Showing posts with label Mathematics. Show all posts
Showing posts with label Mathematics. Show all posts

Sunday, 7 September 2014

Effective resource planning: a how-to guide

Setting up the problem

As mentioned in previous posts, I have developed a love for internet radio. It is a quick-fix cure for someone like me when the stimulus craving kicks in, especially when I have an anxious desire to multitask and do something else at the same time. Which happens. 

There is a particular show that I listen to regularly where a caller raised a very interesting point the other day. A young man dialled in and told the host that he is working his way through a college education which is very expensive because it is the best in the region. His field of study was accounting. The host told him that he was wasting his money as he could study accounting at many other universities for a lower fee and that it wouldn't make a difference to the eventual outcome, which is becoming an accountant.

Boom. Does he even know about the can he just opened? We are not just talking about university degrees now. Everything is coming into play. What are you paying for when you purchase a widget? What utility does the prestige price of the widget have and does it have a valid and measurable ROI? What other hidden costs are there in a price that make the widget completely arbitrary and bring the utility into focus?


Breaking down the problem

Okay, let's walk before we run here. Stay with the university degree story. I want to study accounting and I have several options. Out of my options there are several different prestige categories. Assume I am eligible to study at any university of my choice and that I can afford any of them, but want to make sure I still get the most value for the money that I spend. 

I rank my choices in terms of cost to get one list, prestige to get another, and outcome to get a final list. Outcome can again have two sub lists. The first would be the salary that I would get after obtaining the degree and the second would be the opportunity that I would be afforded with my particular degree. This is because some folks would probably sacrifice money for the opportunity to reach another goal.

You can see a system emerging with a very unique mid-section which needs to be taken into account, the ROI of prestige. The input would be the cost of the degree and the output would be the salary and opportunity. What needs to be considered is if paying more for prestige changes the output. 

To decide on this you would have to take a sample of accounting graduates from each university and see whether or not the salaries prove the theory right, and if so, how long until you break even with your initial investment. Would it really be worth it if the difference in median salaries was so small that it took you twenty years to break even? You can become even more clever here and see whether an expensive/prestigious education is more valuable at high school or university level, or whether it is a combination that yields the best outcome. For measuring opportunity it could be slightly tougher as this would be Boolean problem, measured by candidates who reached their goal and who did not, given their different choice of university.

After this a second question would have to be considered which challenges the assumption of eligibility and the candidates themselves. Do more prestigious institutions draw more ambitious candidates, perhaps with tougher entrance requirements? Would the students own hutzpah be the explanation for the higher salary and not the institution? Again you would have to take a sample of top performers at a few prestigious schools and some at less prestigious schools and see if the outcomes show a difference to determine causality. 

At this confusing stage, I personally feel challenged and, if I am honest, a bit duped. As consumers, when we make a purchase decision with the resources we have, how much do we over or under pay for the utility of the widget? More so, do I regularly consider my own value when I make a purchase to determine the value of the widget? Which one counts more or do the two factors energise each other to a logistic-equation-type of saturation point?


A problem of waste

Ultimately, this is probably a matter of waste reduction. A good way to look at waste reduction is to start at the end and then work your way backwards through the pipeline so you can identify your inputs within your parameters. 

What do you want? Pick a salary, a goal, a company you want to work for, a place you want to live, a function you want your widget to perform, a price you want the widget to sell at, etc.

Now when you look at the options you eliminate those that are not able to provide this outcome. Keep moving backwards step by step until you reach your short list of candidates that are able to get you to your predetermined outcome. At this stage the focus shifts towards your resources.

Rank the candidates by cost and rank by effort. In our previous example, we would consider a student with lower ambition/grades to be high on the effort list. Whip out the maths and find the optimal value for minimising cost and effort and you have your winner! Successfully you have eliminated wasting time on effort and money on cost. It goes without saying that if effort is all the same, then least cost wins, vice versa. 


An interesting parallel

Before I conclude, isn't it cool how the word parallel has a pair of parallel lines in it? There's should be a word for when this happens.

Malcolm Gladwell writes in one of his books (I think that it's Outliers?) that Nobel Prize winners are not always the most clever out of their group of peers in terms of IQ measurements, but that they were clever enough for the outcome of a certain Nobel-prize-worthy discovery, given the inputs of hard work and opportunity. Essentially, and rather humorously, a waste here would be extra IQ points, since they weren't necessary for the outcome. At least they don't cost anything!




To answer the question of school's, here is a great article that gives excellent insight into this specific problem. Take note, however, that for the spending of finite resources there is always an opportunity cost or trade off that has to be taken into account for a complete answer to the questions. 





Friday, 15 August 2014

Choices

I read an article about a recording that was just recently released (you can find the link on my twitter feed, @daansteraan) of former US President Bill Clinton talking about Bin Laden. This recording came from  Melbourne, Australia, from conversation between Clinton and Sky News Australia the day before the 9/11 attacks.

"I nearly got him ... And I could have killed him but I would have had to destroy a little town called Kandahar in Afghanistan and killed 300 innocent women and children and then I would have been no better than him. And so I didn't do it."

It would have been extremely inappropriate for this recording to be released just after the attacks and I wonder how much truth there is to the claim that the holder simply "forgot that he had it."

Not that I would blame him if it wasn't true. If it was a decision that was made I don't think it was a particularly bad one at all.

I have a few thoughts today about decisions and their tiered nature. 

A basic decision comes across as having only one degree of consequence. Determinists would probably argue that exactly the opposite is true and every action has an infinite line of consequences. This arguments reaches an interesting stale mate with Quantum Theory when you starting working backwards and get to the point where you cannot tell where an action began (I am referring to not being able to determine the exact position of an electron in an atom).

Getting back to a basic decision, an example would be when I decide whether I want to put up my arm or not. The consequence is that either my arm goes up or my arm stays down. One tier, one consequence, one decision.  


It is, thankfully and and unfortunately, not that simple (it is always unfortunate when something is not more simple, especially for people who like simplicity). The real decision tree is probably uglier than the hariest crows nest we can imagine. The only hair-line I wan't to write about now is the one where a shadow of degrees of good is cast over it. 



Back to the example. My simple decision of raising my hand or not. As for second tier options, there are many we can imagine. One could be that I raised my hand to answer a question in class. Another could be that I did it to switch on a light. It could be to block a punch from an opponent in a boxing match. It could even be to throw a punch at an opponent. Or an animal. Or a woman. Or a child. 



Consider a shadow of degrees of good.   



Clinton had a threshold for bad behaviour which was not shared by his opponent. Bin Laden's threshold of bad behaviour was much lower (higher) than Clintons. Clintons prevented him from killing Bin Laden when he could have. Bin Ladens didn't stop him from doing much worse. Would it have been worth extending Clintons "badness threshold" to protect his assets? His assets being people who do not die from terrorism or terrorist related activity? I also suppose the asset class is very differently defined since we are talking about people. If it was a different asset like drugs maybe? If you had to smoke a joint to ensure your children don't smoke weed then our asset is "sobriety" and our badness threshold would not be with killing but getting stoned. More later.