GAMS: General Algebraic Modeling System Part2

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GAMS General Algebraic Modeling SystemPart2

• Tanya Borisova and Xiaobing Zhao
• For Graduate Seminar ARE 696 by Dr. Fletcher
• Tatiana.Borisova_at_mail.wvu.edu

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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/scen
  ariostudies_and_the_environment/gams/GAMS20Reader
  .pdf
• and GAMS Users Guide

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Lets start!

• Transportation problem

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GAMS Model Library

• Collection of programs
• You can begin with existing models and modify
  them

• Management Science and OR
• Micro Economics
• Recreational Models
• Statistics
• International Trade
• Macro Economics

• Agricultural Economics
• Applied General Equilibrium
• Economic Development
• Energy Economics
• Finance
• Forestry

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Transportation Problem

• Start GAMS
• Open new project, save it to the desktop (any
  name)
• Open Transportation Problem from the Model
  Library
• type Trnsport
• 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)

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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

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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?

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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?

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Result comparison

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

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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)

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Solve Results Multi-Dimensional Parameters and
Loop Statement(program 4)

• Loop(ControllingSetName, 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)

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You have this line
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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)gt500) - dollar on the
  right
• f(i)(a(i)gt500) 90 - dollar on the
  left
• f(i) will be 90 only if plants i produces
  more than 500

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Dollar-operator (cont.)

• Dollar on the left f(i)(a(i)gt500) 90
• - f(i), such that a(i)gt500, equals 90
• - meaning if (a(i) gt 500), then f(i) 90
• - no assignment is made unless the logical
  condition is satisfied
• Dollar on the right f(i)
  90(a(i)gt500)
• - f(i) 90 if a(i)gt500
• - meaning if (a(i) gt 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.

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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)

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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

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Dollar-operator with Subsets (cont.)

• smalli(i) True for all i that are members of
  smalli, and False otherwise

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Dynamic models Leads and Lags(program 7)

• Simplified population example
• Population grows with time
• population(t) apopulation(t-1)
• Lag relationship between time periods T and T-1
• Lead relationship between time periods T and T1

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Open a new file, save as program7, write a comment
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ORD and CARD(program 8)

• Population(t) at, 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

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

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Large Tables
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FOR statement(program 10)

• Example
• Open new file, save it as Program10, write a
  comment to the program

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WHILE statement(program 11)

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

Numerical relationship operator
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Numerical Relationship Operators
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IF-ELSE STATEMENT(program 12)

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