After significant amount of brain storming with Prateek we have finally concluded that we used half approximation as a technique to analyze a stochastic exponential distribution. Case in point “Desafio”, the operations game at OJAS the annual fest at SPJIMR.

After spending 3 weeks at an MBA course curiosity took its toll; we wanted to test our ROI (return on Investment another management term) what did we learnt from our course , did the 5.53 lacs make a difference. What better way to do this than to see an actual application, a game designed to test out in-depth understanding of statistics and probability ( sometimes i think why Prateek chose this as a test of ROI neither he nor I have ever managed to solve any sums on probability for the past 26-27 years our existence on this planet). Let me mention clearly offence meant to the game it was work of a genius designed by Harvard and was running on the Harvard University servers. But the problem lay with us , we had spent only 3 weeks , I cant even say it was half baked , more appropriate would be to say that the we hadn’t even approached the oven.

So with Prateek (popularly called cool patty) registering us for the game we were certain that using what we know of Statistics and probability which is as good as zilch ,we were surely going to make a fool of ourselves. Well it didn’t matter we were out to seek “justification for 5.53″ and it didn’t occur that. Anyway the game started , we were handed a sheet of paper , 2 sheets to be precise . I still think that the language used was Greek the question sheets didn’t make too much sense. We were reading it and nothing made sense. The question was simple ” Design a restaurants ” but the associated data using which we needed to design the damn restaurants was as bad as it could ever be, nothing made sense. 5 challenges using whose input we had to design were

1). How would you seat the customer whether in batches or no batches

2). Decide on the seating arrangement number of seating in bar and number of seats at the restaurants. Keeping the total number of seats constant break the arrangement into number of seats in the bar and number in the restaurants.

3). Decide on the waiting time for each dinner considering the fact that a customer goes away if the seating is full.

4). What kind of promotional offer you are going to give and between what time considering the bar is open between 6 and 10:30

5). How many chefs will you hire and between what time.

All the questions have associated costs with them and using a simulated 20 runs of each challenge we were required to design a restaurant. When i say simulated 20 runs i mean that with every setting we could have 20 simulated runs and we needed to make a decision on what setting to use.

Well finally using the 20 simulated runs we had to decide & design the restaurant in a given time of one hour. So much for the question , i still am unclear about how to solve it in true blue statistical fashion. But we did manage to solve it using pure and simple half approximation. Yes ladies and gentle men , not binomial distribution , not exponential distribution , no Probability NOTHING , just plain and simple half approximation. The designed restaurants made an average profit of 650$ (remember the game was proprietary of Harvard hence the dollars).Oh i forgot to mention , we did try to install Statpro add-in in excel and try something with it but Prateek if you know what exactly we were trying please add a comment in the blog.

So with $650 we were done, we had so much confidence that we didn’t stand a chance that during the prize distribution ceremony i went to watch Billu Barber while Prateek went off to sleep. I was enjoying the movie (yeah i do enjoy ShahRukh Khan’s movies AT RARE INSTANCES) on second thoughts it was not ShahRukh more of Deepika Padukone shaking “it” on the song with words like Khit Pit and Hit hit. Anyway while Deepika Padukone was mesmerizing me i suddenly got an SMS from Cool Patty, interspersed between the abusive language were the words ” We came first ” . I couldn’t believe him but i was too involved with Miss Deepika to go out and call him .The movie ended i called up and found Prateek Ecstatic about our victory.

The main reason i wrote this piece is to answer the people who asked us the question, which theory did you use to solve the problem. I couldn’t get away with saying that we got lucky because they all retorted “You could have got lucky in at most 2-3 posed challenges but getting lucky on all 5 is not possible”. So here it is “the theory” we used it was plain and simple half approximation and repeated trials of half approximation which gives a cumulative impact of change in center point moving it closer to the correct point. Huh!!! so much for Ken Black.

on February 19, 2009 at 11:25 amkk kishoreNice post !