tucks
The company had a fleet of about 30 tank-trucks and this fleet needed to be sent out every day so that the more than a thousand outlets, in the city and close areas, did not ran out of any of the various products.

My team worked on all three of these problems. Each of these problems is quite substantial. But by far the hardest of these problems is the scheduling of the tank-trucks. So this is the problem that I will talk about here in detail.

This is an example of the Travelling Salesman problem.

This problem is related to the well-know “travelling-salesman” problem, which is accepted as being very hard. But this Banksmeadow problem is much harder than this because: there are 30 tankers that need to be scheduled at the same time, there are more than 1,000 outlets that need to be considered, there was 4 products that need to be catered for, the company must forecast the usage of each outlet for 2 weeks ahead, and then the products must be dropped-off ahead of time – depending on how much space is left in the tankage of the various outlets. So this total problem is massive and difficult.

But, with practise, we humans become exceedingly good at solving problems such as these. There was an old truck driver at Banksmeadow who could do this job incredibly well. He, in his head, could remember the approximate tank levels and usage of all the outlets. From this knowledge he could schedule all these tank-cars remarkably well in only an hour or so. It was hard for me, with all my knowledge of operations research and using the most powerful computers, to schedule the trucks as well as he could.

To solve a problem such as this, we need to follow the natural way an experienced person actually solves the problem in their head. And then, using this general solution, we can solve the job on a computer. But, using a computer, we should get a better result because we would use more accurate figures to begin with and also we can investigate and evaluate many more searches.
There are three stages, which must be carried out in this process:

1)         A Costing Process
Firstly each of the trucks must be approximately costed per hour on the basis of: – how much they cost to buy and how useful they are. Then each of the outlets must be costed on the basis of: – how far away they are, how close they are to other possible outlets and the convenience and size of their various tanks.
          This is a difficult job. But an experienced person tends to learn to do this costing process almost intuitively. Using these costs (and the use of a map) it now possible to work out the value of a truck going from the terminal (or outlet) to an outlet, and delivering a certain amount of product to an outlet (which has sufficient room in their tanks – this assumes that our forecasting system does a reasonable job).

2)          Search Procedures
It is quite impossible, even using the most powerful computers in the current world, to calculate and cost all the possible searches. So we must choose a limited selection of searches.
          The selection of searches I chose was the following:
a)       I chose a few random sequences of the different the tank-trucks to schedule,
b)       For all these truck cases, I first chose to investigate a few of the outlets, which were lowest in product,
c)       After this first outlet has been filled, I chose to investigate a few of the outlets closest to this particular outlet.
Even after limiting the possible number of searches in this way, there will be a huge number of cases to consider. Each particular case will eventually come up this a final total cost. At the end we then, of course, choose the cheapest schedule to actually implement.

3) The costing process must be updated
This costing system must be updated in the usual supply and demand manner.
So, if a tank-truck is consistently not been used enough, then its cost must be reduced. Similarly, if an outlet is not being serviced enough, then its cost must be increased.
In the same way, if a tank-truck is consistently being used too much, then its cost must be increased. Similarly, if an outlet is being serviced too much then its cost must be decreased.
There are a variety of ways in which these costs can be updated. Some of these update methods can involve almost no extra work at all.

This total solution is a very complex process and, from this short discussion, you my reader will only have a very vague feeling as to what is going on. The point I want to make now is that this total problem can be solved on a computer – but it requires a large amount of difficult programming work. And it is very easy for a person to make a mistake and then produce a hopeless schedule.
          (As I am now in a wheelchair, I am now forced to use lifts a lot more. There are two connected lifts in Ashfield mall and a computer program runs these lifts. In scheduling there is well-known error called the “bus-congestion” problem. And this lift system always suffers from this congestion problem. But this bus-congestion problem is well known and it is very easy to overcome. So, if the people who programmed this system couldn’t even recognise a simple well-known problem like this, then it is horrible to imagine what they might do with a really complex problem like this truck problem.)

So now I hope I have persuaded you that this problem can solved on a computer but it is a difficult and complex task. But there is a further problem. This is that no one will thank you for doing this difficult task. The people who are currently doing the task won’t thank you because they actually enjoy using their current abilities. The management won’t thank you because they won’t understand the solution. Management should thank you for producing a more efficient system. But in practise managers prefer to buy more equipment and to hire more staff to increase their status. The last thing they want is to have set of clever guys working beneath them doing something they don’t understand.
          You might imagine that the academic world might appreciate your solution. But they won’t. Essentially this method does nothing new at all – it simply mimics what all people have to do in our supply and demand world. Also the most common accepted mathematical tool “Linear Programming” uses a costing system in a very similar manner. You will never be awarded a PhD for doing a mundane job like this.

But there is one area where people can appreciate a clever system. This is in the playing of games. Let me explain how this system can be used with respect to the following common games.

These 3 properties are up on the top-left.

You can apply this costing system to monopoly. If you study the financial details of all the various properties, then you will see that the light blue properties (Euston St, Pentonville etc) give the best rate of return (when they have hotels on them, which are easily affordable). You can then similarly evaluate the other properties (the stations and the 2 company utilities give the worst rate of return). With this knowledge you can increase your chance of winning considerably.
But I should warn you about taking this game too seriously. No game, which allows more than two players, can be played seriously. The players, who are losing, can gang up against the player who is winning. This situation will result in confusion. Monopoly is just a nice fun game and it should not be played too seriously.

This is the Worldmaster game.

          World Master
I had a very close climbing friend in Oxford and we played a lot of Chess and GO together. He later became a Professor and he invented this game and it sold very well. It is a good fun game, which like monopoly, is based on dice. When we met, many years later with our families for a weeks climbing, he was very keen to show me his game. Previously I had won more often at Chess and GO. He was determined to show me how easily he could beat me in his own game.
            But I decided I would make it hard for him. I studied the game carefully for a whole day, and then I could make an evaluation of the various situations. There was a series of nations on which a player could build facilities. But I could see that Kazakhstan was the best country because it bordered more countries. So I could make a relative evaluation of all the countries.
            Then we played together and I won the first three games. I then explained to John my evaluation system and he started to win. This is the only time in my whole life when my knowledge of this costing strategy has been of any benefit to me at all. But it is a great to remember just this one occasion.

This is an example of the Travelling Salesman problem.

The way that a good player plays chess and the way a computer plays chess are entirely different.
           A computer simply investigates as many moves ahead as possible.
            A human cannot investigate ahead as far. But at the end of an investigation he will evaluate the situation much more carefully. So he will measure the situation in terms of piece values (i.e. pawns 1, bishops and knights 3 etc (this can be carried out a lot more accurately)). But more importantly he will study the stability of the situation very carefully indeed i.e. is there piece that could be under attack. If there is such an attack then he will investigate further until there is stable situation.
            The human way is much closer to my way of solving such problems. Therefore it should be possible to develop computer chess further. I have studied this situation but it is very hard. I gave a talk on the subject called “A Rational method of using Investigating Time when there is a tree structure of possibilities with different probabilities and variances (as in chess)”. In this paper I explained how the various probability functions would need to be combined, when going forwards and backwards in the search processes. But no one could understand my talk. So I gave up. It is a terribly hard problem.
            The trouble with Chess is that the game is much too limited. Good playing almost always results in a draw. If a person wants spend a serious amount of time on such a problem, then they need to consider a better game to investigate. Such a game could be GO.

This what a game of GO looks like.

GO is a much better game than chess because it is a much simpler game (a player just places stones on the intersections of a large board). A player then wins when they control the majority of the squares of the board. As there are an odd number of squares on the board, there cannot be a draw. So GO is a very good game.
I would like to apply my evaluation system to play such a game. When a player places a stone on the board, they try to estimate the number of squares they are likely to dominate and obtain later. So, if player places a stone near a corner, then they have a better chance gaining squares than by placing stones in the middle. And placing stones close to other supporting stones also increases a player’s chances of success. But estimating the gain of these various possibilities is terribly hard. I don’t have anything like enough experience to do this evaluation.
Humans are still much better at playing GO than computers. This is a wonderful thing and it further demonstrates that GO is a much better game than chess. But there is now a superb challenge for a person to work out an evaluation system that will allow a computer system beat a human at GO.
If I had many years ahead of me this is what I would try to do. But I haven’t. So I won’t try to solve this problem. But mathematicians should keep trying to do this.

In this webpage so far I have shown how difficult it is for an applied mathematician, such as myself, to find a problem to solve, which will be appreciated by the rest of the world.
But there are a set and very important problems, which our current world desperately needs to solve. These are all the political problems, which I have talked about at length in this website. This is what I have basically spent my life in solving. And I am glad I have. I know these efforts of mine will not be appreciated because the influential and powerful people of the world prefer the world to remain as it is. (And the majority of other people suck up to these influential and powerful people, so that they can continue to earn a living without fear of getting the sack). But I have always known this.
I am a good scout so I know I must always “do my best”. If more people follow my example then eventually we should manage to create a better world. Let us hope so.

My next normal webpage is: “Academic Activities”.

You might now also like to look back at:
either my “Home Page” (which introduces this whole website and lists all my webpages),
or “My Life” (which introduces this major set of webpages).

Updated on 9/11/2016.