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?
Friday, September 26, 2008
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.
Greeting
Dear Avid Readers,
Welcome to "d a n t z i g" ! This blog is under construction and soon more materials will be available for your reading pleasure.
At your service,
dantzig-er
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