Monday, March 11, 2013

A Simple Example Of Problem Solving Using A Pareto Chart

Lest you think my fish example was some sort of Post-Modern jape, I assure you that it was not. In fact it was only an excerpt of a much longer story about this particular fish. His name is Branford. He lives outside of Copenhagen.

The grape in our last example was only one of many things that Branford tried to eat during the summer  that he provided these results. It was clear that Branford was nibbling on quite a bit of junk and the local officials wished to know how to best focus their efforts in cleaning up the surrounding waters.

Branford was asked to fill out a questionnaire at the end of each day describing the types of things he had tried to nibble on. The results were a mix of common place and strange objects. Some of the more unusual data collected was that Branford apparently nibbled on 28 busts of Hans Christian Anderson and 15 musical instruments.

Because these two findings were sensational and full of drama, many top ranking officials wanted to focus on how to solve the problem of people discarding their old musical instruments and Hans Christian Anderson busts. Branford insisted that it would be more practical to reduce the amount of cans being thrown into the river by Copenhagen's largest pork & beans manufacturer.

But the officials would not listen. In exasperation, Branford pulled some Pareto charts out of his gill-hole. He explained to the officials that this would show empirically that the majority of clean up effort should be focused on the cans.

The first chart he showed them listed all the objects he had nibbled on and their percentage of the total. The red line represents the cumulative percentage of all the junk, adding up to 100%.



Next he showed the officials what would happen if they managed to decrease both the Busts of Hans Christian Anderson and Musical Instruments by 100%. That is eliminate the problem completely.




Branford clearly was able to show that if the Hans Christian Anderson and musical instrument problem were somehow completely solved that it would only decrease the total amount of junk by 12.6%

Everyone agreed that tracking down the persons who had discarded the Hans Christian Anderson busts and instruments in the first place would be challenging. Also, there was no evidence to support the fact that it was the same people throwing out this junk every time. In all likely hood, everyone agreed, Each piece of detritus was put there by a different offender.

Still, an ambitious young chap by the name of Lancelot Von Par was very passionately arguing that a PSA campaign must be embarked on immediately. Commercials must be shot! Actors hired! Pre-Production should have begun months ago! If it was a different offender every time  then everyone must be warned of the dangers of committing such an act!

Branford, calmly let the young man finish. Lancelot was not but 23 and as conniving as he was zealous. Branford knew, for all fish are omnipotent*, that Lancelot was sweet on a girl by the name of Caroline, three years his junior. She was an aspiring actress. Lancelot believed that landing her a starring role in a PSA, airing her beautiful face all across the Scandinavian region would surely win her affections.

Being omnipotent, Branford also knew that Lancelot would never win Caroline's heart. This did not sadden him, for fish have no emotions. Fish are supremely objective.

By this point Lancelot had whipped up several of the more slow-moving officials into a frenzy and everyone was getting ready to go into budgetary hearings. Marshall Macintyre was already planning a grand cast party. He would finally have a reason to call on his long time friend Carl, the Elephant Trainer. There would be booze, dancing girls, trick ponies! A glorious rapture to befit the greatest impresario of all time!

However, the group fell silent as Brandford, the fish showed his next chart and began to speak.


Branford explained:

"The difference can be clearly seen here. We know it will take a lot of time, money and effort to undertake a PSA campaign of questionable results"

An affirmative mutter rippled through the growing crowd.  The silence that had descended upon the group following the unveiling of this final chart had the effect of drawing in bystanders from a nearby park. Everyone was starting to take an interest in what Branford was saying. Now that they could see it in a picture.

"You see? Even if, and that is a very big if, we can completely rid our water system of busts of Hans Christian Anderson and old musical instruments it will not have as much of an impact as if we only reduce 50% of the can waste coming from the pork & bean plant!"

The crowd cheered raucously! It was a revelation. The choice was clear. When it came to spending lots of money and wasting energy on a project that at best would reduce the total waste by 12.6%, they could just walk up to Mr. Porkbean's front door and talk to him about his cans. If that one problem could only be solved by 50% then the total decrease in waste would be 15.3%. Any village idiot could see that 3.3% more efficiency in exchange for a lot less time, money and energy was a no brainer. Lancelot had no reply, his hastily garnered group of supporters had vanished as mist before the morning sun.

With Branford, the fish flopping at the front, the town marched to the doorstep of Henry P. Porkbean's mansion. It was made of old aluminum cans that had been gilded in solid gold. The whole building had then been spray painted with matte grey paint. This had been done for two reasons. The first was non-sensical, to blend in with the clouds whenever it was dreary. The second was more reasonable, to hide all that gold so no one would think to steal it.

Mr. Porkbean was as cautious as he was crazy.

It turned out that the can fix was an easy one. Mr. Porkbean's can collection unit had an unnoticed hole in the bottom. When the wind would blow on those dreary days that Mr. Porkbean's house was invisible, it would shake the collection unit and some cans would fall out.

Mr. Porkbean was more than happy to remedy the situation, because it meant that he would have enough cans by the end of the year to build the racquetball addition to his saber-tooth tiger pit.

Poor Marshall Macintyre never did get to call on his friend Carl the Elephant Trainer, but that doesn't mean we won't get to visit Carl's Empossibly Empressive Elephant Sanctuary some day. Only through the power of narrative, of course as the sanctuary has been closed for almost two decades now. Ever since the great elephant implosion of '92.

I really must take a respite now, for these old memories are dredging up such awful strong emotions. Unlike our omnipotent, water-breathing friends I do have feelings. So yes, someday we may talk of Carl's Empossibly Empressive Elephant Sanctuary, but not today. I just can't stomach this tragedy-spiked goblet of nostalgia. Not this evening.

Please, take this copy of the very same Microsoft Excel 2010 file that Branford used!

Plug in your own information and be a hero like Branford! You may not be able to breath underwater or be omnipotent, but you can still save the day.

*A note on fish omnipotency. While at first glance, it may seem that the original flow chart of a fish eating a grape contradicts** the idea of fish omnipotency. This is not the case and will be covered in a later manuscript.

**If you aren't sure why there would be a potential contradiction, please don't email me. Instead, find a large body of water. Sit by it and watch the horizon. Soon the bright sun splinter reflections from the waves will become dim and bearable. Should you see a more prominent shimmer on the horizon you will know that I have sent for you. This glimmer will be a bottle of enormous size. In it, will be an enormous message. This message will contain the answer you seek. Written in very tiny handwriting. While you are waiting, please fashion a giant cork-screw or knife. You will need it. Some type of reading glasses will also probably be useful. If I remember, I will try to stick some in the bottle. I would put the corkscrew in there too but that wouldn't work. I'll tape one to the outside, but it will probably fall off because all I have is scotch tape. And even if I use all 3,475 rolls of it, it isn't waterproof, so it will probably fall off during the journey. But hey! You never know!

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