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Class Connection: Optimization

Well, today is the last day for my application portfolio and last few hours before I hand over my exam. The phone rings and it’s my wife – Can you pick me up from the airport at 7:30pm? I say – why not? With a hidden hope that her flight gets delayed for an hour or two, I continued giving final touches to my application portfolio, cleaning up the grammar and other knick knacks. And then it happened!

How difficult would it be to schedule aircraft landing and takeoff at busy airports such as Atlanta? Captured by this thought, I quickly made my way to Wikipedia to gather some basic information. Atlanta’s Hartsfield International airport has 5 runways, 151 domestic and 28 international gates. It is the worlds busiest airport by passenger traffic as well as landings and take offs. Aha!! It had 994,346 flight movements in 2007 (a world record).

If I were to take up the assignment of scheduling the landings and take offs for my final project, how would it look like. First,I would have looked at what I want to achieve. Probably, minimum delays would be one objective. Then I would have thought of my decision variables – something like when will a particular flight take off, or when will it land, or when should it leave the departure gate (assuming the time it will take on the tarmac as constant). Then would come the constraints, many of them. Wow…even thinking of them makes me scared. Some would be, a flight should not be incoming, it has spent X amount of time at the gate, movement time after landing, and so on. There are so many uncertainties associated with this modeling. I could think of then doing a Monte Carlo simulation to simulate the incoming and departure of aircrafts. Something like a Poisson distribution may have helped.

A few minutes of thought and I feel glad that I did not broach this subject when discussing my final project. Something tells me that with the tools and resources we have, this simulation would probably have been very difficult and my poor team mates would have put me on the next flight to India. 

Class Connection: Monte Carlo Simulation

I have done a number of cases on pricing strategies. One approach to handle the question is to think about pricing from three different perspectives 1) Cost based pricing 2) Competitor based pricing and 3) Value based pricing (holy grail). So, when the Monte Carlo simulation was described to us in the class, the last thought that crossed (read: did not cross) my mind was that one of the ways price of a product can be estimated is by using Monte Carlo simulation. I came across an article accidently when searching for avenues where Monte Carlo simulation is employed in business world.

In regular modeling we take a finite set of inputs and the results based on those inputs are analyzed. This type of model is typically referred to as deterministic model (getting the same result every time you use the model). But what if the inputs have probabilities/uncertainties associated with them? What if they cannot be determined effectively? How many inputs can you possibly create than will create a representative se? Every time the model is used, a fresh set of output is generated. Now you may say that I can vary the inputs and record the results to analyze. But c’mon, how many times and when will you be satisfied/tired. This is where Monte Carlo Simulation comes in. This method is used for iteratively evaluating a deterministic model using sets of random numbers as inputs.

Can you now join the dots and use Monte Carlo method to price a product? If not, read on. In the simulation as shown by the author, he knows his company’s marginal costs and the target market share required. Similar information for the competitors are either known or have a probability distribution. For e.g. for player B, the marginal cost is $30 – $50, uniformly distributed, because of uncertainty of the exact figure. He then builds a model where the input parameters are the price and the elasticity of the product. Another important consideration to keep in mind is that a lot of theoretical economic assumptions (for a monopolistic market) are made in this model (for details, read the article). The author then proceeds to run the simulation and gets range of prices and elasticity’s out that can be further analyzed to price the product.

This model does have limitations – it does not adopt the holy grail method (value based pricing) approach, there are theoretical constraints, and finally the lack of exact figures pertaining to competitors. Nevertheless, this model can be a very good starting point, and may lead to a fairly accurate estimate of the price. I strongly believe that this approach should be taken (wherever possible) in conjunction with value based pricing in order to assess the validity of the final figure and build a comfort level around that figure.

P.S. – It would have been great if the author would have provided a spreadsheet version of the model in order for us/me to get a complete picture. But thanks to him anyways for the great article.

P.S. – For those who are wondering what that image is all about – It is the famous Monte Carlo Casino after which the Monte Carlo method gets its name. For details read this.