The best possible alternative each time

Ram , a 26 years old MBA student at one of the prestigious institutes in India, is known for his academic excellence and decision making skills. He has been a bright student throughout his life and his family has a lot of hope from him. He is lucky to have parents who don’t force their decision on him and he has been taking his own decisions since class 12th. He is proud of his strategy that he takes the best possible choice at every stage. He has ability to find what is best for him as he has very clear preferences and ability to calculate the payoffs from actions. For example, after completing class 12th, he decided to take admissions in B.Tech. and after completing B.Tech. he choose to work rather than going for higher education. After 2 years of work, he decided to pursue MBA. So far he has taken the best possible alternative, according to his preferences, at each stage of his life and he has reaped benefits of this strategy. Now, he is supposed to sort companies in his preference order from a list of companies that are visiting his campus but he is unable to sort the companies in preference order.

He goes to his best friend Shyam and their discussion goes like this:
Ram: Can you please help me on how to sort companies in preference order?
Shyam: Yes! Of course. How do you take decisions in general?
Ram: I take best possible alternative among all choices at given point in time.
Shyam: Then, you need to solve a problem first.
Ram: Okay. What is the problem?
Shyam: Find the sum obtained from the following decision tree when strategy is to choose the best alternative at each decision node.

Ram: 34 ( 7+12+6+9)



Shyam: Is it the best possible sum?
Ram: Yes. Because what can be better than choosing the best at each decision node. I have chosen 12 over 3 and 6 over 5 and 9 over 2. There cannot be any better sum.
Shyam: What is the sum if you would have chosen 3 over 12 in second period and 1 over 10 in the third period and 99 over 4 in last period?
Ram: 110
Shyam: Now, you see why choosing the best at each decision node is not always optimal. Can you relate this to sorting of companies?
Ram: Yes. I got your point.

This discussion was an eye opener for him as the first strategy is inferior to the second strategy. From that day, Ram changed his strategy for forever and decided to look at the complete picture before taking any decision and dropped the idea of choosing the best possible alternative at each stage. Now, he also knows the answer to the preference order of companies that are visiting his campus.

Note: This article is motivated by limitations of Greedy Algorithms and the decision tree in the article is taken from https://brilliant.org/wiki/greedy-algorithm/


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