Brief Introduction to Modeling and Optimization Software CPLEX LINDO LINGO AMPLE EXCEL Solver Based on Chapter 3 4 Introduction to Mathematical Programming Operations Research Volume 1 4th edition by Wayne L Winston and Munirpallam Venkataramanan Lewis Ntaimo See the NEOS website for a list of state of the art optimization software http www neos mcs anl gov neos 1 L Ntaimo c 2005 INEN420 TAMU Input File Formats LP MPS etc LP Format for linear integer programs OBJECTIVE objective function SUBJECT TO constraints END Max 3x1 2x2 s t 2x1 5x2 8 3x1 7x2 10 End Note that the non negative restrictions are implied by default Input file must be saved as filename lp for LP Format filename mps for MPS Format 2 L Ntaimo c 2005 INEN420 TAMU Example Using LINDO Q Solve the Dakota Problem using LINDO and Perform Sensitivity Analysis Max 60x1 30x2 20x3 s t 8x1 6x2 x3 48 4x1 2x2 1 5x3 20 2x1 1 5x2 0 5x3 8 END 1 Create your text input file and save it as dakota lp LINDO allows you to save it as dakota ltx 2 Start LINDO 3 Click on File and select Open to open your input file 4 Click on Solve and select Solve to solve the LP 5 LINDO will then ask Do range sensitivity analysis Click on Yes 6 LINDO will the show the solution report 3 L Ntaimo c 2005 INEN420 TAMU LINDO Solution Report for the Dakota Problem LP OPTIMUM FOUND AT STEP 2 OBJECTIVE FUNCTION VALUE 1 280 0000 VARIABLE VALUE REDUCED COST X1 2 000000 0 000000 X2 0 000000 5 000000 X3 8 000000 0 000000 ROW SLACK OR SURPLUS DUAL PRICES 2 24 000000 0 000000 3 0 000000 10 000000 4 0 000000 10 000000 NO ITERATIONS 2 RANGES IN WHICH THE BASIS IS UNCHANGED OBJ COEFFICIENT RANGES VARIABLE CURRENT ALLOWABLE ALLOWABLE COEF INCREASE DECREASE X1 60 000000 20 000000 4 000000 X2 30 000000 5 000000 INFINITY X3 20 000000 2 500000 5 000000 ROW 2 3 4 RIGHTHAND SIDE RANGES CURRENT ALLOWABLE ALLOWABLE RHS INCREASE DECREASE 48 000000 INFINITY 24 000000 20 000000 4 000000 4 000000 8 000000 2 000000 1 333333 4 L Ntaimo c 2005 INEN420 TAMU Example Using CPLEX Q Solve the Dakota Problem using LINDO and Perform Sensitivity Analysis Max 60x1 30x2 20x3 s t 8x1 6x2 x3 48 4x1 2x2 1 5x3 20 2x1 1 5x2 0 5x3 8 END 1 Create your text input file and save it as dakota lp in some directory e g c INEN420Project Note that for large models you may need to write a program in C C Java etc to create your input file in LP format 2 Open a DOS command window Click on Start Run and type cmd 3 Change from the default directory to c INEN420Project Use Dos command cd 4 Start CPLEX by typing cplex at the Dos prompt 5 Once CPLEX is started you can type help to get a list of commands 6 Type read dakota lp CPLEX reads in your LP data and is now ready to optimize it 7 Type opt or primopt to optimize your LP 8 Type display to display model data or solution plus sensitivity analysis info of your LP 9 Type write dakota txt and CPLEX will write the solution report for you 5 L Ntaimo c 2005 INEN420 TAMU CPLEX Solution Report for the Dakota Problem PROBLEM NAME dakota lp DATA NAME OBJECTIVE VALUE 280 STATUS OPTIMAL SOLN ITERATION 2 OBJECTIVE RHS RANGES BOUNDS obj MAX SECTION 1 ROWS NUMBER ROW AT ACTIVITY SLACK ACTIVITY LOWER LIMIT UPPER LIMIT DUAL ACTIVITY 1 2 3 4 obj Lumb Fini Carp BS BS UL UL 280 24 20 8 280 24 0 0 NONE NONE NONE NONE NONE 48 20 8 1 0 10 10 SECTION 2 COLUMNS NUMBER COLUMN AT ACTIVITY INPUT COST LOWER LIMIT UPPER LIMIT REDUCED COST 5 6 7 x1 x2 x3 BS LL BS 2 0 8 60 30 20 0 0 0 NONE NONE NONE 0 5 0 6 L Ntaimo c 2005 INEN420 TAMU LINGO AMPLE EXCEL Many LPs solved in practice contain 1000 s of constraints and decision variables Few users of linear programming want to input the constraints and variables each time such an LP is solved For this reason most actual applications of LP use a matrix generators to simply inputting of the LP data Also you can write your own program in C C JAVA etc to read data and create your input files LP or MPS files The packages LINGO and AMPLE are examples of sophisticated matrix generators and much more These packages are the so called optimization modeling languages that enable the user to create many constraints or object function terms by typing one line Excel has the capability to solve linear and often nonlinear programming problems Excel uses the Excel Solver 7 L Ntaimo c 2005 INEN420 TAMU Go out there and learn how to use different optimization software Use HELP documentation to get started INDIVIDUAL ASSIGNMENT Due Tues April 12 2005 Reading LINDO Section 4 9 page 158 LINGO Section 410 page 163 EXCEL Section 4 17 page 202 Problem Solving Solve Example 6 of Chapter 3 Diet Problem on page 69 and perform sensitivity analysis Use the following software and compare the results a LINDO b LINGO c CPLEX d EXCEL 8 L Ntaimo c 2005 INEN420 TAMU