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Excel Solver (by Scott Geller):
Once you have identified your objective function and constraints, you are able to code this into Excel. To start, choose the cells you which to change (typically x_1, x_2, ...). Then choose the cells you which to be affected by the variables (the constraints). To do this, click on the cell and hit the "=" key followed by the actual constraint. You should click on the variable (cell) you wish to modify and multiply it by the desired coefficient (you can do this simply with the "*" key). Once all constraints have been programmed, load the "solver" program from the "tools" menu.  The target cell is the cell that is to be maximized (or minimized). The variables are the cells you which to change. Lastly, add constraints by clicking "Add" and then choosing the constraint. Now you can specify whether the cell needs to be greater than, less than, or equal to a certain value. Once all constraints have been programmed hit the "solve" button and Excel with maximize (or minimize) our target function and directly modify our variables.

LINGO/LINDO (Maximilian Barrows):
LINGO is Windows and Linux only. The installer in the Hillier CD is only for Windows. You can download a trial version of LINGO 11.0 for Windows or Linux from by clicking on Downloads --> Try Lingo

When installing LINGO 9.0 from the Hillier CD, make sure you pay attention to what hard drive it is installing to. On various attempts it installed to E:\ and F:\ rather than C:\.

When starting up LINGO 9.0 for the first time, it may or may not ask you if you want to turn on AutoUpdate. DO NOT, UNDER ANY CIRCUMSTANCES, TURN ON AutoUpdate! The other way to turn it on is to check it in the Help dropdown menu. Every time I turned on AutoUpdate, LINGO would crash. In addition, it would crash every time I started up the program after that. The only fix I'm aware of is to uninstall, delete the LINGO9 folder in your C:\ directory, then reinstall. LINGO 11.0 does not have this problem, but I doubt there are worthwhile updates.

There are 2 main file types in LINGO: .lg4, which are LINGO Models, and .lng, which are LINDO Text Models. They use very different syntax, and I will be covering LINGO files in this document.

Cklick here to see LINGO 8.0 Tutorial. LINGO 9.0 has a few new functions, but the main difference between 8 and 9 is that 9 solves problems faster. The tutorial is a great reference to many functions I don't cover in this document.

There are two basic LINGO files: file1 and file2. The easiest way to use LINGO is to open them up and change the numbers to match your problem.

For help specific to problems we are doing, consult the book. These can be found at the end of Chapters 3 and 4: Appendix 3.1: page 81 (The LINGO Modeling Language) & Appendix 4.1: page 158 (An Introduction to Using LINDO)

Always end a line with ``;'' Whether it's a comment or constraint, end lines with ;
! To make a comment, start with ``!'' Comments should turn green if typed correctly.
LINGO is case insensitive (MAX = max)

When making an optimization function, replace your Z with MAX or MIN (for example: Z = x_1 + 2*x_2 would be input into LINGO as MIN = x1 + 2*x2). If typed correctly, MAX and MIN should turn blue.

LINGO assumes that all variables are >= 0, so you must structure your variables the same way you would a simplex problem (for example: if x1 can be negative, make 2 variables such as x11 and x12, and replace every x1 with x11-x12)

If you type something in square brackets before a function or constraint, that will be the label in your output. Also, what goes into a square bracket should not be any variable in your equations. For example: [Profit] MAX = x1 + 2*x2 would make your Z value in output be labeled with Row PROFIT instead of Row 1.

Ctrl+S or clicking the bullseye at the top will run your program. Close the small grey LINGO Solver Status window that pops up, then look at the Solution Report.

Maple Tutorial (by Paul Sastrasinh).

CPLEX Tutorial
Transportation and Assignment Problems (pdf or text)
Integer Programming (pdf or text)

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