Transcript Document 7311670

How to get started with GAMS
MS&E 348 – Lecture 1/20/04
GAMS Basics
• The General Algebraic Modeling System
(GAMS) is a high-level modeling system for
mathematical programming problems
• It consists of a language compiler and a stable
of integrated high-performance solvers
• GAMS is tailored for complex, large scale
modeling applications, and allows you to build
large maintainable models that can be adapted
quickly to new situations
Some GAMS References
• www.gams.com
• A User’s Guide by Brooke et al.
– GAMS Tutorial by Rosenthal (ch. 2 of above)
Transportation Problem
Canning plants /
Capacity a(i)
Seattle
Markets /
Demand b(j)
Transport cost c(i,j)
New York
Chicago
San Diego
Topeka
Structure of a GAMS model
Input
file_name.gms
Output
file_name.lst
Sets
Echo Print
Data
Reference Maps
Variables
Equation Listings
Equations
Status Reports
Model specification
Results
Solve statement
Program Listing 1/3
* Instance of the transportation problem
* From R. Rosenthal's GAMS Tutorial
sets
i canning plants / seattle, san-diego /
j markets / new-york, chicago, topeka /;
parameters
a(i) capacity of plant i in cases
/ seattle 350
san-diego 600 /
b(j) demand at market j in cases
/ new-york 325
chicago 300
topeka 275 /;
Program Listing 2/3
table d(i,j) distance in thousands of miles
new-york chicago topeka
seattle
2.5
1.7
1.8
san-diego
2.5
1.8
1.4;
scalar f freight in dollars per case per 1000 miles / 90 /;
parameter c(i,j) transport cost in 1000s of dollars per case;
c(i,j) = f*d(i,j)/1000;
variables
x(i,j) shipment quantities in cases
z
total transportation costs in 1000s of dollars;
positive variable x;
Program Listing 3/3
equations
cost define objective function
supply(i) observe supply limit at plant i
demand(j) satisfy demand at market j;
cost .. z =e= sum((i,j), c(i,j)*x(i,j));
supply(i) .. sum(j, x(i,j)) =l= a(i);
demand(j) .. sum(i, x(i,j)) =g= b(j);
model transport /all/;
solve transport using lp minimizing z;
display x.l, x.m;
Implementation
•
From Leland account
– Type input file in standard text editor (emacs, etc.)
– Run with following command: /usr/sweet/apps/gams-2.50/gams file_name.gms
•
Programming styles
– Data -> Model -> Solution
– Model -> Data -> Solution
•
General remarks
– Distinguish between ‘declaration’ and ‘assignment’ or ‘definition’
– An entity of the model cannot be referenced before it is declared to exist
•
Useful feature not discussed in the tutorial: the ‘dollar’ operator
– This powerful feature of GAMS operates with a logical condition $(condition),
which can be read as ‘such that condition is valid’
– Example:
• If (b > 1.5) then a = 2
becomes
• a$(b > 1.5) = 2;
– This operator is very useful to handle exceptions
Other Remarks
• Documentation is crucial. It is returned in the output file
• Compiler options can be used
Example of line: $include file_name
• Advantage of GAMS over Fortran or C: values can be
assigned without ‘do loops’
• Key idea is that the definition of the constraints is exactly
the same regardless of the size of the problem: the user
just enters equations algebraically and GAMS creates
the specific equations appropriate for the model at hand
• Don’t get confused by error messages!
• Read the output file!
• Equation listings are useful for checking the model
• Don’t wait to get started!