COPYRIGHT The LINGO software and its related documentation are copyrighted You may not copy the LINGO software or related documentation except in the manner authorized in the related documentation or with the written permission of LINDO Systems Inc TRADEMARKS LINGO is a trademark, and LINDO is a registered trademark, of LINDO Systems Inc Other product and company names mentioned herein are the property of their respective owners DISCLAIMER LINDO Systems, Inc warrants that on the date of receipt of your payment, the software provided contains an accurate reproduction of the LINGO software and that the copy of the related documentation is accurately reproduced Due to the inherent complexity of computer programs and computer models, the LINGO software may not be completely free of errors You are advised to verify your answers before basing decisions on them NEITHER LINDO SYSTEMS, INC NOR ANYONE ELSE ASSOCIATED IN THE CREATION, PRODUCTION, OR DISTRIBUTION OF THE LINGO SOFTWARE MAKES ANY OTHER EXPRESSED WARRANTIES REGARDING THE DISKS OR DOCUMENTATION AND MAKES NO WARRANTIES AT ALL, EITHER EXPRESSED OR IMPLIED, REGARDING THE LINGO SOFTWARE, INCLUDING THE IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, OR OTHERWISE Further, LINDO Systems, Inc reserves the right to revise this software and related documentation and make changes to the content hereof without obligation to notify any person of such revisions or changes Copyright © 2016 by LINDO Systems Inc All rights reserved Published by 1415 North Dayton Street Chicago, Illinois 60642 Technical Support: (312) 988-9421 E-mail: tech@lindo.com WWW: http://www.lindo.com Contents Contents iii Preface vii New Features xi for LINGO 16.0 xi Getting Started with LINGO Getting Started on Windows Getting Started on a Mac Getting Started on Linux 20 Creating and Solving a Model in LINGO 32 Examining the Solution Report 46 Intro to LINGO’s Modeling Language 48 Additional Modeling Language Features 60 Indicating Convexity and Concavity 64 Maximum Problem Dimensions 65 How to Contact LINDO Systems 66 Using Sets 67 Why Use Sets? 67 What Are Sets? 67 The Sets Section of a Model 68 The DATA Section 74 Set Looping Functions 75 Set-Based Modeling Examples 82 Summary .101 Using Variable Domain Functions 103 Integer Variables 103 Free Variables .122 Bounded Variables 127 SOS Variables .128 Cardinality .132 Semicontinuous Variables .132 Positive Semi-Definite Matrices .134 Data, Init and Calc Sections 139 The DATA Section of a Model .139 The INIT Section of a Model 143 The CALC Section of a Model .144 Summary .149 iv CONTENTS Menu Commands 151 Accessing Menu Commands 151 Menu Commands In Brief 154 Menu Commands In Depth 158 File Menu 158 Edit Menu 176 Solver Menu 189 Window Menu 309 Help Menu 313 Command-Line Commands 319 The Commands In Brief 319 The Commands In Depth 321 LINGO’s Operators and Functions 421 Standard Operators .421 Mathematical Functions 425 Financial Functions .428 Probability Functions .428 Variable Domain Functions 431 Set Handling Functions 432 Set Looping Functions 437 Interface Functions 439 Distributions 440 Report Functions 447 Date, Time and Calendar Functions 458 Matrix Functions 462 Miscellaneous Functions .476 Interfacing with External Files .479 Cut and Paste Transfers .479 Text File Interface Functions 481 LINGO Command Scripts 489 Specifying Files in the Command-line 492 RunLingo .494 Redirecting Input and Output 497 Managing LINGO Files 497 Interfacing With Spreadsheets 499 Importing Data from Spreadsheets 499 Exporting Solutions to Spreadsheets 504 OLE Automation Links from Excel 512 Embedding LINGO Models in Excel 516 Embedding Excel Sheets in LINGO 522 Summary .526 CONTENTS v 10 Interfacing with Databases 527 ODBC Data Sources .528 Importing Data from Databases with @ODBC 535 Importing Data with ODBC in a PERT Model 537 Exporting Data with @ODBC 539 Exporting Data with ODBC in a PERT Model 542 11 Interfacing with Other Applications 547 The LINGO Dynamic Link Library 547 User Defined Functions 591 12 Developing More Advanced Models 595 Production Management Models 596 Logistics Models 612 Financial Models 619 Queuing Models 636 Marketing Models 644 13 Programming LINGO 653 Programming Features 653 Programming Example: Binary Search 687 Programming Example: Markowitz Efficient Frontier .691 Programming Example: Cutting Stock 698 Programming Example: Accessing Excel 704 Summary .711 14 Stochastic Programming 713 Multistage Decision Making Under Uncertainty .713 Recourse Models 715 Scenario Tree 717 Monte Carlo Sampling 719 Setting up SP Models 720 Language Features for SP Models 721 Declaring Distributions 723 Gas Buying Example .730 Stock Option Example 741 Investing Under Uncertainty Example 750 Chance-Constrained Programs (CCPs) 757 15 On Mathematical Modeling 771 Solvers Used Internally by LINGO .771 Type of Constraints .772 Local Optima vs Global Optima 774 Smooth vs Nonsmooth Functions .780 Guidelines for Nonlinear Modeling 781 vi CONTENTS Appendix A: Additional Examples of LINGO Modeling 783 Appendix B: Error Messages 873 Appendix C: Bibliography and Suggested Reading 925 Acknowledgements 927 Index 929 Preface LINGO is a comprehensive tool designed to make building and solving mathematical optimization models easier and more efficient LINGO provides a completely integrated package that includes a powerful language for expressing optimization models, a full-featured environment for building and editing problems, and a set of fast built-in solvers capable of efficiently solving most classes of optimization models LINGO's primary features include: Algebraic Modeling Language LINGO supports a powerful, set-based modeling language that allows users to express math programming models efficiently and compactly Multiple models may be solved iteratively using LINGO's internal scripting capabilities Convenient Data Options LINGO takes the time and hassle out of managing your data It allows you to build models that pull information directly from databases and spreadsheets Similarly, LINGO can output solution information right into a database or spreadsheet making it easier for you to generate reports in the application of your choice Complete separation of model and data enhance model maintenance and scalability Model Interactively or Create Turnkey Applications You can build and solve models within LINGO, or you can call LINGO directly from an application you have written For developing models interactively, LINGO provides a complete modeling environment to build, solve, and analyze your models For building turn-key solutions, LINGO comes with callable DLL and OLE interfaces that can be called from user written applications LINGO can also be called directly from an Excel macro or database application LINGO currently includes programming examples for C/C++, FORTRAN, Java, C#.NET, VB.NET, ASP.NET, Visual Basic, Delphi, and Excel Extensive Documentation and Help LINGO provides all of the tools you will need to get up and running quickly You get the LINGO Users Manual (in printed form and available via the online Help), which fully describes the commands and features of the program Also included with Super versions and larger is a copy of Optimization Modeling with LINGO, a comprehensive modeling text discussing all major classes of linear, integer and nonlinear optimization problems LINGO also comes with dozens of realworld based examples for you to modify and expand Powerful Solvers and Tools LINGO is available with a comprehensive set of fast, built-in solvers for linear, nonlinear (convex & nonconvex), quadratic, quadratically constrained, and integer optimization You never have to specify or load a separate solver, because LINGO reads your formulation and automatically selects the appropriate one A general description of the solvers and tools available in LINGO follows: viii PREFACE General Nonlinear Solver LINGO provides both general nonlinear and nonlinear/integer capabilities The nonlinear license option is required in order to use the nonlinear capabilities with LINDO API Global Solver The global solver combines a series of range bounding (e.g., interval analysis and convex analysis) and range reduction techniques (e.g., linear programming and constraint propagation) within a branch-and-bound framework to find proven global solutions to nonconvex nonlinear programs Traditional nonlinear solvers can get stuck at suboptimal, local solutions This is no longer the case when using the global solver Multistart Solver The multistart solver intelligently generates a sequence of candidate starting points in the solution space of NLP and mixed integer NLPs A traditional NLP solver is called with each starting point to find a local optimum For non-convex NLP models, the quality of the best solution found by the multistart solver tends to be superior to that of a single solution from a traditional nonlinear solver A user adjustable parameter controls the maximum number of multistarts to be performed Barrier Solver The barrier solver is an alternative way for solving linear, quadratic and conic problems LINGO's state-of-the-art implementation of the barrier method offers great speed advantages for large-scale, sparse models Simplex Solvers LINGO offers two advanced implementations of the primal and dual simplex methods as the primary means for solving linear programming problems Its flexible design allows the users to fine tune each method by altering several of the algorithmic parameters Mixed Integer Solver The mixed integer solver’s capabilities of LINGO extend to linear, quadratic, and general nonlinear integer models It contains several advanced solution techniques such as cut generation, tree reordering to reduce tree growth dynamically, and advanced heuristic and presolve strategies Stochastic Solver The stochastic programming solver supports decision making under uncertainty through multistage stochastic models with recourse The user describes the uncertainty by identifying the distribution functions, either built-in or user-defined, describing each random variable The stochastic solver will optimize the model to minimize the cost of the initial stage plus the expected cost of future recourse actions over the planning horizon Advanced sampling modes are also available for approximating continuous distributions LINGO's stochastic solver also supports chance-constrained models, where one or more sets of constraints are allowed to be violated according to a specified probability PREFACE ix Model and Solution Analysis Tools LINGO includes a comprehensive set of analysis tools for debugging infeasible linear, integer and nonlinear programs, using advanced techniques to isolate the source of infeasibilities to the smallest subset of the original constraints It also has tools to perform sensitivity analysis to determine the sensitivity of the optimal basis to changes in certain data components (e.g objective vector and right-hand-size values) Quadratic Recognition Tools The QP recognition tool is a useful algebraic pre-processor that automatically determines if an arbitrary NLP is actually a convex, quadratic model QP models may then be passed to the faster quadratic solver, which is available as part of the barrier solver option When the barrier solver option is combined with the global option, LINGO will automatically recognize conic models, in addition to convex quadratic models Linearization Tools Linearization is a comprehensive reformulation tool that automatically converts many non-smooth functions and operators (e.g., max and absolute value) to a series of linear, mathematically equivalent expressions Many non-smooth models may be entirely linearized This allows the linear solver to quickly find a global solution to what would have otherwise been an intractable nonlinear problem INDEX Dual Formulation, 290 DUAL function, 447 Dual values, 47 enabling, 889 integer programming, 121 nonzeros, 882 ranges, 357 Dual Values, 207, 226 DUALCO, 387 DUALCO parameter, 356 DUALPR parameter, 387 Duplicate names, 877, 890 DYNAMB model, 616 Dynamic Link Library, 547–90 functions, 552–58 Dynamic programming, 616, 799, 824, 835 E Echo Input, 220 ECHOIN parameter, 383 Economic order quantity, 801, 847 Edit Menu, 155 Edit Menu Commands in Brief, 155 Edit|Copy, 176 Edit|Cut, 176 Edit|Find, 181 Edit|Insert New Object, 184 Edit|Links, 188 Edit|Match Parenthesis, 183 Edit|Object Properties, 189 Edit|Paste, 176 Edit|Paste Function, 183 Edit|Paste Special, 176 Edit|Redo, 176 Edit|Replace, 182 Edit|Select All, 181 Edit|Select Font, 184 Edit|Undo, 176 Efficient Frontier, 691 EIGEN function, 466 Eigen values, 776 Eigenvalues, 466 Eigenvectors, 466 Elapsed Runtime Box, 36 ELSE Statement, 667 EM, 289 Embedding files, 516–25 ENDIF Statement, 667 End-of-file, 484 End-of-record Mark (~), 481, 484, 604, 878 ENDSUBMODEL, 653 Enforce Bounds In Calc and Data Sections, 240 Eppen/Martin model, 819 Equality relation, 47, 423 Equilibrium network, 828 Erlang busy probability, 429, 849 Erlang loss probability, 429, 636, 804 ERRDLG parameter, 384 Error In Dialogs, 214 Error messages, 384, 557, 559, 873–924 EV, 289 EVMU, 289 EVPI, 289 Examining the Solution, 46 Excel, 215 exporting, 511 linking with LINGO, 499, 553 OLE automation, 512–26 OLE function, 499, 510 TEXT function, 487 Exciting LINGO, 175 Exclamation point, 419 Exercise price, 627, 833 Exit, 419 Exit Command, 175 EXP function, 426 Expected rate of return, 625 Expected Value of Modeling uncertainty, 289 Perfect information, 289 Policy based on mean outcome, 289 Wait-and-see model's objective, 289 Explicit Deterministic Equivalent, 290, 297 Scenario, 299 Explicit listing, 72 Exponential distribution, 724 Exponential smoothing, 636, 862 Export File command, 154 Export summary report ODBC based, 544 OLE based, 511 Exporting attributes, 539 databases functions, 539–45 reports, 363 MPI files, 349 pasting out, 480 spreadsheets functions, 504–12 reports, 363 Exporting MPI Files, 174 935 936 INDEX Exporting MPS Files, 172 Expressions, 780 EXTEND command, 362 Extended Solver Status Box, 36 EZCOUNT model, 868 EZMREPAR model, 639, 802 EZNEWS model, 803 F F distribution, 724 Factorial function, 868 Feasibility Tolerances, 244 Features Not Supported on Linux, 29 Features, new, vii File data, 497 format ASCII, 48, 349, 479, 481, 497 BAS, 588 binary, 498 LDT, 497 LG4 saving, 497 LNG, 497 LRP, 497 LTF, 497 MPI, 349 MPS exporting, 350 header, 585 log files, 923 names, 60 script files, 489–91 FILE, 481 File Format, 218 File Format Box, 218 FILE function, 439, 481–85 examples, 491, 603 File Menu, 154 File Menu Commands in Brief, 154 File|Close, 166 File|Export File, 172 File|License, 174 File|Log Output, 168 File|New, 158 File|Open, 159 File|Print, 166 File|Save, 165 File|Save As, 165 File|Take Commands, 169 File|User Database Info, 175 FILFMT parameter, 382 Fill Out Database Tables, 215 Fill Out Ranges, 215 Filter, 72 Final linear feasibility tolerance, 373 Final nonlinear feasibility tolerance, 374 Final Nonlinear Feasibility Tolerances, 251 Financial models, 428, 619–35 Finite source, Poisson, 639 Fixed costs, 116 Fixed ordering charge, 830 Fixed Var Reduction, 233 Fixed variables, 772, 880 FLFTOL parameter, 373 Floating point operations, 373 FLOOR function, 426 Flow Cover, 390 Flow cuts, 391 Flow of Control, 667 FLWCTS, 391 FNFTOL parameter, 374 FOR function constraints, 62, 79 error messages, 878, 880 nesting, 81 sets, 69, 438 syntax, 76 variables, 109, 125 FOR Function, 667 FORCEB parameter, 415 Forcing Constraints, 235, 263 Forecasting, 122, 854, 862 FORMAT function, 448 FORTRAN pointer functions, 552 user defined functions, 591 Forward Analytical Derivatives, 252 FPA function, 428 FPL function, 428 Fragmentation ratio, 322 Free variables, 122–27 Free Variables, 229 FREEZE command, 365, 376, 888 Functions, 67 callback, 580–90 DLL, 552–58 factorial, 868 interface functions, 481, 889 non-differentiable, 780 probability, 428–31 set-looping, 74–81, 437 user defined, 591–94 INDEX utility, 648 variable domain, 881 G Gamma distribution, 724 GCD cuts, 390 GCDCTS, 391 GEN, 334, 670 GEN command, 79 GENDUAL, 672 General Box, 214 General equilibrium of an economy, 805 General integer variables, 103, 104–9 Generalized Upper Bound (GUB) Cuts, 307 Generate command, 79 Generate Command, 290 Generate Model Only, 295 Generated Model Report Deterministic Equivalent, 290 Dual Formulation, 290 Primal Formulation, 290 Generated Model Report Algebraic Format, 290 Generated Model Report, 291 Generated Model Report Dual Formulation, 295 Generated Model Report Scenario, 299 Generating the Model, 222, 234 Generation Time, 240 Generator Memory Limit Box, 232 Generator memory used, 322 Generator Memory Used Box, 36 Geometric distribution, 725 Getting Started, Getting Started on Linux, 20 GIN function dual values, 121 examples, 109 syntax, 104 GLBBRN parameter, 400 GLBBXS parameter, 400 GLBDLT parameter, 399 GLBOPT parameter, 399 GLBREF parameter, 400 GLBUBD parameter, 400 GLBVBD parameter, 399 Global delta tolerance, 399 Global optimality tolerance, 399 Global optimum, 392, 552, 774, 776 Global Optimum, 281 Global solver, 395, 897 Global Solver, 36, 276, 277, 280, 281, 477, 898 Global Solver Tab, 276 GO command, 353 GOMCTS, 391 Gomory, 391 Gomory cuts, 390 GP1, 299 GP2, 299 Gradient, 772, 780 Graph Partitioning, 299 Graph Partitioning Heuristic, 272 Greatest common divisor, 391 Growth rate, 619 GUB cuts, 345, 390, 391 GUBCTS, 391 Gumbel distribution, 724 H Handle usage, 322 Hansen, P., 828 Hayes, J.M., 790 Header file, 585 Heap compacts, 322 HELP command, 322 Help Menu, 313 Help Menu Commands in Brief, 157 Help Topics Command, 157, 313 HEUCUT parameter, 414 HEURIS parameter, 377 Heuristics, 256, 399, 824, 866, 869 HIDE command, 338 Hieftje, G.M., 790 Holding costs, 801, 819 Home mortgage calculation, 871 HUMNTM parameter, 399 Hurdle, 267 HURDLE parameter, 378 Hypergeometric distribution, 429, 725, 856 Hyperplanes, 779 I IF function, 476 IFC Statement, 667 ILFTOL parameter, 373 ILP, 36 Implicit set members, 895 Implied indexing, 77 Import LINDO File Command, 154 937 938 INDEX Importing, 159 attributes, 536 command scripts, 489–91 databases, 500, 535–39 FILE function, 481–85 pasting in, 479–80 spreadsheets, 499–504 IN function, 432, 878, 883 Include file, 484 Index, 341, 875, 876, 888 implied, 77 internal, 60 placeholder, 72 INDEX function, 433 error messages, 875, 880 examples, 112 parameters, 384 INDEX Function, 239 Inequality relation, 423 Infeasibility Field, 36 Infeasible, 303 Infeasible model, 47, 351, 552, 883 INFTOL parameter, 374 Init section, 143–49 importing, 500 Initial linear feasibility tolerance, 373 Initial nonlinear feasibility tolerance, 374 Initial Nonlinear Feasibility Tolerances, 251 Initializing data error messages, 895 variables, 781 Initializing variables, 143 INLP, 36 INSERT function, 434 Insert New Object command, 523 Insert New Object Command, 155 Installing LINGO Windows, Installing LINGO on a Mac, Installing LINGO on Linux, 20 Installing LINGO on Windows, INT function, 426 Integer Pre-Solver Tab, 255 Integer programming branch-and-bound constraint cuts parameters, 377, 391, 399 definition, 104, 653, 771 direction, 388 heuristics, 399 dual values, 121 Integer Programming, 259, 263 Integer Solver Tab, 260 Integer variables binary (0/1) examples, 609 functions, 103 priority, 388 syntax, 110–20 examples, 600 general, 103, 104–9 limits, 65 solutions, 782 variable domain functions, 103–22 Integers, 260, 267 INTEGRAL function, 426 Integrality Box, 262 Integrality tolerance, 374 Integration, 426 Interest rate, 627 Interface functions, 481, 889 Interface Options, 213 Interfacing with other applications, 547–94 Interior point algorithm, 386 Interior Point Algorithm Models, 243 Interrupting the solver, 923 Interval analysis, 277 invalid function, 882 Invalid switch, 883 Inventory system demand backlog, 815 newsboy model, 803, 830 PERT, 537–39, 542–45, 839 INVERSE function, 469 IPTOLA parameter, 378 IPTOLR parameter, 378 IQP, 36 Iterations, 222, 251 definition, 375 dynamic link library, 582 limit, 374, 375 steepest edge, 385, 387 Iterations Field, 36 ITERS function, 451 ITRLIM parameter, 375 ITRSLW parameter, 374 J Job shop scheduling, 808 Just-in-time production, 601, 822 INDEX K K-Best Feature, 268, 269 KBESTS Parameter, 405 Kehoe, T.J., 805 Kendall correlation, 726 Kernighan, B., 866 Kill Scripts on Limit Option, 227 KILLSC Paramater, 405 Knapsack cover, 391 Knapsack cover cuts, 390 Knapsack problem, 110–16, 361, 809 KNPCTS, 391 L Laplace distribution, 724 Laporte, G., 866 LATCTS, 391 Latin-hyper-square, 720 Lattice, 391 Lattice cuts, 390 LCORE1 – LCORE4 parameters, 406 LCORES Parameter, 405 LDT format, 497 Lead time, 601, 604 Learning curve, 810 LENPAG parameter, 379 LFTCTS, 391 LG4 File Format, 218 LG4 format saving, 497 LGM function, 426, 868 Libraries (DLL), 547–90 License Command, 154, 174, 316 License Key, 2, 10 Lift cuts, 391 Lifting cuts, 390 Limits, 226, 251 BND function, 128, 881 constraints, 117 cuts, 390 iterations, 374, 375 sets, 48 software version, 65 Lin, S., 866 LINDO API, 349 LINDO contact information, 66 LINDO Files, 290 LINDO Model, 158 Line Count Limits, 221 Linear formula, 772 939 Linear loss function, Poisson, 429 Linear Optimality Tolerance Box, 247 LINEAR Parameter, 403 Linear regression, 810, 854 Linear Regression, 471 Linear solver, 653, 771 Linear Solver Tab, 242 Linear vs Nonlinear, 295 Linearization, 235, 397, 898 LINGO.CNF, 888 LINLEN parameter, 380 Linux, 29 Printing a file, 31 Saving a Model, 31 Solving the Model, 30 Little s-big S policies, 830 LNBIGM parameter, 397 LNDLTA parameter, 397 LNG File Format, 218 LNG format, 497 LNRISE parameter, 397 Local optimum, 552, 774 Log files, 553, 556, 923 Log Files, 168 LOG function, 144, 426 Log Output Command, 154, 168 LOG10 function, 426 Logarithm, 629, 790, 810, 868 Logarithmic distribution, 725 LOGB function, 426 Logical expressions examples, 605, 848 operators, 72, 423 Logistic distribution, 724 Logistics models, 612–18 Lognormal distribution, 724 Look Command, 156, 308 LOOK command, 341, 873 Loop Optimization, 240 LOOPOP parameter, 413 Lot sizing, 819 Lower Bound, 229 Lower Triangular, 299 LOWMEM parameter, 402 LP, 36 LP File Format, 159 LP Solver Box, 264 LRP format, 497 LS_DINFO_MIP_BEST_OBJECTIVE_LNG, 555 LS_DINFO_MIP_BOUND_LNG, 555 LS_DINFO_OBJECTIVE_LNG, 555 LS_DINFO_SUMINF_LNG, 555 940 INDEX LS_IINFO_BRANCHES_LNG, 555 LS_IINFO_CONSTRAINTS_LNG, 555 LS_IINFO_CONSTRAINTS_NONLINEAR_LNG, 555 LS_IINFO_ITERATIONS_LNG, 555 LS_IINFO_NONZEROS_LNG, 555 LS_IINFO_NONZEROS_NONLINEAR_LNG, 555 LS_IINFO_VARIABLES_INTEGER_LNG, 555 LS_IINFO_VARIABLES_LNG, 555 LS_IINFO_VARIABLES_NONLINEAR_LNG, 555 LSclearPointersLng, 553 LScloseLogFileLng, 553 LSdeleteEnvLng, 554 LSERR_INFO_NOT_AVAILABLE_LNG, 559 LSERR_INVALID_INPUT_LNG, 559 LSERR_INVALID_NULL_POINTER_LNG, 559 LSERR_NO_ERROR_LNG, 559 LSERR_OUT_OF_MEMORY_LNG, 559 LSERR_UNABLE_TO_OPEN_LOG_FILE_LNG, 559 LSexecuteScriptLng, 554 LSgetCallbackInfoLng, 555, 580 LSopenLogFileLng, 556 LSsetCallbackErrorLng, 557 LSsetCallbackSolverLng, 557, 580 LSsetPointerLng, 558 LTF format, 497 M Mac LINGO Applications Menu, 318 Machine repairman model, 639, 802, 821 Macintosh Installing, Marketing models, 644–51 Markov chain model, 644, 812 Markowitz portfolio selection, 619, 623, 626, 807 Markowitz, H., 619, 807 Match Parenthesis Command, 155 Matching model, 814 Material requirements planning, 601, 822 Mathematical functions, 425 Mathematical notation, 48–53 Matrix Displaying, 299 Matrix Picture, 299 Matrix decomposition, 399 Matrix Decomposition, 248 Matrix determinants, 464 Matrix form, 342, 645 Matrix functions, 462 Matrix inversion, 469 Matrix transpose, 476 MAX function, 76, 78, 438, 610, 780 Max Passes, 258 Max Scenarios Limit, 288 MAXCTP parameter, 390 MAXCTR parameter, 399 Maximum array length, 884 McCormick, G., 858 MEM command, 322 Members of sets, 71 Membership filter, 72 Memory, 36, 232 allocated, 322, 376, 552 usage, 322 virtual, 377 working, 873, 878 Memory usage, 239, 241 Menu commands, 519 Menu Commands, 151, 158 Menu Commands in Brief, 154 Menu Commands In Depth, 158 Menu tips, 382 Menus, 151 Method, 242, 243 Method Box, 243 METRIC model, 815 Mexican steel model, 816 MICONE, 36 MIN function, 76, 78, 780 Minimal cost queuing, 850 Minimize memory usage, 241 MOD function, 426 Model Class Field, 36 MODEL command, 325, 873 Model Generator Tab, 231 Model reduction, 386 Model Reduction, 242, 243 Model Regeneration, 234 Model Statistics command, 156, 307 Model Window, 158 Modeling language, 48–53, 60–63, 67 Models infeasible, 47, 351, 552, 883 nonlinear, 143, 395, 781–82 titles, 63 types, 771 unbounded, 351, 552, 882 Mortgage calculation, 871 MPI File Format, 159 INDEX MPI files, 349 MPI Files, 172 MPS File exporting, 350 format, 894 MPS File command, 154 MPS File Format, 159 MPS Files, 172 MPS Format, 154, 290 Multicore, 223 Multilevel distribution, 826 Multiple Cores, 246 Multiple Linear Regression, 471 Multiple Solutions for MIPs, 268, 269 Multiprod capacitated lot sizing, 819 MULTIS, 392 Multistart, 36, 281 Multistart solver, 392, 897 Multistart Solver, 281 Multithreading, 223, 272 Mutli-Core Option, 246 MXMEMB parameter, 376 MYUSER.DLL, 591 N NAME function, 451 Naming conventions constraints, 60, 876 duplicate names, 890 file names, 877 parameters, 387 sets, 875, 877 Naming Conventions, 32, 229 NCRASH parameter, 385 Necessary set, 351 Necessary Set, 303 Negative Binomial distribution, 725 Negative variables, 122–27 Nested Benders Decomposition, 287 Nesting, 81 FOR functions, 880 TAKE command, 874 Netarc Format, 204 Netnode Format, 204 Network Charts, 204 Network equilibrium, 828 New command, 873 New Command, 158 New features, vii New Model, 158 NEWLINE function, 451 Newsboy problem, 803, 830 Next Command, 312 NLP, 36 NLP Solver, 281 Node selection, 379 Node Selection, 268 NODESL parameter, 379 Non-Basic solutions, 248 Non-differentiable functions, 780 Nonlinear limits, 65 models, 143, 781–82 solver, 653, 771 Nonlinear models, 395 Nonlinear Optimality Tolerance, 251 Nonlinear Rows Displaying, 295 Nonlinear Solver Options, 250 Nonlinear Solver Strategies, 253 Nonlinear Solver Tab, 250 Nonlinear vs Linear, 295 Nonlinearities Displaying, 295 Non-Native File Formats, 159 NONNEG Parameter, 404 Non-Negativity, 229 Nonoptimal solution, 883 Nonzeroes Box, 36 Nonzeros, 345 dual price, 882 NOPTOL parameter, 374 Normal distribution, 724, 795 NORMINV function, 428 NORMSINV function, 428 NSLPDR parameter, 385 NSLPSV parameter, 415 NSTEEP parameter, 385 NTHRDS parameter, 415 NTMODE parameter, 416 NUMBIN parameter, 414 Numeric Integration, 426 Numeric precision, 552 Numerical derivatives, 252 O OBJBND function, 451 OBJCTS, 391 OBJCTS parameter, 375 Object Linking and Embedding, 498 Object, Insert New, 523 Objective coefficient ranges, 357, 358 941 942 INDEX Objective coefficients, 46 Objective cuts, 391 Objective Field, 36 Objective function cuts, 390 developing, 50 examples financial models, 621, 625, 633 marketing models, 650 plant location, 613 production models, 598, 609 ODBC, 215, 527–45 administrator, 529, 545 datasources linking, 365 ODBC function, 539 exporting, 539–45 importing, 535–39 ODBC function, 439 OLE automation importing, 512–16 OLE function, 439 exporting reports, 511 syntax, 505–11 importing, 499–504 Omitting values, 142 Online Registration, 314 Open command, 873, 924 Open Command, 159 Open Data Base Connectivity, 527–45 Opening a File, 159 Opening a Sample Model, Opening a Sample Model on a Mac, 14 Opening a Sample on Linux, 24 Operators, 421–24, 875, 877, 882 Optimal solution, 392, 552, 774 Optimality Box, 265 Optimality Tolerance, 247, 280 Optimization Modeling with LINGO, 595 Options Command, 211, 213, 214, 217, 218, 220, 221, 222, 226, 232, 238, 239, 241, 250, 251, 252, 253, 256, 257, 260, 267 Options pricing, 627, 835 Oracle, 534 OROUTE parameter, 382 Output, 217 Overbooking, Airline, 831 P PAGE command, 363 Page Length, 221 Page Size Limits, 221 Parallel LP Solves, 246 Parallel Option, 223 Parameters error messages, 885, 888 pre-defined, 356, 364, Error! Not a valid bookmark in entry on page 373 user defined, 140 Parent sets, 71 Parentheses, 922 Pareto distribution, 724 Partial Pricing, 245 Partitioning Models, 272 Passwords databases, 365 error messages, 886, 887 HIDE command, 338 Paste command, 480 PAUSE, 678 PAUSE command, 363 PBN function, 428 PCX function, 428 Pearson correlation, 726 PEB function, 429, 849 PEL function, 429, 636, 804, 850 PELA function, 429 PERT, 537–39, 542–45, 839 Peters, D.G., 790 PFD function, 429 PFS function, 429, 639 PHG function, 429, 856 PI function, 426 PIC, 673 PICONE, 36 Picture command, 156, 299 PICTURE command, 342 PILP, 36 PINLP, 36 PIQP, 36 Plant location, 390, 391, 612, 788 Platforms, 319 PLOCTS, 391 Pluto Dogs, 82, 108 POINTER function, 440 data section, 550, 552 DLL, 553, 558 Poisson finite source, 639 linear loss function, 429 probability distribution, 429, 636, 803 random variable, 429 INDEX Poisson distribution, 725 Portfolio selection Markowitz, 619, 623, 626, 807 scenario based, 796, 843 Portfolio Selection, Markowitz, 691 Positive Semi-Definite Matrices, 134 POW function, 427 Powerstation FORTRAN pointer functions, 552 user defined functions, 591 PPL function, 429 PPS function, 429 PRBLVL parameter, 386 Precedence relations, 607, 609 PRECIS parameter, 412 Precision, 218 Present value, 428 Previous Command, 312 Prices Black & Scholes, 629, 833 options, 627, 835 strategies, 387 Pricing Strategies, 226, 242, 245 Primal Formulation, 290 Primal/dual interior point algorithm, 386 Primitive set defining, 68–70 examples, 68, 82–86, 87 exporting, 539 names, 877 Primitive Sets, 238, 239 PRIMPR parameter, 387 Print Command, 166 Print Preview Command, 168 Print Setup Command, 167 Printing a file, 46, 166, 168 Priority, 261 PRIORITY function, 121 Priority option, 388 PRNCLR parameter, 392 Probabilities, 624 Probability distribution binomial, 428, 831, 835 Erlang busy, 429, 849 Erlang loss, 429, 636, 804 Erlang queuing, 636 exponential, 636 hypergeometric, 429, 856 normal, 430, 795 Poisson, 429, 636, 639, 803 steady state, 644, 812 t distributions, 795 943 transition, 644 Probability functions, 428–31 Probing, 259, 386 Procedures, 681 PROD function, 438 Product form inverse, 772 Product Mix Models, 32 Production, 819 planning, 819 product mix, 116–20, 838, 842 rates, 801 schedules, 601, 822 Production management models, 596–611 Programming Example Binary Search, 687 Cutting Stock, 698 Markowitz Efficient Frontier, 691 Project Evaluation and Review Technique, 537–39, 542–45, 839 Prompts, 319, 325 Properties command, 493 Proportionality, 772 PSL function, 429 PSN function, 430, 795 PTD function, 430, 795 Purchase transition matrix, 645 Q QP, 36 QRAND function, 430, 895 Quadratic functions, 845 Quadratic Recognition, 253 Quasi-random numbers, 430 Question mark prompt, 325 Queuing models examples Erlang, 636–43, 804, 849–50 machine repairman, 802 steady state, 851 probabilities, 429 QUIT command, 419 R R/C format names, 222, 229 parameter, 387 R/C Format Names for MPS I/O, 229 RAND function, 431, 795 Random Generator Seed, 286 Random numbers, 430, 431, 795, 812, 895 944 INDEX Random Variables, 287 Range analysis, 895 dual values, 357 names defining, 510 exporting (OLE), 506 exporting (WKX), 512 importing (OLE), 504 OLE automation, 513 reports command-line, 356 error messages, 887 Range Analysis, 207 Range command, 47 Range Command, 156, 207, 226 RANGE command, 356 RANGED function, 451 RANGEU function, 452 Rate of return, 621, 625 RCMPSN parameter, 387 RCTLIM parameter, 390 Read error, 879 Redirecting I/O, 497 REDUCE parameter, 386 Reduced cost, 46 ranges, 357 Reduced cost significance, 247 Reduction, 243 Refactoring, 248 REFRAQ parameter, 408 Regeneration, 234 Register, 314 Register Command, 157 REGRESS function, 471 Regression analysis, 471 Regression Analysis, 810, 854 Relational operators, 423, 875 Relationships, 782 Relative Integrality, 263 Relative integrality tolerance, 374 Relative Limit, 258 Relative Optimality, 266 RELEASE, 674 RELINT parameter, 374 REOPTB parameter, 389 REOPTX parameter, 389 Reports, 382 export summary report ODBC based, 544 OLE based, 511 generating, 347 range report command-line, 356 error messages, 887 solution report command-line, 353 exporting, 544 naming constraints, 62 tolerances, 373, 389 width, 364 statistics, 344 REPROD parameter, 418 Reproducibility, 229 Reproducibility of Solution, 229, 418 Reproducibility of Solutions, 256 Resource limits, 48, 117 Right-hand side range report, 358 Risk downside risk, 796 portfolio selection, 619–26, 807, 843 sampling, 856, 860 RLPF command, 329 RMPI command, 326 ROUND function, 427 ROUNDDOWN function, 427 Rounding, 104, 109, 389 Round-off Error, 228 ROUNDUP function, 427 Row name, 876 RunLingo, 494 Runtime, 36 Runtime Limits Box, 222, 226 RVRT command, 349 S Sales forecasting, 861 Sample Continuous Only, 287 Sample Models, 32 sample size, 726 Sample Size, 286 Sampling, 287, 430, 856, 858, 860 Save As Command, 165 Save Command, 165 SAVE command, 349 Saving a Model, 46, 165 Scalar variables examples, 48, 51, 609, 838 initializing, 140 SCALEM parameter, 386 SCALEW parameter, 408 Scaling, 228, 373, 781, 897 INDEX Scaling the Model, 242, 249 Scaling Warning Threshold, 228 Scarce capacity, 819 Scenario portfolio selection, 623, 796, 843 Scenarios, 288 Scenarios Limit, 288 SCENE command, 343 Scholes, M., 627, 833 Schrage, L., 122, 595, 793 SCLRDL parameter, 392 SCLRLM parameter, 392 Script files, 489–91 command-line, 331 DLL, 554 OLE automation importing, 512–16 Script Files, 169, 220 Script processor, 550 Second Order Derivatives, 252 Second-Order Cone, 36 SECORD Parameter, 404 Seed, 286 Seed value, 895 SELCON parameter, 385 Select All command, 480 Selective constraint evaluation, 385 Selective Constraint Evaluation, 254 Semi-Definite, 135 Semi-variance risk, 623, 626 Send Reports to Command Window, 220 SET, 680 SET command, 888 Set Looping Functions, 240 Set-looping functions, 74–81, 437 Sets, 48–59, 67–101, 895 derived sets defining, 68, 71–74, 894 dense, 609, 895 examples blending models, 87–90, 598 financial models, 624 marketing models, 649 production models, 604, 609 exporting, 539 errors, 893 implicit, 895 names, 875 necessary, 351 primitive set defining, 68–70 examples, 68, 82–86, 87 exporting, 539 names, 877 sufficient, 351, 353 Sets section, 68–74, 482 Setup cost, 801, 819 Shack4Shades, 122 Shadow prices, 47, 357 Shipping problem, 48, 67, 612, 826 Shortcuts, 154 Shortest route problem, 616 Show as 0, 217 SHOWNL command, 344 SIGN function, 427 Simple Benders Decomposition, 287 Simplex method, 772 cold start, 390 parameters, 386 warm start, 389 Simplex Method, 243 Simpson’s Rule, 426 SIN function, 427 SINH function, 427 SIZE function, 437 Slack, 307 Slack or Surplus, 47, 373, 611 Slack variables, 345, 599 Slope, 123, 780 Slow, 240 Slow progress iteration limit, 374 SLP Directions, 254 SLP Solver, 254 SMAX function, 427 SMIN function, 427 Smooth expressions, 636, 780, 862 Smooth models, 277 SMPI, 675 SMPI command, 349 SMPS, 675 SMPS command, 350 SOLU, 676 Solution Command, 156, 191 Solution Display Box, 217 Solution report command-line, 353 exporting, 544 naming constraints, 62 tolerances, 373, 389 width, 364 Solution Reports, 45, 193 Solution Reproducibility, 229 Solution Reproducibility, 418 Solutions infeasible, 47, 351, 552, 883 945 946 INDEX non-optimal, 883 optimal, 392, 552, 774 unbounded, 351, 552, 882 undefined, 883 undetermined, 552 SOLVE, 655 Solve command, 525 Solve Command, 156, 189 SOLVE Command, 227 SOLVEL parameter, 386 Solver, 653, 771 branch-and-bound constraint cuts parameters, 377, 391, 399 definition, 104, 653, 771 direction, 388 heuristics, 399 global, 395 interrupting, 923 linear, 653, 771 method, 386, 895 multistart, 392 nonlinear, 653, 771 Solver Menu, 156, 189 Solver Menu Commands in Brief, 156 Solver Method, 243 Solver Status Box, 36 Solver status window error messages, 923 model classification, 772, 773 options, 381 Solver Status Window, 36 Solver Type Field, 36 Solver|Debug, 303 Solver|Options, 211 Solver|Range, 207 Solver|Solution, 191 Solver|Solve, 189 Solvers Used Internally by LINGO, 242, 243, 250, 260 Solving the Model, 35, 189, 242, 243 SONGS model, 864 Sorting, 865 SOS variables syntax, 128 SP Big M Coefficient, 288 SP Seed, 286 SP Solver Method, 287 SP Solver Tab, 285 Spanning tree model, 824 Sparse derived set, 90–96, 96–101, 877 Sparse set, 71 SPBIGM parameter, 414 Spearman correlation, 726 Splash screen, 382 Splash Screen, 216 SPLOADSCENE, 682 SPMAX, 682 SPMAXS parameter, 412 SPMEAN, 682 SPMTHD parameter, 410 SPNUMSCENE, 682, 683 SPPRBSCENE, 683 Spreadsheets data section, 48 exporting functions, 504–12 reports, 363 importing, 499–504 interfacing with, 479, 481, 499–526 SPSCON parameter, 409 SPSEED parameter, 409 SPSMSZ parameter, 408 SPSTDDEV, 683 SPXVAL parameter, 410 SQL, 534 SQR function, 427 SQRT function, 427 STABAR parameter, 382 Stack space, 875 Staff scheduling, 82, 486, 490, 798 DLL, 547–73, 550 Starting LINGO on a Mac, 10 Starting LINGO on Linux, 21 Starting LINGO on Windows, Starting Points, 281 State Field, 36 State of the model, 882, 883 Statistics, 307, 344, 773 STATS command, 344 Status bar, 382 Status Bar, 215 STATUS function, 453 Status Window, 216, 232 Status Window Command, 157, 311 STAWIN parameter, 381 Steady state, 642, 851 equations, 641 probability, 644, 812 queuing model, 641, 851 Steepest edge, 385, 387 Steepest Edge, 254 Steepest-Edge Pricing, 245 INDEX STM2DWK function, 462 STM2HR, STM2MIN functions, 460 STM2YMD function, 459 STM2YR, STM2MON functions, 460 STMNOW function, 461 Stochastic Programming Declaring Distributions, 723 Gas Buying Core Model, 731 Gas Buying Example, 730 Introduction, 713 Investing Under, 751 Investing Under Uncertainty Example, 750 Language Features, 721 Monte Carlo Sampling, 719 Multistage Decision Making, 713 Recourse Models, 715 Scenario Tree, 717 Setting up SP Models, 720 Stock Option Core Model, 742 Stock Option Example, 741 Stochastic Programming, 285, 286, 287 Deterministic Equivalent, 290, 297 Scenario, 299 Stock options, 627 STOP Statement, 669 Straight line relationships, 772 Strategies, 281 Strategies Box, 281 Stratified sampling design, 858 STRLEN function, 454 Strong branch, 389 Strong Branch, 268 STRONG parameter, 389 Student t distribution, 724 SUBMODEL, 653 SUBOUT parameter, 400 Successive linear programming, 772 Successive Linear Programming, 254 Sufficient set, 351, 353 Sufficient Set, 303 SUM function, 76, 77, 112, 438 Sum of a set, 438 Sum of squared prediction, 861 Surface Chart, 201 Sweeney, D., 617 Symetric Stable distribution, 724 Syntax, 139 coloring, 392 Syntax Coloring, 219 T t distribution, 795 TABLE function, 454 Table of Contents, iii TAKE, 220 TAKE command, 331 command scripts, 489 Take Commands command, 489 Take Commands Command, 154, 169 TAN function, 427 TANH function, 427 TATSLV Paramater, 405 Technical support, 66 Terminal width parameter, 364, 885 TERSE command, 363 Terse Output, 217 TERSEO parameter, 380 Text files, 48, 349, 479, 481, 497 TEXT function, 440 command scripts, 491 Tiered distribution, 826 Tile Command, 312 TIM2RL parameter, 379 TIME command, 419 TIME function, 458 Time Limits, 227 Time To Relative, 266 Time to relative tolerance, 379 Timesharing system, 639, 802 TIMLIM parameter, 375 TITLE command, 63 Tolerances, 242, 251, 263, 267 command-line, 321, 364, 366–79 examples, 646 Tolerances Box, 267, 280 Tool tips, 382 Toolbar, 151, 217, 383, 519 Button Definitions, 152, 153 Mac, 153 Windows, 152 Toolbar box, 217 TOOLBR parameter, 383 Traffic congestion, 829 Transfer method command line, 511, 544 Transition probability, 644, 812 Transportation model, 872 datasources, 528 exporting, 509 importing, 502 sets, 48 947 948 INDEX TRANSPOSE function, 476 Traveling salesman problem, 866 Triangular distribution, 724 Truncating, 104, 351 Two-sided constraints, 875 Types, 259 U Unary Minus Priority, 232 UNARYM Parameter, 403 Unbounded, 303 Unbounded solution, 351, 552, 882 Undefined arithmetic operation, 385, 881, 883 Undefined solution, 883 Undetermined solution, 552 Uniform distribution, 724 Unit normal linear loss, 429 Unity coefficients, 345 Unix, 497 Update, 315 Update interval, 381 USEPNM parameter, 384 User Database Info, 175 User defined functions, 591–94 USER function, 478 USER Function, 887 User ID, 365 User interrupt, 923 Utility functions, 648 V Values transferred command-line, 512 Variable Bounds, 240 Variable Box, 36 Variable domain functions, 881 Variable Upper Bounds Box, 280 Variables bounds, 399, 400 guidelines for, 781 syntax, 127 decision variables examples, 609, 613, 624 ranges, 356 defining, 50 fixed variables, 772, 880 free variables, 122–27 initializing, 781 integer variables binary examples, 609 functions, 103 priority, 388 syntax, 110–20 examples, 600 general, 103, 104–9 solutions, 782 variable domain functions, 103–22 limits, 65 negative, 122–27 production models, 598, 604 random, 429 scalar examples, 48, 51, 609, 838 initializing, 140 slack, 345, 599 SOS syntax, 128 transportation models, 618 Variance, 619, 626, 627 Vehicle routing problem, 869 VERBOSE command, 363 Verbose Output, 217 Viewing a Model, 308 Virtual memory, 377 Visual Basic, 548 macros in Excel, 512, 515 Visual Basic NET, 548 Visual C++, 548 callback function, 581 user defined function, 592 Volatility, 627 W Warm Start, 264 Warm start option, 389 WARN function, 478, 646, 880, 890 Weibull distribution, 724 What If analysis, 141 What is LINGO Windows, WHILE Statement, 668 WIDTH command, 364, 885 Williams, T., 617 Window Menu, 157, 309 Window Menu Commands in Brief, 157 Windows Commands, 309 Windows Commands in Brief, 154, 155, 156, 157 Winston, W., 122, 862 Wireless Widgets INDEX examples, 48 importing, 482, 502 sets, 68, 90 WNLINE parameter, 382 WNTRIM parameter, 382 Working memory, 878 Workstations, 607, 641, 643 Worst bound, 379 WRAP function, 124, 437 WRITE, 677 Write access, 888, 889, 923 WRITE function, 456 WRITEFOR function, 456, 457 Writing to files, 485 WS, 289 X XDETEQ command, 345 Y YMD2STM function, 458 949 [...]... chmod 755 /LINGO- LINUX-64x86-16.0.run -v You may then start the install program by entering: /LINGO- LINUX-64x86-16.0.run If you are installing LINGO with normal user rights, the install program defaults to putting LINGO in your $HOME /lingo1 6 folder If your LINGO license permits multiple users, then you can install LINGO as a super user, in which case, LINGO defaults to installing in the /opt /lingo1 6 folder,... Installing LINGO on a Mac LINGO for the Mac is distributed as a DMG file, or disk image file, titled LINGO- OSX-64x86-16.0.dmg If you double-click on this file you should see a window similar to the following: To install LINGO onto your Mac, drag the LINGO icon in the window to the Applications folder icon This will place a copy of LINGO in the /Applications folder of your hard drive The Mac version of LINGO. .. also recommend that you drag a copy of the LingoDocs folder in the above window to your hard drive The LingoDocs folder contains copies of LINGO' s sample models and documentation You may want to place this folder in your $HOME folder (subsequent documentation will assume this is the case) Starting LINGO on a Mac Once LINGO is installed, you will find a new LINGO icon in the /Applications folder on your... to start LINGO Once LINGO is running, your screen will resemble the following: The outer window is the main frame window, and all other windows will be contained within this main frame window The top of the main frame window also contains a toolbar for executing various LINGO commands The smaller child window labeled Lingo Model - Lingo1 .lng is a new, blank model window In the Developing a LINGO Model... information regarding LINGO' s current state Both the toolbar and the status bar can be suppressed through the LINGO| Preferences command GETTING STARTED 13 Many copies of LINGO come with their licenses pre-installed However, some versions of LINGO require you to input a license key If your version of LINGO requires a license key, you will be presented with the following dialog box when you start LINGO: Your... to run LINGO in demo mode by clicking the Demo button In demo mode, LINGO has all the functionality of a standard version of LINGO with the one exception that the maximum problem size is restricted Demo licenses expire after 180 days Opening a Sample Model on a Mac In the Installing LINGO on a Mac section above, we suggested that you install the LingoDocs folder in your $HOME directory The LingoDocs... of LINGO Modeling The sample model directory is titled Samples and is stored directly off the main LINGO directory To open a sample model in LINGO, follow these steps: 1 Pull down the File menu and select the Open command Migrate to where you installed your copy of the LingoDocs folder: GETTING STARTED 2 Double-click on the LingoDocs folder then double-click on the Samples folder contained in the LingoDocs... install the new copy of LINGO To uninstall the existing copy of LINGO, click on the Windows Start button, select the Settings command, select Control Panel, then double-click on the Add or Remove Programs icon You should then be able to select LINGO and have the old version removed from your system 2 CHAPTER 1 Starting LINGO on Windows Once LINGO is installed, you will find a new Lingo icon on your desktop:... this window 12 CHAPTER 1 Unlike the Windows version of LINGO, the command menus do not appear at the top of the main frame window, but appear in the Finder's menu bar whenever LINGO is the active application Below, we see the six LINGO menus — Lingo, File, Edit, Solver, Window and Help — in the Finder's menu bar at the top of the screen: See the LINGO Commands section for details on the toolbar and... STARTED 3 regarding LINGO' s current state Both the toolbar and the status bar can be suppressed through the use of the Options command The smaller child window labeled LINGO Model - LINGO1 is a new, blank model window In the next section, we will be entering a sample model directly into this window Many copies of LINGO come with their licenses pre-installed However, some versions of LINGO require you ... system 2 CHAPTER Starting LINGO on Windows Once LINGO is installed, you will find a new Lingo icon on your desktop: You may double-click on the icon to start LINGO Once LINGO is running, your screen... Installing LINGO on Windows Installing the LINGO software is straightforward To setup LINGO for Windows, place your CD in the appropriate drive and run the installation program SETUP contained in the LINGO. .. nonlinear problem New Features for LINGO 16.0  LINDO Systems is proud to introduce LINGO 16.0 The new features added to LINGO since the initial release of LINGO 15.0 include the following: LP