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stetson01 - Introduction to Operations Research Matthew...

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Introduction to Operations Research Matthew Galati [email protected] Department of Industrial and Systems Engineering, Lehigh University Service Parts Solutions, IBM Corporation Introduction to Operations Research – p.1
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Outline What is Operations Research? Optimization Problems and Applications Personal Examples Introduction to Operations Research – p.2
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What is Operations Reseach? Operations Research (OR) started just before World War II in Britain with the establishment of teams of scientists to study the strategic and tactical problems involved in military operations. The objective was to find the most effective utilization of limited military resources by the use of quantitative techniques. Following the war, numerous peacetime applications emerged, leading to the use of OR and management science in many industries and occupations. Occupational Outlook Handbook - http://stats.bls.gov/oco/ocos044.htm. Introduction to Operations Research – p.3
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Definitions Model: A schematic description of a system,theory, or phenomenon that accounts for its known or inferred properties and may be used for further study of its characteristics. System: A functionally related group of elements, especially: The human body regarded as a functional physiological unit. An organism as a whole, especially with regard to its vital processes or functions. A group of physiologically or anatomically complementary organs or parts: the nervous system; the skeletal system. A group of interacting mechanical or electrical components. A network of structures and channels, as for communication, travel, or distribution. A network of related computer software, hardware, and data transmission devices. Introduction to Operations Research – p.4
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Definitions Operations Research (OR) is the study of mathematical models for complex organizational systems. Optimization is a branch of OR which uses mathematical techniques such as linear and nonlinear programming to derive values for system variables that will optimize performance. Introduction to Operations Research – p.5
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Models Linear Programming Typically, a single objective function, representing either a profit to be maximized or a cost to be minimized, and a set of constraints that circumscribe the decision variables. The objective function and constraints all are linear functions of the decision variables. Software has been developed that is capable of solving problems containing millions of variables and tens of thousands of constraints. Network Flow Programming A special case of the more general linear program. Includes such problems as the transportation problem, the assignment problem, the shortest path problem, the maximum flow problem, and the minimum cost flow problem. Very efficient algorithms exist which are many times more efficient than linear programming in the utilization of computer time and space resources.
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