Tuesday, February 28, 2012

Ask the Delphic Oracle

Indiatimes' main page carried an edited version of this article on Operations Management and the applications of mathematical analytics there.

Ask the Delphic Oracle
This article is in collaboration with Prof. Krishnan Shankar, Professor of Mathematics at the University of Oklahoma. 
“Ask the Delphic Oracle” is a new column in the Times of India. As part of this column, we plan to run a new puzzle every month. We will allow three to four weeks for you to solve the puzzle. Please write in with your answers to: askthedelphicoracle@gmail.com. We will publish the names of the people who answered the puzzle correctly (randomly chosen out of the first fifty). Good luck!
Ask The Oracle:
Q. I am an Australian in California. I have noticed that a lot of Indians here drive Toyotas. Why do so many Indians drive Toyotas?
Answer. While we put our business analyst hats on, may we point out that there are excellent reasons to own a Toyota? The main reason is, of course, the quality of the car. But how is Toyota able to produce cars of such high quality? Behind the answer to this question lies the story of the machine that changed the world.
Before there were Hondas and Toyotas, there were Fords. The big idea that Henry Ford came up with was that of the assembly line. Henry Ford realized that if you organize a car factory floor like a meat packing assembly line where each worker gets to specialize on one piece of the job, then the productive efficiency dramatically increases. From this was born the modern automobile assembly operations setup, the machine that changed the world.  The Ford automobile assembly operations setup was further improved upon by the Toyota Motor Company by means of the Toyota Production System. The Toyota Production System consists of a unique combination of social and technical processes that makes it possible for them to create very high quality cars with low rates of failure. This makes Toyotas cheap to own in terms of total cost of ownership and easy to maintain, but this is clear only after you have been educated on many different aspects of the matter of car ownership. Although Toyotas are expensive to buy, they pay off in the long term, and have low total cost of ownership. It is not surprising then that Indians in America, given their high level of price sensitivity, like to own Toyotas.
The Oracle Asks:
Why are Toyota cars of such good quality? Why are shipping containers sometimes sent halfway across the world half full? Why do clothing stores such as Pantaloon and J. C. Penny have so many extra trousers sitting around on shelves? If the average expected sales of iPads is 100 units per month, does it make sense for a store to have more than a hundred tablets in stock? These and many other questions may be answered using operations management techniques.
The field of operations management gained prominence in the 1950’s when it was realized that operations research techniques could be applied to a vast variety of problems. Operations research abstracts out problems to their mathematical essence and solves them using various optimization techniques. Once a solution for a particular problem is obtained, the same result can be applied to a variety of business sectors. The latter three problems described in the first paragraph may arise in domains as diverse as shipping, clothing retail and technology, but they can all be answered using, surprisingly enough, a single mathematical model.  We don’t propose to answer all these questions in the space of this column.  We will save that up for a future column. In the meantime, you would do well to look up a reference on operations research models (in particular, the newsvendor model and the EOQ model) to get the answers to the above questions. Some of the answers may surprise you. For instance, as Prof. Sam Savage at Stanford University puts it, plugging in average inputs to a problem do not yield average outputs. So, if in the average case, you expect a hundred units per month, you may be better off keeping more than a hundred in stock to address excess demand.
This month, we pay a tribute to operations management and the Toyota Motor Company with a puzzle with an operations management theme. As mathematics enthusiasts, we see mathematics everywhere. In this column, we plan to present to you a new puzzle each month. As we have noted above, we will allow three to four weeks for you to solve it. Please write in with your answers. We will publish a list of the people who answered the puzzle correctly (five randomly chosen out of the first fifty if the response is large). Good luck!

The full original article is available here. Do write to us at askthedelphicoracle@gmail.com with your answer to the puzzle.

Update:  For this month's puzzle, please use the following as your subject line : "Chandrayaan 12". Another update : we are planning to pick one entry (randomly chosen from the first fifty responses), not fifty. We are looking for insightful responses to the puzzle as well, and so even if you think that you don't have the correct answer, you are welcome to share with us a line or two on what you found interesting about the puzzle. Happy solving!