Chapter 02 - BUS 104 Decision Analysis & Management Science...

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BUS 104 Decision Analysis & Management Science Professor Yunzeng Wang
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Introduction to Optimization and Linear Programming Chapter 2
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Introduction We all face decision about how to use limited resources such as: Oil in the earth Land for dumps Time Money Workers
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Mathematical Programming. .. MP is a field of management science that finds the optimal, or most efficient, way of using limited resources to achieve the objectives of an individual or of a business. Optimization
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Applications of Optimization Determining Product Mix Manufacturing Routing and Logistics Financial Planning
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Characteristics of Optimization Problems Decisions Constraints Objectives
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General Form of an Optimization Problem MAX (or MIN): f 0 (X 1 , X 2 , …, X n ) Subject to: f 1 (X 1 , X 2 , …, X n )<=b 1 : f k (X 1 , X 2 , …, X n )>=b k : f m (X 1 , X 2 , …, X n )=b m Note: If all the functions in an optimization are linear, the problem is a Linear Programming (LP) problem
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Linear Programming (LP) Problems MAX (or MIN): c 1 X 1 + c 2 X 2 + … + c n X n Subject to: a 11 X 1 + a 12 X 2 + … + a 1 n X n <= b 1 : a k 1 X 1 + a k 2 X 2 + … + a kn X n >=b k : a m 1 X 1 + a m 2 X 2 + … + a mn X n = b m
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An Example LP Problem Blue Ridge Hot Tubs produces two types of hot There are 200 pumps, 1566 hours of labor, and 2880 feet of tubing available. Aqua-Spa Hydro-Lux Pumps 1 1 Labor 9 hours 6 hours Tubing 12 feet 16 feet Unit Profit $350 $300
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5 Steps In Formulating LP Models: 1. Understand the problem. 2. Identify the decision variables. X 1 =number of Aqua-Spas to produce X 2 =number of Hydro-Luxes to produce 3. State the objective function as a linear combination of the decision variables. MAX: 350X 1 + 300X 2
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(continued) 4. State the constraints as linear combinations of the decision variables. 1X 1 + 1X 2 <= 200} pumps 9X 1 + 6X 2 <= 1566 } labor 12X 1 + 16X 2 <= 2880 } tubing 5. Identify any upper or lower bounds on the decision variables. X
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This note was uploaded on 04/30/2010 for the course BUS 104 taught by Professor Hamouda during the Spring '08 term at UC Riverside.

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Chapter 02 - BUS 104 Decision Analysis & Management Science...

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