Thursday, November 6, 2008
Tuesday, October 14, 2008
World University Rankings 2008 - Technology
Source : The Times Higher Education - Quacquarelli Symonds
World University Rankings in Engineering and IT
1 MASSACHUSETTS Institute of Technology (United States) 100.0
2 University of California, BERKELEY (United States) 93.9
3 STANFORD University (United States) 85.3
4 CALIFORNIA Institute of Technology (United States) 81.6
5 University of CAMBRIDGE (United Kingdom) 76.2
6 CARNEGIE MELLON University (United States) 71.6
7 IMPERIAL College London (United Kingdom) 70.9
8 GEORGIA Institute of Technology (United States) 68.9
9 University of TOKYO (Japan) 67.4
10 University of TORONTO (Canada) 66.0
11 National University of SINGAPORE (Singapore) 64.5
12 TSINGHUA University (China) 63.4
13 ETH Zurich (Switzerland) 63.1
14 University of OXFORD (United Kingdom) 61.6
15 PRINCETON University (United States) 61.5
16 University of CALIFORNIA, Los Angeles (United States) 61.4
17 DELFT University of Technology (Netherlands) 60.4
18 MCGILL University (Canada) 60.1
19 HARVARD University (United States) 59.6
20 University of ILLINOIS (United States) 58.4
21 TOKYO Institute of Technology (Japan) 57.0
22= KYOTO University (Japan) 56.8
22= University of BRITISH COLUMBIA (Canada) 56.8
24= CORNELL University (United States) 56.4
24= HONG KONG University of Science and Tech (Hong Kong) 56.4
World University Rankings in Engineering and IT
1 MASSACHUSETTS Institute of Technology (United States) 100.0
2 University of California, BERKELEY (United States) 93.9
3 STANFORD University (United States) 85.3
4 CALIFORNIA Institute of Technology (United States) 81.6
5 University of CAMBRIDGE (United Kingdom) 76.2
6 CARNEGIE MELLON University (United States) 71.6
7 IMPERIAL College London (United Kingdom) 70.9
8 GEORGIA Institute of Technology (United States) 68.9
9 University of TOKYO (Japan) 67.4
10 University of TORONTO (Canada) 66.0
11 National University of SINGAPORE (Singapore) 64.5
12 TSINGHUA University (China) 63.4
13 ETH Zurich (Switzerland) 63.1
14 University of OXFORD (United Kingdom) 61.6
15 PRINCETON University (United States) 61.5
16 University of CALIFORNIA, Los Angeles (United States) 61.4
17 DELFT University of Technology (Netherlands) 60.4
18 MCGILL University (Canada) 60.1
19 HARVARD University (United States) 59.6
20 University of ILLINOIS (United States) 58.4
21 TOKYO Institute of Technology (Japan) 57.0
22= KYOTO University (Japan) 56.8
22= University of BRITISH COLUMBIA (Canada) 56.8
24= CORNELL University (United States) 56.4
24= HONG KONG University of Science and Tech (Hong Kong) 56.4
Sunday, October 12, 2008
A Brief Introduction to Mathematical Programming
Mathematical Programming is a powerful framework for decision making. It helps us to systematically model a set of possible decisions and search for the optimal one(s). In this framework, the objective and constraints are formulated as mathematical functions of parameters and variables x, let say f(x) and g(x), respectively. Notice that bold faces indicate that they are vectors and matrices. These functions are typically algebraic. Thus, the general form of a mathematical program is the following:
minimize f(x)
subject to g(x) = 0
Maximize f(x) can be treated as minimize -f(x). Inequalities can be transformed into equalities g(x) = 0 by introducing slack and surplus variables.
There are several classes of mathematical programming. Linear Programming (LP) concerns with cases in which f(x) and g(x) are linear functions while Nonlinear Programming (NLP) deals with cases with at least one of the functions is nonlinear. All variables involved in LP and NLP are continuous, they can take any real numbers satisfying the constraints. If some variables have to take discrete values then the corresponding equivalents for LP and NLP are Mixed Integer Linear Programming (MILP) and Mixed Integer Nonlinear Programming (MINLP).
How can we utilize mathematical programming to attack The Farmer Bill's Problem ?
minimize f(x)
subject to g(x) = 0
Maximize f(x) can be treated as minimize -f(x). Inequalities can be transformed into equalities g(x) = 0 by introducing slack and surplus variables.
There are several classes of mathematical programming. Linear Programming (LP) concerns with cases in which f(x) and g(x) are linear functions while Nonlinear Programming (NLP) deals with cases with at least one of the functions is nonlinear. All variables involved in LP and NLP are continuous, they can take any real numbers satisfying the constraints. If some variables have to take discrete values then the corresponding equivalents for LP and NLP are Mixed Integer Linear Programming (MILP) and Mixed Integer Nonlinear Programming (MINLP).
How can we utilize mathematical programming to attack The Farmer Bill's Problem ?
Friday, September 26, 2008
The Farmer Bill's Problem
Every long journey begins with a first step. Starting our journey towards the science and technology of decision making, lets meet Bill, the farmer. He is facing one delicate problem. Can we help him?
Farmer Bill is planning his planting for the coming year. He expects to raise two crops: potatoes and wheat. He has 100 acres of land available for planting and will be able to devote 160 days of labor to his crops. He expects an acre of wheat to require four days of labor, while an acre of potatoes requires only one day.
He has $ 1100 that he can use for the start-up costs of planting and cultivating. It costs $ 10 an acre to plant and cultivate potatoes, while the corresponding costs for an acre of wheat are $ 20.
If Bill expects a revenue of $ 40 per acre of potatoes and $ 120 an acre for wheat, how many acres of each should he plant in order to achieve the highest possible revenue?
Farmer Bill is planning his planting for the coming year. He expects to raise two crops: potatoes and wheat. He has 100 acres of land available for planting and will be able to devote 160 days of labor to his crops. He expects an acre of wheat to require four days of labor, while an acre of potatoes requires only one day.
He has $ 1100 that he can use for the start-up costs of planting and cultivating. It costs $ 10 an acre to plant and cultivate potatoes, while the corresponding costs for an acre of wheat are $ 20.
If Bill expects a revenue of $ 40 per acre of potatoes and $ 120 an acre for wheat, how many acres of each should he plant in order to achieve the highest possible revenue?
Saturday, September 20, 2008
Chemical Engineers and Decision Making
Who said that the science and technology of decision making is a privilege only for mathematicians, operations researchers, industrial engineers, economists, management scientists, and the likes? Chemical engineers have played their own vital roles in shaping the science and technology of decision making.
They have conceptualized some of the most practically useful (and beautiful!) decision making theory and algorithms.
They have invented some of the most efficient state-of-the-art computational tools and software for decision making.
Thus, it is not surprising that some of the most challenging decision making problems are chemical engineers's day-to-day breakfasts.
To honor their contributions, here is a (partial) list of their hallmarks:
Name (Highest Degree in ChemE) [Current Institution]
John von Neumann (BS) [deceased]
John Nash (BS) [Princeton University]
Thomas Magnanti (BS) [Massachusetts Institute of Technology]
George Nemhauser (BS) [Georgia Institute of Technology]
Ignacio Grossmann (PhD) [Carnegie Mellon University]
Lorenz Biegler (PhD) [Carnegie Mellon University]
Nikolaos Sahinidis (PhD) [Carnegie Mellon University]
will be updated.....
They have conceptualized some of the most practically useful (and beautiful!) decision making theory and algorithms.
They have invented some of the most efficient state-of-the-art computational tools and software for decision making.
Thus, it is not surprising that some of the most challenging decision making problems are chemical engineers's day-to-day breakfasts.
To honor their contributions, here is a (partial) list of their hallmarks:
Name (Highest Degree in ChemE) [Current Institution]
John von Neumann (BS) [deceased]
John Nash (BS) [Princeton University]
Thomas Magnanti (BS) [Massachusetts Institute of Technology]
George Nemhauser (BS) [Georgia Institute of Technology]
Ignacio Grossmann (PhD) [Carnegie Mellon University]
Lorenz Biegler (PhD) [Carnegie Mellon University]
Nikolaos Sahinidis (PhD) [Carnegie Mellon University]
will be updated.....
Friday, September 19, 2008
The Science and Technology of Decision Making
We live to accomplish our objectives. Objective represents our dreams, goals, and ideals. According to the nature of the objective, we aim to either the highest level or the lowest level of objective. The first is called as maximization while the last is called as minimization. For example, we want to maximize our monthly revenues. We also want to minimize our time consumed in working a tedious job.
The world is full with parameters and variables. Parameters are things that remain constant; they are not for use to decide. Variables are things that we can control up to a certain degree. One variable is related to parameters and other variables by a set of constraints. These constraints limit our freedom in making decisions on variables. Let say, we cannot afford to purchase a jet plane because of our budget constraint. In this case, the price of the plane is a parameter and our decision to whether to puchase it or not is a variable.
In order to reach the objective, we need to manipulate variables in the presence of parameters and constraints. We need to choose specific values for variables that satisfy all constraints and maximize or minimize our objective, that is the optimal decision. The process to determine the optimal decision is called as decision making. We have the innate ability to intuitively make decisions. However, some problems demand systematic rational approaches for decision making far beyond human intuition.
Decision making is ubiquitous in our life. It appears from the simplest routine, such as choosing the shortest route from our apartments to our offices, to the complex engineering activity of designing a chemical plant with the most desirable economical profit. The science of decision making studies the theory and algorithms needed to answer the question of "How we systematically determine the optimal decision for a given problem?" Indeed, it is arguably one of the most fundamental questions in human civilization yet to be fully answered! The practice of applying the science of decision making in real life problems results in the technology of decision making. This technology comes in the form of tools and software that help us in making decisions.
The world is full with parameters and variables. Parameters are things that remain constant; they are not for use to decide. Variables are things that we can control up to a certain degree. One variable is related to parameters and other variables by a set of constraints. These constraints limit our freedom in making decisions on variables. Let say, we cannot afford to purchase a jet plane because of our budget constraint. In this case, the price of the plane is a parameter and our decision to whether to puchase it or not is a variable.
In order to reach the objective, we need to manipulate variables in the presence of parameters and constraints. We need to choose specific values for variables that satisfy all constraints and maximize or minimize our objective, that is the optimal decision. The process to determine the optimal decision is called as decision making. We have the innate ability to intuitively make decisions. However, some problems demand systematic rational approaches for decision making far beyond human intuition.
Decision making is ubiquitous in our life. It appears from the simplest routine, such as choosing the shortest route from our apartments to our offices, to the complex engineering activity of designing a chemical plant with the most desirable economical profit. The science of decision making studies the theory and algorithms needed to answer the question of "How we systematically determine the optimal decision for a given problem?" Indeed, it is arguably one of the most fundamental questions in human civilization yet to be fully answered! The practice of applying the science of decision making in real life problems results in the technology of decision making. This technology comes in the form of tools and software that help us in making decisions.
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