Description

This problem finds a least cost shipping schedule that meets
requirements at markets and supplies at factories.

GAMS Connect is used to read and write CSV files.
Note: In this example, the CSV data can also be read by using a simple
table statement without doing further preprocessing.

Category : GAMS Data Utilities library

Main file : connect03.gms   includes :  connect03.gms

$title Simple Connect Example with CSV files (CONNECT03,SEQ=146)

$onText
This problem finds a least cost shipping schedule that meets
requirements at markets and supplies at factories.

GAMS Connect is used to read and write CSV files.
Note: In this example, the CSV data can also be read by using a simple
table statement without doing further preprocessing.


Dantzig, G B, Chapter 3.3. In Linear Programming and Extensions.
Princeton University Press, Princeton, New Jersey, 1963.

This formulation is described in detail in:
Rosenthal, R E, Chapter 2: A GAMS Tutorial. In GAMS: A User's Guide.
The Scientific Press, Redwood City, California, 1988.

The line numbers will not match those in the book because of these
comments.

Keywords: linear programming, transportation problem, scheduling
$offText

$onEcho > distance.csv
i,new-york,chicago,topeka
seattle,2.5,1.7,1.8
san-diego,2.5,1.8,1.4
$offEcho

$onEcho > capacity.csv
i,capacity
seattle,350
san-diego,600
$offEcho

$onEcho > demand.csv
j,demand
new-york,325
chicago,300
topeka,275
$offEcho

Set i 'canning plants', j 'markets';

Parameter d(i<,j<)  'distance in thousands of miles'
          a(i)      'capacity of plant i in cases'
          b(j)      'demand at market j in cases';

$onEmbeddedCode Connect:
- CSVReader:
    file: distance.csv
    name: d
    indexColumns: 1
    valueColumns: "2:lastCol"
- CSVReader:
    file: capacity.csv
    name: a
    indexColumns: 1
    valueColumns: 2
- CSVReader:
    file: demand.csv
    name: b
    indexColumns: 1
    valueColumns: 2
- GAMSWriter:
    symbols: all
$offEmbeddedCode

Scalar f 'freight in dollars per case per thousand miles' / 90 /;

Parameter c(i,j) 'transport cost in thousands of dollars per case';
c(i,j) = f*d(i,j)/1000;

Variable
   x(i,j) 'shipment quantities in cases'
   z      'total transportation costs in thousands of dollars';

Positive Variable x;

Equation
   cost      'define objective function'
   supply(i) 'observe supply limit at plant i'
   demand(j) 'satisfy demand at market j';

cost..      z =e= sum((i,j), c(i,j)*x(i,j));

supply(i).. sum(j, x(i,j)) =l= a(i);

demand(j).. sum(i, x(i,j)) =g= b(j);

Model transport / all /;

solve transport using lp minimizing z;

embeddedCode Connect:
- GAMSReader:
    symbols:
      - name: x
- Projection:
    name: x.l(i,j)
    newName: x_level(i,j)
- CSVWriter:
    file: shipment_quantities.csv
    name: x_level
    unstack: True
endEmbeddedCode