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Linear Programming

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Incorporates Large-Scale Linear Programs Solver. Unlimited Number of Constraints & Variables

BUY linear programming GIPALS

GIPALS is linear programming environment that incorporates large-scale linear programs solver and easy, intuitive graphical user interface to direct specify or import and solve any type of constrained optimization problems arising in various industrial, financial and educational areas. A constrained optimization problem is stated as a linear program with UNLIMITED number of decision variables and constraints. The linear program solver is based on Interior-Point method (Mehrotra predictor-corrector algorithm) and optimized for large sparse linear programs by implementing the state-of-art algorithm to order the constraints matrix. The user can specify the linear program constraints in a dense form using the grids or in a sparse form using the particular constraints editor. The dense form is suitable for small and medium linear programs with non-zeros prevail over zeros. In this form the constraints can be directly copied/pasted from/to MS Excel spreadsheets by Windows clipboard. The sparse form is designed to specify / view / edit large linear programs with tens and hundreds of thousand variables and constraints. GIPALS can import linear programs from Mathematical Programming System (MPS) data format that is an industry standard for the description of a variety of linear programs. Any linear program specified in GIPALS' user interface could be exported to MPS format. The solution of the linear programs can be saved as CSV (comma-delimited spreadsheet), Tab-delimited or HTML file. Key features of GIPALS: Simple and natural way to specify a linear program without any special mathematical knowledge; Robust Interior-Point method for fast and reliable solution; Support the industrial standard format of linear programs; Report the solutions in widely used formats including spreadsheets and HTML

A constrained optimization problem is stated as a linear program that size can reach up to 500 thousand decision variables and constraints.

The linear program solver is based on interior-point method (Mehrotra predictor - corrector algorithm) and optimized for large sparse linear programs. The solver exploits a sparsity of the constraint matrix by implementing state-of-art ordering algorithm to preserve the matrix sparsity and hence reduce the calculation time dramatically. Almost every stage of the linear programming calculation can be saved in the debug files or traced for the deep analysis.

The user can specify the linear program constraints in a dense form using the grids or in a sparse form using the particular constraints editor. The dense form is suitable for small and medium linear programs with non-zeros prevail over zeros. In this form the constraints can be directly copied/pasted from/to MS Excel spreadsheets by Windows clipboard. The sparse form is designed to specify / view / edit large linear programs with tens and hundreds of thousand variables and constraints. Any constraint can be disabled / enabled from the calculation by the user at any time.

GIPALS can import linear programs from Mathematical Programming System (MPS) data format that is an industry standard for the description of a variety of linear programs. Any linear program specified in GIPALS' user interface could be exported to MPS format.

The solution of the linear programs can be saved as CSV (comma-delimited spreadsheet), Tab-delimited or HTML file.

Key features of GIPALS:

  • Simple and natural way to specify a linear program without any special mathematical knowledge
  • Robust Interior-Point method for fast and reliable solution
  • Support the industrial standard format of linear programs
  • Report the solutions in widely used formats including spreadsheets and HTML

Optimization is both an art and a science.

Optimization plays an important role in the real world. It can dramatically decrease the cost of production and sequentially increase the revenue. Optimization also helps to make a decision. Making a decision is what all the people and businesses do every day and optimization is a method to make such decision that would satisfy all people or businesses needs to achieve a goal with less possible efforts.

There are two major types of optimization: Unconstrained and Constrained.

This Software considers a constrained optimization as the most important type because it deals with limited resources that are typical in the real world. Any productions or financial institutions have limited resources or "constraints" (such as labor, financial and natural) and they must operate within these constraints. Therefore an optimization with limited resources is called "constrained optimization".

General constrained optimization task consist of five stages:

  1. Problem description and definition of a goal
  2. Model statement: define decision variables, constraints and an objective
  3. Numeric solution: calculation the decision variables and objective values
  4. Post process analysis and revision of the model statement
  5. Making a decision

The first stage is done by a problem originator who wants to perform an optimization and make a decision. Second stage is usually provided by a system analyst who can describe an optimization task in terms of mathematical model and define all decision variables and their ranges, constraints and objective function. Third and fourth stages are the most computation-intensive stages and can be done by a special optimization toolkit that allows to specify the mathematical model, calculate it and provide a possibility to alter the model and re-calculate it. The last stage is the goal of the optimization and it is provided by the problem originator according to the results from the system analyst.

The first two stages and the last one are unique and can vary from a case to case even in the same data domain. Therefore these two stages must be done by the problem originator and the system analyst in each particular situation.

In contrast, the third and fourth stages of constrained optimization are very good formalized. There are several mathematical methods have been developed to perform them and one of these method is a Linear Programming that has been a very successful method. The optimization model is stated as Linear Program and all constraints and the objective function are defined as linear combinations of the decision variables.

This Software has developed a new constrained optimization environment GIPALS that incorporates the linear programming method and simple, intuitive graphical user interface (GUI) to specify an optimization model without any special mathematical knowledge.

linear programming GIPALS Start

Linear programming examples

There are several examples of linear programming intended to make the users of GIPALS familiar with it. These examples are included in GIPALS installation and can be found in ..\GIPALS\Examples folder.

See Screen Shots: Variables Page | Calculation Process | Constraint Page (Compact view) | Matrix Palette Dialog | Result Page | Debug Options Dialog

GIPALS Linear Programming $197.95 - 15000 Constraints & Variables | $297.00 - Unlimited Number of Constraints & Variables

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