21. Pysimplex: Mixed Integer Linear Programming Modules (beta 0.1) Mixed integer/linear programming modules. http://www.pythonpros.com/arw/pysimplex/

pysimplex: Mixed Integer Linear programming modules (beta 0.1) Yet what are such gaieties to me Whose thoughts are full of indices and surds? x**2 + 7*x + 53 Lewis Carroll Pysimplex provides some basic symbolic programming tools for constructing, solving and optimizing systems of linear equations and inequalities. It includes an implementation of the classical SIMPLEX linear optimization algorithm as well as a filter for parsing and optimizing linear models encoded using the standard MPS format. Perhaps the most compelling aspect of these modules is the way they allow the user or programmer to construct models in a straightforward symbolic manner. For example the following constraint model x>=1 and y>=1 and x+2*y-1.5 >= and y-3*x-0.9 >= may be constructed at the python command line as follows: and the following interaction computes the maximal value for the objective function -x-y within this system of constraints. Thus the maximum value for -x-y is achieved at x=1.0 and y=3.9. More interestingly these modules also allow the optimization of an objective function subject to linear constraints and additional constraints that some of the variables must have integer or binary (0 or 1) values. The function below finds the smallest number of whole currency units whose value sum to within 3 cents less than 1199.03 dollars.

22. The Diet Problem The Diet Problem An Application of linear programming. The recent changeof web server at Argonne and the loss of some of the source http://www-fp.mcs.anl.gov/otc/Guide/CaseStudies/diet/

The Diet Problem: An Application of Linear Programming The recent change of web server at Argonne and the loss of some of the source code for this Case Study has rendered it inoperable. We are currently trying to fix it. We apologize for any inconvenience. CLICK HERE for the demo! Or try the following version without tables What's New Edit the Constraints! Helpful Suggestions for Infeasible Diets!! Description of the diet problem The goal of the diet problem is to find the cheapest combination of foods that will satisfy all the daily nutritional requirements of a person. The problem is formulated as a linear program where the objective is to minimize cost and meet constraints which require that nutritional needs be satisfied. We include constraints that regulate the number of calories and amounts of vitamins, minerals, fats, sodium and cholesterol in the diet. The mathematical formulation is simple, but you will find out by running the model that people do not actually choose their menus by solving this model. Our nutritional requirements can be met yet our concerns for taste and variety go unheeded. We would never drink gallons of vinegar nor include a few boullion cubes in our meals; however, such "optimal" menus have been created using this model. Read more about the history of the diet problem for more interesting facts.

23. Computational Geometry, Algorithms And Applications Recent book with a focus on applications, by Mark de Berg, Marc van Kreveld, Mark Overmars, and Otfried Schwarzkopf. Includes chapters on linesegment intersection, polygon triangulation, linear programming, range searching, point location, Voronoi diagrams, arrangements and duality, Delaunay triangulations, geometric data structures, convex hulls, binary space partitions, robot motion planning, visibility graphs. http://www.cs.ruu.nl/geobook/

About the book Cover Table of contents Errata (1st edition) Errata (2nd edition) ... Order Implementation CGAL LEDA More software Further reading Books Bibliography Web sites Comments to geobook@cs.uu.nl Last modified Oct 9, 2000 Computational Geometry: Algorithms and Applications Second Edition Mark de Berg Marc van Kreveld Mark Overmars Utrecht (the Netherlands) Otfried Schwarzkopf Hong Kong (China) published by Springer-Verlag 2nd rev. ed. 2000. 367 pages, 370 fig. Hardcover DM 59 ISBN: 3-540-65620-0 You can order the book here This textbook on computational geometry has 367 pages. The pages are almost square with a large margin containing over 370 figures. To get an idea about the style and format, take a look at the Introduction or chapter 7 on Voronoi diagrams Computational geometry Computational geometry emerged from the field of algorithms design and analysis in the late 1970s. It has grown into a recognized discipline with its own journals, conferences, and a large community of active researchers. The success of the field as a research discipline can on the one hand be explained from the beauty of the problems studied and the solutions obtained, and, on the other hand, by the many application domains-computer graphics, geographic information systems (GIS), robotics, and others-in which geometric algorithms play a fundamental role. For many geometric problems the early algorithmic solutions were either slow or difficult to understand and implement. In recent years a number of new algorithmic techniques have been developed that improved and simplified many of the previous approaches. In this textbook we have tried to make these modern algorithmic solutions accessible to a large audience. The book has been written as a textbook for a course in computational geometry, but it can also be used for self study.

24. OR/MS Today - LINEAR PROGRAMMING SOFTWARE SURVEY OR/MS Today 2001 linear programming SOFTWARE SURVEY Be sure to take a look at thecompanion article to this survey linear programming by Robert Fourer. http://www.lionhrtpub.com/orms/surveys/LP/LP-survey.html

OR/MS Today 2001 LINEAR PROGRAMMING SOFTWARE SURVEY The information in this survey was provided by the vendors in response to a questionnaire developed by Robert Fourer. The survey should not be considered as comprehensive, but rather as a representation of available Linear Programming packages. Questionnaires were sent to 60 vendors drawn from previous survey participants, the OR/MS Today database and other sources. It includes the products of those vendors who responded by July 1, 2001. If you know of a Linear Programming package that is not in this survey, please contact Jennie Farnsworth at (770) 431-0867, ext. 225 or e-mail them to jen@lionhrtpub.com . They will be included in the online version. The survey is broken down into nine separate tables (plus a vendor contact list) for easier downloading and viewing: Table 1: Software Description: Type: Form: Independent Application, Callable Library, Source Code, Add-in to General-purpose Software Table 2: Platforms Supported: DOS, PC/Windows (95, 97, NT), LINUX, UNIX, Mac OS, Other (specify) Multiprocessor Support: Shared Memory, Distributed Memory

25. OR/MS Today - April 1997 - Linear Programming Survey April 1997 • Volume 24 • Number 2 Software Survey linear programming. Goto the online version of the 1997 linear programming Survey http://www.lionhrtpub.com/orms/orms-4-97/Linear-Programming.html

Software Survey: Linear Programming 1997 update indicates change has mainly been evolutionary, but a few significant trends emerge By Robert Fourer This is the fourth in a series of surveys of software for linear programming. As in the case of earlier surveys in 1990, 1992 and 1995, information has been gathered by means of a questionnaire sent to LP software vendors by the editors of OR/MS Today . Results are summarized by product in the table following this article, after which contact details are listed. Scope of the survey The products surveyed thus have a common purpose and share many aspects of design. Nevertheless, they are best understood as incorporating two complementary but fundamentally different kinds of software. The latter packages represent modeling software that provides a convenient environment for formulating, solving and analyzing LPs. A typical modeling system is designed around a computer language for expressing LP models, and offers features for reporting, model management or application development in addition to a translator for the language. Modeling systems require a solver, and typically offer a choice of them as also indicated in the table. Trends and new developments Most of the packages listed in this version of the OR/MS Today survey were in existence at the time of the preceding survey. The "New Features" and "Other Techniques" columns suggest that change has mainly been evolutionary, but do point to a few significant trends.

26. Linear Programming - Formulation linear programming formulation. You will recall from the Two Mines example thatthe conditions for a mathematical model to be a linear program (LP) were http://www.ms.ic.ac.uk/jeb/or/lp.html

OR-Notes J E Beasley OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). They were originally used by me in an introductory OR course I give at Imperial College. They are now available for use by any students and teachers interested in OR subject to the following conditions A full list of the topics available in OR-Notes can be found here Linear programming - formulation You will recall from the Two Mines example that the conditions for a mathematical model to be a linear program (LP) were: all variables continuous (i.e. can take fractional values) a single objective (minimise or maximise) the objective and constraints are linear i.e. any term is either a constant or a constant multiplied by an unknown. LP's are important - this is because: many practical problems can be formulated as LP's there exists an algorithm (called the simplex algorithm) which enables us to solve LP's numerically relatively easily. We will return later to the simplex algorithm for solving LP's but for the moment we will concentrate upon formulating LP's.

27. Linear Programming - Solution here. linear programming solution. To get in solution technology. Someother linear programming solution examples can be found here. http://www.ms.ic.ac.uk/jeb/or/solvelp.html

OR-Notes J E Beasley OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). They were originally used by me in an introductory OR course I give at Imperial College. They are now available for use by any students and teachers interested in OR subject to the following conditions A full list of the topics available in OR-Notes can be found here Linear programming - solution To get some insight into solving LP's consider the Two Mines problem that we had before - the LP formulation of the problem was: Since there are only two variables in this LP problem we have the graphical representation of the LP given below with the feasible region (region of feasible solutions to the constraints associated with the LP) outlined. all feasible solutions to the original inequality constraint (e.g. all We determine the optimal solution to the LP by plotting (180x + 160y) = K (K constant) for varying K values (iso-profit lines). One such line (180x + 160y = 180) is shown dotted on the diagram. The smallest value of K (remember we are considering a minimisation problem) such that 180x + 160y = K goes through a point in the feasible region is the value of the optimal solution to the LP (and the corresponding point gives the optimal values of the variables). Hence we can see that the optimal solution to the LP occurs at the vertex of the feasible region formed by the intersection of 3x + y = 8 and 4x + 6y = 24. Note here that it is

28. Home Page Uses techniques to measure financial risk, optimize staffing, and predict wait times. Customized analyses and training feature Monte Carlo simulation, linear programming, and queuing models. http://www.calculatedriskinc.com/

29. [B/D] - The Bayes Linear Programming Language B/D The Bayes linear programming Language. Welcome to the home ofB/D. From this page, you can download the B/D software, and http://fourier.dur.ac.uk:8000/stats/bd/

[B/D] - The Bayes Linear Programming Language Welcome to the home of [B/D]. From this page, you can download the [B/D] software, and accompanying documentation. In time it will also contain update release notes, macro libraries, etc. To run the software you will need to take either the co-processor or the no-coprocessor version of the main program from the [B/D] for Windows link. Neither of these files contain documentation. You will almost certainly have to read some documentation. Sorry about that. Three tutorial guides and a reference manual are supplied in various formats - follow the [B/D] Documentation link to find them. The [B/D] manual is also available online in html format, as [B/D] manual online . Your best bet is to read the document entitled Bayes linear methods II in conjunction with the document Bayes linear methods I , which sets out the basic theory, concepts, and notation. Before you take anything, be warned! [B/D] supplies tools to help you organise and analyse your beliefs and data. You cannot use it without thinking, and it does not contain the usual statistical macros. If you're looking for a package to apply, for example, standard linear regression mindlessly, look elsewhere. See the Bayes linear home page for more details.

30. Linear Programming Activity linear programming Experiment graphically with the value of linear functionsof the form f(x,y) = ax + by + c subject to linear constraints on x and y http://www.exploremath.com/activities/Activity_page.cfm?ActivityID=31

31. Energy And Materials Policy Design linear programming models for environmental policy analysis, with emphasis on CO2 policies. Focus on trade effects, technological change, data, publications, model code. Covers iron and steel, petrochemicals, waste, biomass. http://www.resourcemodels.org/

NEW (19/2/2003) Technology learning for the IEA ETP model Presentation Paper This site may be relevant for you in case: You want to study environmental materials policies; You want to understand or validate modelling studies published in scientific journals; You want to assess the quality of these models for your own policy design; You want to build new models of your own. In order to open some of the files on this site you need WinZip Adobe-Acrobat reader Each study focuses on one category of materials/activities and is presented separately. Click on the links in the table below in order to get more information regarding a specific materials/activity category and spatial scope. Documentation Techno-economic life cycle modeling Gielen, D.J., Moriguchi, Y.: Paper presented at ISIE inaugural conference, 12/11-14/11 2001, Noordwijk. Techno-economic life cycle modeling (presentation) To contact us: Email: Dolf GIELEN

32. Linear Programming - Ignizio Cavalier linear programming by James P. Ignizio and Tom M. Cavalier, Prentice Hall InternationalSeries in Industrial and Systems Engineering, 666pp (1994). http://www.personal.psu.edu/tmc7/lpbook.html

33. Linear Programming -- From MathWorld linear programming, The problem of maximizing optimization theory. linear programmingis extensively used in economics and engineering. Examples from http://mathworld.wolfram.com/LinearProgramming.html

Applied Mathematics Optimization Linear Programming The problem of maximizing a linear function over a convex polyhedron, also known as operations research optimization theory , or convex optimization theory . Linear programming is extensively used in economics and engineering. Examples from economics include Leontief's input-output model, the determination of shadow prices, etc., while an example of an engineering application would be maximizing profit in a factory that manufactures a number of different products from the same raw material using the same resources. Linear programming can be solved using the simplex method (Wood and Dantzig 1949, Dantzig 1949) which runs along polytope edges of the visualization solid to find the best answer. Khachian (1979) found a polynomial-time algorithm . A much more efficient polynomial-time algorithm was found by Karmarkar (1984). This method goes through the middle of the solid (making it a so-called interior point method ), and then transforms and warps. Arguably, interior point methods were known as early as the 1960s in the form of the barrier function methods, but the media hype accompanying Karmarkar's announcement led to these methods receiving a great deal of attention. Criss-Cross Method Ellipsoidal Calculus Interior Point Method Kuhn-Tucker Theorem ... Vertex Enumeration References Bellman, R. and Kalaba, R.

34. Linear Programming Grapher (Two Variables) linear programming Grapher (Two Variables) a Utility for Finite Mathematics(2e). Enter the linear programming problem here. Xmin http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/LPGrapher/lpg.html

Linear Programming Grapher (Two Variables) a Utility for Finite Mathematics (2e) Return to Main Page More On-Line Utilities Topic Summary for Linear Programming ... Everything for Finite Math Use of this system is pretty intuitive. Enter your linear programming problem (with two variables x and y) in the space below, and press "Solve" to solve without showing the feasible region, or "Graph" to solve it and also show the feasible region for your problem. Press "Example" to see an example of a linear programming problem already set up. To solve a linear programming problem with more than two unknowns, use the Simplex Method Tool In some browsers, you might have to jiggle the graph window size a little to make the graph appear. Solution Display Some browsers (including some versions of Internet Explorer) use a sans serif proportional width font in text boxes. This will cause the display of solutions to appear a little messy. You can remedy this by changing the "Sans Serif" font in your browser preferences to "Courier" or some other fixed-width font, and then reloading the page. Warning The graphing routine will tax your browser, and it might crash and cause your computer to crash with it. Thus

35. Summary Linear Programming linear programming (LP) Problem The graphical method for solving linear programmingproblems in two unknowns is as follows. A. Graph the feasible region. http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/Summary4.html

Summary of Chapter 4 in Finite Mathematics and Topic: Linear Programming Return to Main Page True/False Quiz Review Exercises On-Line Tutorial ... Everything for Calculus Chapter 3 Summary Chapter 5 Summary Utilities: Linear Programming Grapher Pivot and Gauss-Jordan Tool Excel Pivot and Gauss-Jordan Tool Simplex Method Tool ... Simplex Method for Minimization Problem Linear Programming (LP) Problem A linear programming problem is one in which we are to find the maximum or minimum value of a linear expression ax + by + cz + . . . (called the objective function ), subject to a number of linear constraints of the form Ax + By + Cz + . . . N or Ax + By + Cz + . . . N. The largest or smallest value of the objective function is called the optimal value , and a collection of values of x, y, z, . . . that gives the optimal value constitutes an optimal solution . The variables x, y, z, . . . are called the decision variables Example Here is an example of an LP problem: Find the maximum value of p = 3x subject to z x + 2y + z x 0, y 0, z

36. Annotated Bibliography On Linear Programming Models ITORMS title. ANNOTATED BIBLIOGRAPHY ON linear programming MODELS. This bibliographyconsists of the early papers on linear programming model formulations. http://catt.bus.okstate.edu/itorms/volumes/vol1/papers/murphy/

ANNOTATED BIBLIOGRAPHY ON LINEAR PROGRAMMING MODELS Frederic H. Murphy Temple University Philadelphia PA Go to the Overview Go to the Bibliography OVERVIEW This bibliography consists of the early papers on linear programming model formulations. It includes some papers that are not about linear programming models but are relevant to understanding the early literature. Examples of these non-LP papers are the Markowitz portfolio model, some integer programming models and papers on input-output analysis. The summaries of the paper are mine and not abstracts, since many of the papers from this era did not have abstracts. I have not read the papers that do not have summaries because I was not able to get copies of them. The value of this bibliography resides in bringing together a literature that is still relevant for understanding LP modeling issues and modeling in general. By scanning the papers, one can see the evolution of issues and trends in the thinking of those involved in developing the field. Personal creativity in model formulation often follows the same pattern as historical creativity, that is, the first formulation of a new model, and this bibliography allows one to trace the historical roots of model formulation. See Murphy and Panchanadam (1995) for an example of how this bibliography can be used for current research.

37. Dipartimento Di Informatica - Università Di Torino Department of Informatics. Research groups concentrate on knowledge representation and reasoning, machine learning, natural language processing, databases and information systems, decision making models and management systems, informatic technology, linear programming, integer linear programming, game theory, logic programming and automated reasoning, mathematical logic, performance analysis, modelling in biology and medicine, cooperative systems, multidimensional signal processing, security and computer networks, semantics and logics of computation. http://www.di.unito.it/

U S TUDI DI T ORINO phone number Information HowToReachUs People Research ... University home Administrator: wwwadm[at]di.unito.it Last update: 1 Oct 2002

38. LP_SOLVE Linear Programming Code LP_SOLVE linear programming Code. FTP site for lp_solve; Mail to author MichelBerkelaar; linear programming FAQ; Download Files (local site) Problem Links. http://www.cs.sunysb.edu/~algorith/implement/lpsolve/implement.shtml

LP_SOLVE: Linear Programming Code The non-commercial linear programming code of choice appears to be , written in ANSI C by Michel Berkelaar, who claims to have solved problems as large as 30,000 variables and 50,000 constraints. Lp_solve can also handle (smaller) integer and mixed-integer problems. It is available by anonymous ftp from ftp://ftp.es.ele.tue.nl/pub/lp_solve, but is not in the public domain. A user community for lp_solve exists, which has ported it to a variety of different platforms. FTP site for lp_solve Mail to author Michel Berkelaar Linear Programming FAQ Download Files (local site) Problem Links Linear Programming (9) Post comments Read comments View the statistics for this implementation ... The Stony Brook Algorithm Repository go to front page This page last modified on Apr 29, 1996.

39. 1.2.6 Linear Programming 1.2.6 linear programming. INPUT OUTPUT. Excerpt from The Algorithm Design ManualThe standard algorithm for linear programming is called the simplex method. http://www.cs.sunysb.edu/~algorith/files/linear-programming.shtml

1.2.6 Linear Programming INPUT OUTPUT Input Description: A set of linear inequalities, a linear objective function. Problem: Find the assignment to the variables maximizing the objective function while satisfying all inequalities. Excerpt from The Algorithm Design Manual : The standard algorithm for linear programming is called the simplex method . Each constraint in a linear programming problem acts like a knife that carves away a region from the space of possible solutions. We seek the point within the remaining region that maximizes (or minimizes) $f(X)$. By appropriately rotating the solution space, the optimal point can always be made to be the highest point in the region. Since the region (simplex) formed by the intersection of a set of linear constraints is convex, we can find the highest point by starting from any vertex of the region and walking to a higher neighboring vertex. When there is no higher neighbor, we are at the highest point. While the basic simplex algorithm is not too difficult to program, there is a considerable art to producing an efficient implementation capable of solving large linear programs. For example, large programs tend to be sparse (meaning that most inequalities use few variables), so sophisticated data structures must be used. There are issues of numerical stability and robustness, as well as which neighbor we should walk to next (so called pivoting rules ). Finally, there exist sophisticated

40. Linear Programming - Simplex Method linear programming Simplex Applet. By Pedro Miguel Silva and Tiago Castro GuiseVersion 1.0 - Lisbon, July 1998, updated on October 1999 linear programming http://algos.inesc.pt/lp/

Linear Programming - Simplex Applet By Pedro Miguel Silva and Tiago Castro Guise Version 1.0 - Lisbon, July 1998, updated on October 1999 You are visitor number to this page since last reboot. Simplex Applet: The available LP algorithms are: Simplex Method, Revised Method, Primal Dual and Simplex Dual. Enter Your Linear Program: ... Applet Controls here, if you had java in your browser. How the Applet Works: Buttons: Solve - Solve your linear program. Abort Abort the execution of the algorithm. Clear - Allows you to clear fields. About - Brings up an about window. Choice Menus: First Choice Menu - With this options you can chose clear the field results or clear the field linear program. It is also, available the options of no clear fields and clear all fields. Second Choice Menu - Chose the algorithm you want Simplex, Revised Simplex, Primal Dual or Simplex Dual. . Third Choice Menu - Chose output options. Linear Programming: A linear program is a problem a problem that can be expressed as follows: min cx (Standard Form) subject to Ax = b x >= Where "x" is the vector of variables to be solved, "A" is the matrix of known coefficients and "c" and "b" are vectors of known coefficients. The Expression "cx" is called the objective function and the equations "Ax = b" are called the constraints.

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