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Unformatted text preview: IE 521 Advanced Optimization Lecture 1 Dr. Zeliha Akc ¸a September 2011 1 / 31 Reading I Lecture covers Bertsimas Sections 1.1, 1.2, 1.4 and some other resources. I P. E. Gill, W. Murray, M. Saunders, J. Tomlin, M. Wright, ”George B. Dantzig and Systems Optimization”, 2007. I Check the website for NEOS: ”http://neosserver.org/neos/” I I use Prof. Ted Ralphs’s (my advisor) IE406 lecture notes as reference. 2 / 31 System Engineering and Modeling I System = A set of elements that are functionally related to accomplish an objective I Production systems Financial systems Political systems Distribution systems Computer systems Biological and health systems Military systems I Systems can be analyzed by constructing models. I We will learn one of the modeling techniques in this course. I Analysis using models is employed in every sector for different type of problems. 3 / 31 Modeling Techniques I What is the purpose of modeling? To better understand and analyze a problem To experiment and do tests which can not be done with real system To use as a decision support system I Examples of models Statistical models Simulation models Economic models Mathematical Programming Models 4 / 31 System Modeling 1. Analyze the system: The elements of the system, the functional relationship between these, the way that they affect each other and system objectives are determined. 2. Observe the system: Collect data to determine the parameters required to define the system. 3. Construct ( formulate ) a model to define the system. 4. Solve the model and test its validity. 5. Create and test different scenarios considering the objectives. 6. Evaluate and report the operations and the results of the system. 5 / 31 Examples of Systems and Models I Airline operations ⇒ Assignment of fleet to the flights, ⇒ Crew scheduling (assignment of cockpit and cabin personel to flights), ⇒ Construct flight timetable, etc. I Production and distribution systems ⇒ Distribution of the products to customers or distribution centers from deports, ⇒ Determination of how many of each product to produce, planning of the usage and purchasing of supplies, etc. 6 / 31 Mathematical Programming Models I What is mathematical programming ? I Also known as optimization . I Main components of a mathematical programming are: ⇒ Decision variables: describe the state of the system, represent the decisions required to operate the system ⇒ Constraints: define the characteristics of the system, allowable limits for a state of the system. ⇒ Objective function: A value that asses how well the operation of the system is....
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 Fall '11
 ZelihaAkça
 Optimization, objective function, objective function value, mathematical programming models

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