qt computer invasion

Interaction with T. N. Badri

Associate Professor of Operational Research; Great Lakes Institute of Management, Chennai

Between 3:30 to 4:45 PM

Anjali mudra

About the Venue: Lake Veeranam

The first Paranthaka Chozhar (907-955 A.D.), the grandson of Vijayalaya Chozhar, was known as the “Great Lion Who Conquered Madurai and Eezham.” The founder of the Chozha Empire, he became famous in history for having laid the golden roof over the gopuram of the Chidambaram temple. Besides many titles bestowed on him was the prestigious one, Veeranarayanan.

About Lake Veeranam

The Rashtrakutas in the north were very strong during Paranthakar’s reign. Expecting an invasion from Maniaketam, Paranthakarstationed a huge army in Thirumunaipadi under the command of his son, the crown prince Rajadhithan. Since thousands of soldiers waited there idly, Rajadhithan thought of a plan to help the people.

About Lake Veeranam

He had realized that huge quantities of water were flowing wastefully into the sea through Kollidam, known to devotees as Vada Kaveri. In order to conserve this water, he employed the soldiers to dig a huge lake and store at least a part of the catchment. He named this lake Veeranarayananafter his father.

Kalki Krishnamurthy, Ponniyan Selvan -The First Floods, p. 17. Macmillan India Ltd.

Quantitative Techniques

– The computer invasion

Subject overview

• Statistical Methods for Decision Making

Descriptive Statistics

Inferential Statistics

• Quantitative Methods

Deterministic Models

Role of Computers

Probabilistic ModelsP. C. Mahalanobis


This is the analysis of data that is obtained from a census or election or opinion poll. It may be data obtained from a manufacturing process or from the log sheet at a service center.

R. A. Fisher Karl Pearson W. E. Deming


One can display the data in various ways, the least suggestive or interpretable of which is a complete listing of all the observations.

Sometimes we may want a complete listing of

all observations.

More helpful are histograms, pie-charts, control charts and representations.


The mean, median and mode are measures

obtained from the data. They are meant to

give us some idea of the distribution of the data.

So too, the variance and standard deviation tell

us about the spread of the data about the mean.


Skewness and Kurtosis give us a handle on the symmetry and peakedness of the data.

There are formulas for all of these measures and we will cover them in the course in the first term. There are also spreadsheet formulas and packages such as SPSS to calculate them.


• A sample from a population should be random. This is very important to rule out bias in conclusions.

• The Sample Mean is the mean of the random sample. An amazing fact about the Sample Mean is that no matter what shape the distribution of the data, the sample mean is approximately normally distributed.


• This is why the Normal Distribution is considered the most important distribution.

• Since the estimates are based on only one sample, we can only be confident about the accuracy of the estimate within a given interval.

• We will come across 90% confidence intervals and 95% confidence intervals and 99% confidence intervals.


• Hypotheses usually question:

1. the population mean equalling some value

2. equality of two population means

3. equality of two population proportions

4. more than two population means

5. more than two population proportions


Travelling Salesman Problem. A salesman has to visit a number of customers in distant cities and then return to the depot.

In what order should he visit the customers?

This is a difficult combinatorial problem as the number of customers increases.


Stable Marriage Problem. There are a number of boys and girls looking to be married. How do we find an assignment that is most stable?

This is a combinatorial problem, that can be solved.

One can think of assigning jobs to MBAs based on suitability or drivers to routes.


Other combinatorial problems are bin-packing, set-covering, sequencing and scheduling, network design, storage and retrieval.

Typically in the workplace situation, we first think of a “feasible solution”, one that works.

Later we search for a more economical solution if there is one. This is called the “Optimal solution”.

Role of Computersin Deciding Propositions

In the 1930s pioneering computer scientists such as Alan Turing were wrestling with what were called Decidability Problems.

These were problems posed as questions that were so strange that it was hard to say even by using a computer, whether the answer was yes or no.

Alan Turing

Role of Computers in Quantitative Techniques

On the other hand there were problems where the Yes or No answer could be obtained after some computer search. These were the decidable problems.

In the 1950s a few researchers like Jack Edmonds started developing similar ideas of easy and difficult problems for the Combinatorial problems.

Jack Edmonds


Some problems were classified as easy. These were those where even the rarest instance could be solved in polynomial time.

Some instances of the Harder problems required exponential time to solve.

I will next explain what is meant by polynomial and exponential time.


• What is the size n of a problem?

• To be precise it is the number of symbols required to describe an instance of the problem.

• Usually the number of objects in the problem is a good estimate of this size.


1s = 1000000microseconds

1 second 1 minute 1 hour 1 day 1 month 1 year 1 century

1000000 60000000 36000000008640000000

0 2.592E+12 3.1104E+13 3.1104E+15microsec

lg n

Very Large

NumberVery Large

NumberVery Large Number

Very Large Number

Very Large Number

Very Large Number

Very Large Number super fast

sqrt(n) 1E+12 3.6E+15 1.296E+19 7.464E+21 6.718E+24 9.674E+26 9.674E+30very fast

n 1000000 60000000 36000000008640000000

0 2.592E+12 3.1104E+13 3.1104E+15fast

n lg n 62746 2801418 133378059 27551475137187085640

4 7.8655E+11 6.7699E+13fast medium

n^2 1000 7745.966692 60000 293938.769 1609968.94 5577096.01 55770960.1medium

n^3 100 391.48676 1532.61887 4420.8377 13736.5709 31448.896 145972.84slow

2^n19.93156

9 25.83845 31.74534 36.33031 41.23720 44.82216 51.46602very slow

n! 9 12 12 14 15 16 17super slow

Speed of solving problems of size n: worst case scenario


0

5000

10000

15000

20000

25000

30000

0 10 20 30 40 50 60

8n^2

64nLogn

Polynomial time v. Logarithmic time

0

5E+15

1E+16

1.5E+16

2E+16

2.5E+16

3E+16

3.5E+16

4E+16

0 10 20 30 40 50 60

100n^2

2^n


Polynomial time v. Exponential time

Role of Computersin Quantitative Techniques

Some problems were such that a candidate solution could be validated or invalidated in polynomial time.

There were others were even the validation or invalidation took exponential time. For such NP-Hard problems we look for Heuristics which give us a less than best solution but do not take forever to find the solution.

Richard Karp

Role of Computersin Quantitative Techniques

• These categories of easy and hard problems are based on how long the algorithms take for the worst case scenario of data.

• There is also a notion of average case scenario. Some methods that are exponential time for one or two contrived instances do surprisingly well on average. The Simplex method is one such algorithm.

George DantzigNarendra Karmarkar

Probabilistic Models

• Models where the inputs are not fixed are called probabilistic models.

• The numbers may change from day to day or period to period.

• These may cost or price of a commodity or duration of a task or activity.

• Such models require the use of probability in addition to the methods of deterministic models.

qt computer invasion

Documents

sample mean

analysis of data

huge lake

random sample

lake veeranarayanan

lake veeranamhe

important distribution

inferential statisticsa