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4120-lecture2 - Computational Methods for Management and...

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Computational Methods for Management and Economics Carla Gomes Lecture 2 Reading: Chapter 2, and 3.1 of textbook
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Outline of Lecture OR Modeling Approach Mathematical Programs Introduction to Linear Programming An example
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Overview of OR Modeling Approach
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OR Nature Operations research involves “research” approach resembles the scientific method OR – “search for optimality” (best, optimal solution) is an important theme in OR. OR - team approach (mathematics, statistics and probability theory, economics, business administration, computer science, and engineering and other areas relevant to the particular organization OR adopts an organizational point of view – i.e., it tries to meet the goals of the overall organization.
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Overview of OR Modeling Approach 1. Define the problem of interest and gather the relevant data 1. Formulate a mathematical model to represent the problem 2. Develop a computer base procedure for deriving solutions to the problems from the model 3. Test the model and refine it as needed 4. Prepare for ongoing application of the model as prescribed by the management 5. Implement
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1. Define the problem of interest and gather the relevant data Need to develop a well-defined statement of the problem to be considered. objectives, constraints (e.g., what can be done with available resources) inter-relationships between the area to be studied and other areas in the organization possible alternative course of actions time limits for making a decision . . . Difficult phase - ill-defined nature and it’s difficult to be taught. It depends on the particular problem and domain of activity.
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2. Formulate a mathematical model to represent the problem Formulate the problem into a way that is convenient for analysis – typically using a mathematical model. Mathematical models – idealized representations expressed in terms of mathematical symbols and expressions. Famous mathematical models F = ma (Newton’s second law of motion) The net force on a body is equal to its mass multiplied by its acceleration. E=mc² (Einstein’s famous equation of mass energy equivalence).
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Mathematical model of a business problem: Decision variables - they represent quantifiable decisions to be made, under our control, say x 1, x 2 , …, x n . The respective values are to be determined.
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