Bài giảng Operations Management - Chapter 19: Linear Programming

Linear ProgrammingMcGraw-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 programmingFormulate a linear programming model from a description of a problemSolve simple linear programming problems using the graphical methodInterpret computer solutions of linear programming problemsDo sensitivity analysis on the solution of a linear programming problem19-*Student SlidesLPA powerful quantitative tool used by operations and other manages to obtain optimal solutions to problems that involve restrictions or limitationsApplications include:Establishing locations for emergency equipment and personnel to minimize response timeDeveloping optimal production schedulesDeveloping financial plansDetermining optimal diet plans19-*Student SlidesLP ModelsMathematical representations of constrained optimization problemsLP Model Components:Objective functionA mathematical statement of profit (or cost, etc.) for a given solutionDecision variablesAmounts of either inputs or outputsConstraintsLimitations that restrict the available alternativesParametersNumerical constants19-*Student SlidesList and define the decision variables (D.V.)These typically represent quantitiesState the objective function (O.F.)It includes every D.V. in the model and its contribution to profit (or cost)List the constraintsRight hand side valueRelationship symbol (≤, ≥, or =)Left Hand SideThe variables subject to the constraint, and their coefficients that indicate how much of the RHS quantity one unit of the D.V. representsNon-negativity constraints19-*Student SlidesMS Excel can be used to solve LP problems using its Solver routineEnter the problem into a worksheetWhere there is a zero in Figure 19.15, a formula was enteredSolver automatically places a value of zero after you input the formulaYou must designate the cells where you want the optimal values for the decision variables19-*Student Slides19-*Student SlidesIn Excel 2010, click on Tools on the top of the worksheet, and in that menu, click on SolverBegin by setting the Target CellThis is where you want the optimal objective function value to be recordedHighlight Max (if the objective is to maximize)The changing cells are the cells where the optimal values of the decision variables will appear19-*Student SlidesAdd a constraint, by clicking addFor each constraint, enter the cell that contains the left-hand side for the constraintSelect the appropriate relationship sign (≤, ≥, or =)Enter the RHS value or click on the cell containing the valueRepeat the process for each system constraint19-*Student SlidesFor the nonnegativity constraints, enter the range of cells designated for the optimal values of the decision variablesClick OK, rather than AddYou will be returned to the Solver menuClick on OptionsIn the Options menu, Click on Assume Linear ModelClick OK; you will be returned to the solver menuClick Solve19-*Student Slides19-*Student SlidesThe Solver Results menu will appearYou will have one of two resultsA SolutionIn the Solver Results menu Reports boxHighlight both Answer and SensitivityClick OKAn Error messageMake corrections and click solve19-*Student SlidesSolver will incorporate the optimal values of the decision variables and the objective function into your original layout on your worksheetsStudent Slides19-*Student Slides19-*Student Slides19-*