Lecture 9_Outline - Linear Programming

Lecture 9_Outline - Linear Programming - Lecture 9 -...

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Lecture 9 - Outline 1 Lecture 9: Linear Programming (Textbook: Supplement E) Objectives z Basic Concepts z Formulation z Computer Solution z Sensitivity Analysis z Transportation/Transshipment Modeling Basic Concepts and Formulation Linear programming is an optimization process - A single objective function states mathematically what is being maximized or minimized - Decision variables represent choices that the decision maker can control - Constraints are limitations that restrict the decision variables. One of three types: , , = - The feasible region - Parameter or a coefficient - Linear objective function and constraints - Nonnegativity Formulating a Problem Step 1. Define the Decision Variables. Step 2.Write Out the Objective Function. Step 3. Write Out the Constraints. As a consistency check, make sure the same unit of measure is being used on both sides of each constraint and the objective function Problem 1 (Example E.1): The Stratton Company produces 2 basic types of plastic pipe. Three resources are crucial to the output of pipe: extrusion hours, packaging hours, and a special additive to the plastic raw material. Below is next week’s situation. All data are expressed in units of 100 feet of pipe. The contribution to profits and overhead per 100 feet of pipe is $34 for type 1 and $40 for type 2. Formulate a linear programming model to determine how much of each type of pipe should be produced to maximize contribution to profits and to overhead.
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Lecture 9 - Outline 2
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Lecture 9 - Outline 3 Formulating a Problem with Inequalities ¾ Typically the constraining resources have upper or lower limits. ¾ e.g., for the Stratton Company, the total extrusion time must not exceed the 48 hours of capacity available, so we use the sign. ¾ Negative values for constraints x 1 and x 2 do not make sense, so we add nonnegativity restrictions to the model: x 1 0 and x 2 0 (nonnegativity restrictions) ¾ Other problem might have constraining resources requiring > , > , = , or < restrictions. Graphical Solution Procedure
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Lecture 9 - Outline 4 ¾ Most linear programming problems are solved with a computer. ¾ However, insight into the meaning of the computer output, and linear programming concepts in general, can be gained by analyzing a simple two-variable problem graphically. ¾ Graphic method of linear programming : A type of graphic analysis that involves the following five steps: ¾ plotting the constraints ¾ identifying the feasible region ¾ plotting an objective function line ¾ finding a visual solution ¾ finding the algebraic solution I) We begin by plotting the constraint equations , disregarding the inequality portion of the constraints (< or >). Making each constraint an equality (=) transforms it into the equation for a straight line. ¾
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This note was uploaded on 02/14/2011 for the course MGSC 395 taught by Professor Zimmer during the Fall '10 term at South Carolina.

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Lecture 9_Outline - Linear Programming - Lecture 9 -...

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