1. GAMS General Algebraic Modeling System Presentation No.2 Instructor: Dr. Abbas Seifi Prepares by: Masoud Barah Applied OR Modeling Course

2. Plan for Today  GAMS model library  Transportation Problem  new market (Morgantown)  contract on supply Definition Comparison of the results with and without the contract – 2 ways  higher freight costs for the smaller plant – 2 ways to define  Population Model  Population for subsequent years  Useful Features (if we have time)  Alias statement  Large tables  If-else, for, and while statements presentation is based on http://www.sls.wageningen- ur.nl/enr/education/scenariostudies_and_the_environment/gams/GAMS%20Reader.pdf and GAMS User’s Guide

3. Lets start!  Transportation problem

4. GAMS Model Library  Agricultural Economics  Applied General Equilibrium  Economic Development  Energy Economics  Finance  Forestry  Management Science and OR  Micro Economics  Recreational Models  Statistics  International Trade  Macro Economics Collection of programs You can begin with existing models and modify them

5. Transportation Problem  Start GAMS  Open new project, save it to the desktop (any name)  Open Transportation Problem from the Model Library  type “Transport”  Save the file to the desktop (“Program1”, use “Save as” in “File” menu)  What changes should we make to add a new market to the system? (Morgantown)

6. New Market (program 1)  Add a new market – MorgantownWV  New member of set j  Demand = 40 (hypothetical)  Distances: Seattle – Morgantown = 2.2 thousands miles San Diego – Morgantown = 2.1 thousands miles  Write a comment to your program using  “*” – one-line comment  “$Ontext … $Offtext” – multiple-lines comment  Save the file, Run

7. Results  What is the model status?  What plant supplies to Morgantown ? How many cases?  What are the minimal transportation costs?  What story do the marginal values for equations tell?  How will the costs change if we “force” Seattle plant to supply 10 cases to Morgantown?

8. Contract on Supply (program 2)  Save your program as Program2, write comments  contract on delivery of 10 cases from Seattle to Morgantown x.fx(“Seattle”, “Morgantown”) = 10;  Turn off echo print $Offlisting – After defining model title, starting on the first position in the line  Turn off equation and column listing option limrow = 0, limcol = 0;  How do the minimal transportation costs change?

9. Result comparison  Compare the costs and shipment patterns with and without the contract  save Solve results in a parameter  multi-dimensional parameters, Loop statement

10. Save Solve Results in a New Parameter (program 3)  Save your program as Program3, write comments  Delete the contract definition from the model  After the Solve statement, declare new Parameters RES1(i,j) and cost1 and assign them the values x.L(i,j) and z.L;  Define the contract  Give another Solve statement  Declare new Parameters RES2(i,j) and cost2, and assign them the value of x.L(i,j) and z.L  Compare cost1, cost2, RES1 and RES2 (Display statement)

12. Solve Results: Multi-Dimensional Parameters and Loop Statement (program 4) Loop(Controlling Set Name, Commands);  Loop: repeat the set of commands for all elements of the controlling set  Save your program as Program4, write comments  Delete the end of your program starting with the first Solve statement  Type instead: (new slide)

13. You have this line

14. Freight Costs depend on Plant Size (program 5)  If producer is small, freight costs are higher  $-operator: GAMS’ way to say ‘only if’ f(i) = 90$(a(i)>500); - dollar on the right f(i)$(a(i)>500) = 90 ; - dollar on the left f(i) will be 90 only if plants i produces more than 500

15. Dollar-operator (cont.)  Dollar on the left: f(i)$(a(i)>500) = 90; - “f(i), such that a(i)>500, equals 90” - meaning if (a(i) > 500), then f(i) = 90 - no assignment is made unless the logical condition is satisfied  Dollar on the right: f(i) = 90$(a(i)>500); - “f(i) = 90 if a(i)>500” - meaning if (a(i) > 500), then f(i) = 90, else f(i) = 0 - assignment is always made.  no variables can be used do define logical condition for GAMS technical reasons.

16. Dollar-operator (cont.)  Save your program as Program5, write comments  Transportation costs are higher for a smaller producer  Comment out declaration of Scalar f  Add f(i) to the set of Parameters  Make freight costs higher by $5/case if the plant produces less than 500 cases  Print the values of parameter f (Display statement)

18. Dollar-operator with Subsets (program 6)  Save your program as program6, add comments  One can define subsets containing part of the elements of another set using a Set statement

19. Dollar-operator with Subsets(cont.)  smalli(i) = “True” for all i that are members of smalli, and “False” otherwise

20. Dynamic models: Leads and Lags (program 7)  Simplified population example  Population grows with time  population(t) = a*population(t-1)  Lag: relationship between time periods T and T- 1  Lead: relationship between time periods T and T+1

21. Tip: Open a new file, save as program7, write a comment

22. ORD and CARD (program 8)  Population(t) = a**t, t = 1, 2, …  ORD: gives the relative position of a member in a set  Example: ORD(“1975”) = 1 ORD(“1976”) = 2  CARD: the total number of elements in the set  Example: CARD(T) = 30

23. Tip: Open a new file, save it as program8, write comments

24. Alias Statement (program 9)  give another name to a previously declared set Alias (t,tp);  Example:  Open new file, save it as Program9, write comments

25. Large Tables

26. FOR statement (program 10)  Example  Open new file, save it as Program10, write a comment to the program

27. WHILE statement (program 11)  Example  Open new file, save it as Program11, write comments Numerical relationship operator

28. Numerical Relationship Operators

29. IF-ELSE STATEMENT ( program 12)  Example  Open new file, save it as Program12, write a comment