Formulation of a General ProblemAGEC 641 Lab, Fall 2011

Mario Andres Fernandez

Based on material written by Gillig and McCarl; Improved upon by many previous lab instructors.Special thanks to Yuquan “Wolfgang” Zhang

Simple Problem

Variable Specification

Equation Specification

Model Statement

Solve Statement

What if we had much more data?

negativenonXXXlaborXXXlandXXXprofitXXXMax

CottonWheatCorn

CottonWheatCorn

CottonWheatCorn

CottonWheatCorn

0 , , 500*8 *4 *6

100 *115*90*109

iX

bX

bXts

XMax

i

i

i

i

,0

a

a ..

c

1,2,3i2i2

1,2,3i1i1

1,2,3ii

iX

jbXts

XMax

i

ji

i

,0

,a ..

c

1,2,3iij

1,2,3ii

GAMS and Algebra

• Suppose xi is defined with three elements

• Algebra:

• GAMS: z=SUM(i,x(i));– i: set in GAMS– Z: a scalar or variable– X(i): parameter or variable defined over i– The sum automatically treats all cases of i

i

i xxxx 321

STEPS1. SET definitions2. Data Entry3. Variable Specification4. Equation Specification

a) Declarationb) Algebraic structure

5. Model Statement6. Solve Statement

SET DefinitionAlgebra: subscripts GAMS: sets SET ItemName optional explanatory text / element1 optional explanatory text element2 optional explanatory text /;

SET Definition

SETS ItemName optional explanatory text for item / Element1 optional text, Element2 optional text /;

Data Entry

Scalar

Parameters

Tables

SCALAR

For items that are not set dependent

SCALAR ItemName optional text /value/;SCALAR LandAvailable Total Land /100/;

SCALAR SLandAvailable /100/Pricecorn 1992 price per bushel /2.2/;

PARAMETER Basic format PARAMETER ItemName(setdependency) / element1 associated value, element2 associated value /;

TABLEBasic formatTABLE ItemName(set1, set2) optional text

set2elem1 set2elem2set1elem1 value11 value21set1elem2 value21 value22 ;

Direct AssignmentBasic formatPARAMETER ItemName(set1, set2) optional text;PARAMETER ItemName(set1, set2) = expression;

Parameter CalcRevenue(crop) calculate revenues by crop ;

CalcRevenue(crop) = Revenue(crop)*Production.L(crop) ;

Parameter TotalRevenue calculate total revenue;TotalRevenue=sum(crop, revenue(crop)*Production(crop)) ;

j

jX

j i

jiX

Sum (index, names(index))Sum(j, X(j))

Sum(index1, sum(index2, names(index1, index2)))Or Sum(j, Sum(i, X(j, i))) Or Sum((j, i), X(j, i))

c

cc YX *Summation

Variable DeclarationsBasic formatVARIABLE VarName1(set-dependency) optional text

VarName2(set-dependency) optional text ;

Equation DeclarationsBasic formatEQUATION EquName1(set-dependency) optional text

EquName2(set-dependency) optional text ;

Equation DeclarationsGeneral Structure: EquationName(Set-Dependency)..LHS EquationRelationType ( =e=, =l=, =g= ) RHS

Solution Reports

Shadow price: marginal values of resources.

Reduced costs: marginal cost if a non-basic variable is forced to enter the solutions.