Chapter 19 - Linear programming. After studying this chapter you will be able to: Describe the type of problem that would lend itself to solution using linear programming, formulate a linear programming model from a description of a problem, solve simple linear programming problems using the graphical method. | Linear Programming McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. You should be able to: Describe the type of problem that would lend itself to solution using linear programming Formulate a linear programming model from a description of a problem Solve simple linear programming problems using the graphical method Interpret computer solutions of linear programming problems Do sensitivity analysis on the solution of a linear programming problem 19- Student Slides LP A powerful quantitative tool used by operations and other manages to obtain optimal solutions to problems that involve restrictions or limitations Applications include: Establishing locations for emergency equipment and personnel to minimize response time Developing optimal production schedules Developing financial plans Determining optimal diet plans 19- Student Slides LP Models Mathematical representations of constrained optimization problems LP Model Components: . | Linear Programming McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. You should be able to: Describe the type of problem that would lend itself to solution using linear programming Formulate a linear programming model from a description of a problem Solve simple linear programming problems using the graphical method Interpret computer solutions of linear programming problems Do sensitivity analysis on the solution of a linear programming problem 19- Student Slides LP A powerful quantitative tool used by operations and other manages to obtain optimal solutions to problems that involve restrictions or limitations Applications include: Establishing locations for emergency equipment and personnel to minimize response time Developing optimal production schedules Developing financial plans Determining optimal diet plans 19- Student Slides LP Models Mathematical representations of constrained optimization problems LP Model Components: Objective function A mathematical statement of profit (or cost, etc.) for a given solution Decision variables Amounts of either inputs or outputs Constraints Limitations that restrict the available alternatives Parameters Numerical constants 19- Student Slides List and define the decision variables (.) These typically represent quantities State the objective function (.) It includes every . in the model and its contribution to profit (or cost) List the constraints Right hand side value Relationship symbol (≤, ≥, or =) Left Hand Side The variables subject to the constraint, and their coefficients that indicate how much of the RHS quantity one unit of the . represents Non-negativity constraints 19- Student Slides MS Excel can be used to solve LP problems using its Solver routine Enter the problem into a worksheet Where there is a zero in Figure , a formula was entered Solver automatically places a value of zero after you input the formula You must designate the cells .
