GAMS General Algebraic Modeling System

Presentation No.2

GAMS General Algebraic Modeling System

Presentation No.2

Instructor: Dr. Abbas SeifiPrepares by: Masoud Barah

Applied OR Modeling Course

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 onhttp://www.sls.wageningen-ur.nl/enr/education/scenariostudies_and_the_environment/gams/GAMS%20Reader.pdf

and GAMS User’s Guide

Lets start!

Transportation problem

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

Transportation Problem

Start GAMSOpen 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)

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

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?

Contract on Supply(program 2)

Save your program as Program2, write commentscontract on delivery of 10 cases from Seattle to

Morgantownx.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?

Result comparison

Compare the costs and shipment patterns with and without the contract save Solve results in a parameter multi-dimensional parameters, Loop statement

Save Solve Results in a New Parameter (program 3)

Save your program as Program3, write comments

Delete the contract definition from the modelAfter 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 contractGive another Solve statementDeclare new Parameters RES2(i,j) and cost2, and

assign them the value of x.L(i,j) and z.LCompare cost1, cost2, RES1 and RES2 (Display

statement)

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 commentsDelete the end of your program starting with the

first Solve statement Type instead: (new slide)

You have this line

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

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.

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)

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

Dollar-operator with Subsets(cont.)

smalli(i) = “True” for all i that are members of smalli, and “False” otherwise

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

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

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

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

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

Large Tables

FOR statement(program 10)

ExampleOpen new file, save it as Program10, write a comment to

the program

WHILE statement(program 11)

Example Open new file, save it as Program11, write comments

Numerical relationship operator

Numerical Relationship Operators

IF-ELSE STATEMENT(program 12)

Example Open new file, save it as Program12, write a comment