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– Stochastic Programming (SP) with EMP - the stochastic programming (SP) extension of GAMS Extended
Mathematical Programming (EMP).
– Mathematical Programming System for General Equilibrium analysis (MPSGE) - A mathematical programming
system for general equilibrium analysis which operates as a subsystem within GAMS.
* MPSGE Models in GAMS
* Demand Theory and General Equilibrium: An Intermediate Level Introduction to MPSGE
* Constant Elasticity of Substitution Functions: Some Hints and Useful Formulae
* A Library of Small Examples for Self-Study
* Comparing the Performance of Flexible Functional Forms
* General Equilibrium with Public Goods
* Kevin O'Rourke: CGE and Economic History
* Linking Implan Social Accounts to MPSGE
* A partial list of publications based on MPSGE
* The MPSGE guide is also available as PDF
Here are some points to remember when using the list format.
1. The list of domain elements and their respective parameter values can be laid out in almost any way you like. The only
rules are that the entire list must be enclosed in slashes and that the element-value pairs must be separated by commas
or entered on separate lines.
2. There is no semicolon separating the element-value list from the name, domain, and text that precede it. This is because
the same statement is being used for declaration and assignment when you use the list format. (An element-value list
by itself is not interpretable by GAMS and will result in an error message.)
3. The GAMS compiler has an unusual feature called domain checking, which verifies that each domain element in the
list is in fact a member of the appropriate set. For example, if you were to spell 'Seattle' correctly in the statement
declaring Set i but misspell it as 'Seatle' in a subsequent element-value list, the GAMS compiler would give you an
error message that the element 'Seatle' does not belong to the set i.
4. Zero is the default value for all parameters. Therefore, you only need to include the nonzero entries in the element-value
list, and these can be entered in any order .
GAMS Summation (and Product) Notation
Before going into equation definition we describe the summation notation in GAMS. Remember that GAMS is designed for
standard keyboards and line-by-line input readers, so it is not possible (nor would it be convenient for the user) to employ the
standard mathematical notation for summations.
The summation notation in GAMS can be used for simple and complex expressions. The format is based on the idea of always
thinking of a summation as an operator with two arguments: Sum(index of summation, summand) A comma separates
the two arguments, and if the first argument requires a comma then it should be in parentheses. The second argument can be
any mathematical expression including another summation.
As a simple example, the transportation problem contains the expression
The effect of this statement is to declare the parameter d and to specify its domain as the set of ordered pairs in the Cartesian
product of i and j. The values of d are also given in this statement under the appropriate heading. If there are blank entries
in the table, they are interpreted as zeroes.
As in the list format, GAMS will perform domain checking to make sure that the row and column names of the table are
members of the appropriate sets. Formats for entering tables with more columns than you can fit on one line and for entering
tables with more than two dimensions are given in Chapter Data Entry: Parameters, Scalars and Tables.
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