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SOFTHUB SYSTEMS TRAINING MANUAL FOR LINGO 11 By: UWADONE Emmanuel

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Table of Contents About Softhub Systems Introduction to LINGO 11.0……………………………………..……………………………..4

How To Create a LINGO Model …………………….………………………………………..12

Solving a LINGO Model…………………………………………………………………….…13

Using Sets in LINGO……………………………………………………………………….….15

The LINGO Data Section………………………………………………………………………17

Variable Types in LINGO……………………………………………………………….…..…19

LINGO Operators and Functions……………………………………………………….……...20

Solving Linear Programming, Integer Programming, Binary Integer Programming Problems

Using Lingo ……………………………………………………………..………………….….23

LINGO Programming Examples……..………………………………………………………...28

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About Softhub Systems

SoftHub is a cutting edge IT Company that specialises in the following services

Webhosting

Web development

Application Development

IT training

Business Development

Consultancy Services

Networking Services

Financial and Human Capital Management Software solutions

08067847553

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1.0 Introduction to LINGO 11 LINGO is a software tool designed to efficiently build and solve linear, nonlinear, and integer

optimization models. It is licensed to Lindo Systems Inc.

1.1 LINGO 11.0 includes several new features, including:

Simplex Solver Improvements: The simplex solvers include a number of new features:

Large linear models solve an average of 80% faster using the newly enhanced dual and primal

simplex solvers.

The new release includes several enhancements to the sparse LU decomposition routines and the

addition of advanced basis repairing techniques.

Relative to earlier releases, the Simplex solvers offer improved handling of numerically difficult

problems.

Improvements in the dual simplex method that is used to reoptimize at each branch in the branch-

and-bound tree on integer models, allowing more branches to be processed per second in the search

tree.

Better handling of numerically difficult linear and integer models.

MIP Solver Improvements: LINGO's MIP solver improvements include:

The MIP solver is now an average of 40% faster on a wide range of integer models.

An advanced implementation of Feasibility Pump heuristic speeds the finding of feasible solutions on

many difficult problems.

An advanced implementation of the Relaxation Induced Neighborhood Search (RINS) technique finds

improved integer solutions faster.

General and local branching strategies have been improved to exploit model structure.

Rounding techniques have been expanded to exploit a wider range of constraint structures.

Performance has been improved on probing through out the branch-and-bound tree.

Cut management has been improved.

Global Solver Improvements:

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The global solver includes a number of enhancements for solving non-convex,

nonlinear models to global optimality:

New discrete space constraint propagation and convex-cut generation improve performance on

nonlinear models with integer variables and/or non-smooth functions.

A multi-formulation capability improves bounding performance and enhances tractability through

efficient cut generation.

Barrier Solver Improvements: The barrier solver improvements include:

The barrier method solves large-scale linear and quadratic models an average of 20% faster.

Improved handling of numerically difficult models.

Nonlinear Solver Improvements: The general nonlinear solver improvements include:

On average, the nonlinear solver is now 25% faster oo highly nonlinear and complex models.

An efficient implementation of Algebraic Second Order Derivatives has resulted in improved speed

and solution precision.

Solve Linear Programs in Multiple Cores:

When solving linear programs on a multi-core machine, users can specify that

two, or more, of LINGO's four different LP solvers are to be run in parallel on

different cores. LINGO then returns the solution from the first solver to finish

optimization.

K-Best MIP Solver: LINGO's new K-Best MIP solver will return the K best solutions (based on

objective value) to integer models, where K is a user controlled parameter. You

may then scroll through the K solutions, examine them, and select the one of

most interest based on the value of a tradeoff variable.

Generate and Display Dual Formulations: You may now generate the dual formulation of a linear programming model

with the LINGO|Generate|Dual command.

Support of Semicontinuous Variables:

Many models require certain variables to either be 0, or lie within some non-

negative range, e.g., 10 to 20. Modeling this condition in LINGO in the past

meant having to add an additional 0/1 variable and two additional

constraints. LINGO now allows you to set semi-continuous variables directly

with the @SEMIC statement.

Support of SOS (Special Ordered Sets) Variables of Type 1, 2 and 3 and

Cardinality: You may now specify sets of binary variables that are of type SOS1 (at most.one

nonzero), SOS2 (at most two nonzero and adjacent) and SOS3 (variables must

mk:@MSITStore:C:/LINGO11/lingo11.chm::/multi_core.htm mk:@MSITStore:C:/LINGO11/lingo11.chm::/k_bestintroduction.htm mk:@MSITStore:C:/LINGO11/lingo11.chm::/lingo_generate_.htm mk:@MSITStore:C:/LINGO11/lingo11.chm::/semicontinuous_variables.htm mk:@MSITStore:C:/LINGO11/lingo11.chm::/sos_variables.htm mk:@MSITStore:C:/LINGO11/lingo11.chm::/cardinality.htm

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sum to 1). The cardinality feature allows you to specify sets of variables where,

at most, k variables can be nonzero. These functions allow the MIP solver to

handle models more efficiently and cuts down on the number of constraints

required in your models.

Access Excel, Databases and Text Files in Calc Sections: In prior releases, LINGO was only able to access external data sources using

static links in the Data sections of models. The @OLE, @ODBC, @TEXT and

@POINTER functions are now available in Calc sections, allowing you to

dynamically build links for importing and exporting data. These import/export

functions may also be placed in a loop, which is useful for solving multiple

instances of a model in a loop.

@RANK Sorting Function:

The @RANK sorting function may be used in calc sections to efficiently sorts

vectors and return the ranks of their members in a separate vector.

Support of Additional Trigonometric Functions: Support of the following trigonometric functions has been added: ACOS, ASIN,

ATAN, ATAN2, COSH, SINH, TANH, ASINH, ACOSH, and ATANH. These

functions are fully supported by the global solver, allowing for global solutions

to highly non-convex, trigonometric models.

Help System Updated to HTML for Windows Vista Compatibility:

LINGO's online help files have been ported to compiled HTML for native

support under Windows Vista.

@POINTER Allows Imports and Exports of Set Members from Calling

Applications:

In addition to numerical data, @POINTER can now import and export set

members via a memory location passed by a calling application.

ASP.NET Programming Example: An example illustrating how to call LINGO from ASP.NET is now included in

the \LINGO11\Programming Samples folder.

@SOLU, @OBJBND, @DEBUG and @TIME Functions in Calc

Sections: The @SOLU function in calc sections generates standard LINGO-style solution

reports, @OBJBND returns the bound on the current objective, @DEBUG

debugs infeasible or unbounded models, and @TIME returns the elapsed solver

time.

mk:@MSITStore:C:/LINGO11/lingo11.chm::/programmingexcelthemodel.htm mk:@MSITStore:C:/LINGO11/lingo11.chm::/utility_functions.htm mk:@MSITStore:C:/LINGO11/lingo11.chm::/mathematical_functions.htm mk:@MSITStore:C:/LINGO11/lingo11.chm::/passingsetmembersthemodel.htm mk:@MSITStore:C:/LINGO11/lingo11.chm::/passingsetmembersthemodel.htm mk:@MSITStore:C:/LINGO11/lingo11.chm::/output_statements.htm mk:@MSITStore:C:/LINGO11/lingo11.chm::/report_functions.htm mk:@MSITStore:C:/LINGO11/lingo11.chm::/model_control.htm mk:@MSITStore:C:/LINGO11/lingo11.chm::/report_functions.htm

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1.2 The LINGO Interface

1.