Introduction to GAMS:Formulation of a general problem

Prof. Boyan Bonev Ivanov, Ph.D.

Email: bivanov@bas.bg

Institute of Chemical Engineering-BAS

What is GAMS?

Formulation of a General Problem

Formulation of a General Problem

Formulation of a General Problem

STEPS1. SET definitions (crop)2. Data entry (Ccrop, acrop,resource,bresource)3. Variable specifications4. Equation specificationsa. declarationb. algebraic structure5. Model statement6. Solve statement

Set Definition

In algebraic modeling, we commonly have subscripts.In GAMS, the corresponding items are sets. A set definition has severalpotential parts.

SET ItemName optional explanatory text for item/ element1 optional explanatory text for element ,element2 optional explanatory text for element / ;

S={a,b,c} Set S /a,b,c/In general, the syntax in GAMS for simple sets is as follows:

set set_name ["text"] [/element ["text"] {,element ["text"]} /]{,set_name ["text"] [/element ["text"] {,element ["text"]} /] ;

Set Definition

set cq "nutrients" / N, P2O5 / ;

set cq "nutrients" / N P2O5 / ;

set cq "nutrients" / N “Text 1” P2O5 “Text 2” / ;

set cq "nutrients“ / N “Text 1” P2O5 “Text 2” / ;

Set Definition

Set f "final products" /yncrude "refined crude (million barrels)" lpg "liquified petroleum gas(million barrels)" ammonia "ammonia (million tons)" coke "coke (million tons)" sulfur "sulfur (million tons)" /;

set t "time“ /1991 * 2000 /;

setss "Sector" / manuf agri services government /r "regions" / north eastcoast midwest sunbelt / ;

Set Definition

Defined set names Explanatory Text

Element names

Data Entry

Data are entered via four different types of GAMScommands

1) Scalar – for items that are not set dependent

2) Parameters – for items that are vectors (can be multidimensional)

3) Tables – for items with 2 or more dimensions

4) Parameters – direct assignment

Data Entry – SCALAR command

Scalar commands:

In general, the syntax in GAMS for a scalar declaration is:

scalar(s) scalar_name [text] [/signed_num/] { scalar_name [text] [/signed_num/]} ;

Scalars rho "discount rate" / .15 / irr "internal rate of return" life "financial lifetime of productive units" /20/;

Basic format:

SCALAR ItemName optional text / value / ;

Example:

SCALAR LandAvailable Total Land / 100 / ;

Data Entry – PARAMETER command

In general, the syntax in GAMS for a parameter declaration is:parameter(s) param_name [text] [/ element [=] signed_num {,element [=] signed num} /] {,param_name [text] [/ element [=] signed_num {,element [=] signed num} /]} ;

Basic format:

PARAMETER ItemName(Set) optional text / element1 value , element2 value value2 / ;

Example:

PARAMETERRevenue(Crop) Revenues from crop production / Corn 109 Wheat 90 Cotton 115 /ResourceAvailable (Resource) Resource availability / Land 100 Labor 500 / ;

Data Entry – PARAMETER command

Set i "steel plants“ / hylsa "monterrey" hylsap "puebla" / j "markets" / mexico-df, monterrey, guadalaja / ;

parameter dd(j) “distribution of demand” / mexico-df 55, guadalaja 15 / ;

Parameter a(i) / seattle = 350, san-diego = 600 / b(i) / seattle 2000, san-diego 4500 / ;

Set i "steel plants“ / seattle "monterrey" san-diego "puebla" /

Data Entry – TABLE command

In general, the syntax in GAMS for a table declaration is:

table table_name [text] EOL element { element } element signed_num { signed_num} EOL {element signed_num { signed_num} EOL} ;

sets i "plants" / inchon,ulsan,yosu / m "productive units" atmos-dist "atmospheric distillation unit" steam-cr "steam cracker" aromatics "aromatics unit" hydrodeal "hydrodealkylator" / ;

Table ka(m,i) "initial cap. of productive units (100 tons per yr)" inchon ulsan yosuatmos-dist 3702 12910 9875steam-cr 517 1207aromatics 181 148hydrodeal 180 ;

Data Entry – TABLE command

Basic format:TABLE ItemName(set1dep,set2dep) optional text set2elem1 set2elem2Set1element1 value11 value12

Set1element2 value12 value22 ;

Example:

Elements fromCrop set (2nd set)

Elements from Resource set (1st set)

Data Entry – Direct assignment

Basic format:

PARAMETER ItemName(set1dep,set2dep) optional text ; ItemName(set1dep,set2dep) = some expression ;

Example:

Summation Digression

Formulation – Variable Declarations

Basic format:

VARIABLE VarName1(setdependency) optional text VarName2(setdependency) optional text … ;

Example:

Formulation – Variable Declarations

variables k(t) capital stock (trillion rupees) c(t) consumption (trillion rupees per year) i(t) investment (trillion rupees per year) utility utility measure ;

VARIABLE TYPES

Formulation – Variable Declarations

variables k(t) capital stock (trillion rupees) c(t) consumption (trillion rupees per year) i(t) investment (trillion rupees per year) utility utility measure ;

positive variables k(t) capital stock (trillion rupees) c(t) consumption (trillion rupees per year) ;

negative variables i(t) investment (trillion rupees per year);

binary variables utility utility measure ;

EQUATION DECLARATIONS

THE SYNTAX

Equation[s] eqn_name text {, eqn_name} ;

AN ILLUSTRATIVE EXAMPLE

EQUATION DEFINITIONS

THE SYNTAX

eqn_name(domain_list).. expression eqn_type expression ;

AN ILLUSTRATIVE EXAMPLE

equations obj ;obj.. phi =e= phipsi + philam + phipi - phieps ;

Variables phi, phipsi, philam, phipi, phieps ;

EQUATION DEFINITIONS

SCALAR EQUATIONS

dty.. td =e= sum(i, y(i)) ;

INDEXED EQUATIONS

dg(t).. g(t) =e= mew(t) + xsi(t)*m(t) ;

bd(j,h).. b(j,h) =e= dd(j,h) - y(j,h) ;yd(j,h).. y(j,h) =l= sum(i, p(i,j)*x(i,j)) ;

ARITHMETIC OPERATORS IN EQUATION DEFINITIONS

dem(i) .. y(i) =e= ynot(i)*(pd*p(i))**thet(i) ;

EQUATION DEFINITIONS

EXPRESSIONS IN EQUATION DEFINITIONS

Model Specification

" Model Specification

MODEL statements are used to identify models that will besolved. They involve 2 steps

step 1: gives the name of the model

step 2: specifies the names of the equations that will be included in the model enclosed in slashes / / or the word ALL

MODEL FarmIncome /EQ1, EQ2, EQ3/ ;

MODEL FarmIncome /ALL/ ;

Solve Specification

" Solve Specification

SOLVE causes GAMS to apply a solver to the named modeland identifies the variable to be optimized along with thedirection of optimization

SOLVE FarmIncome USING LP MAXIMIZING Profit ;

CLASSIFICATION OF MODELS

ORGANIZATION OF GAMS PROGRAMS

References

http://www.pse.ice.bas.bg:8080/WWW_Systems_engineerig_laboratory/Distance_learning_systmeng/Distance_systmeng_LT.htm