1. Formulation of a General Problem AGEC 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

2. Simple Problem Variable Specification Equation Specification Model Statement Solve Statement

3. What if we had much more data?

4. GAMS and Algebra Suppose x i 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

5. STEPS 1.SET definitions 2.Data Entry 3.Variable Specification 4. Equation Specification a) Declaration b) Algebraic structure 5. Model Statement 6. Solve Statement

6. SET Definition Algebra: subscripts  GAMS: sets SET ItemName optional explanatory text / element1 optional explanatory text element2 optional explanatory text /;

7. SET Definition SETS ItemName optional explanatory text for item / Element1 optional text, Element2 optional text /;

8. Data Entry Scalar Parameters Tables

9. SCALAR For items that are not set dependent SCALAR ItemName optional text /value/; SCALAR LandAvailable Total Land /100/; SCALAR S LandAvailable /100/ Pricecorn 1992 price per bushel /2.2/;

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

11. TABLE Basic format TABLE ItemName(set1, set2) optional text set2elem1 set2elem2 set1elem1 value11 value21 set1elem2 value21 value22 ;

12. Direct Assignment Basic format PARAMETER ItemName(set1, set2) optional text; PARAMETER ItemName(set1, set2) = expression; Parameter CalcRevenue(crop) calculate revenues by crop ; CalcRevenue(crop) = Revenue(crop)*Production.L(crop) ;

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

14. Variable Declarations Basic format VARIABLE VarName1(set-dependency) optional text VarName2(set-dependency) optional text ;

15. Equation Declarations Basic format EQUATION EquName1(set-dependency) optional text EquName2(set-dependency) optional text ;

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

17. Solution Reports Shadow price: marginal values of resources. Reduced costs: marginal cost if a non-basic variable is forced to enter the solutions.