Description

This model is a stochastic extension of the TRNSPORT model from the GAMS model
library. Here the demand at each market is uncertain. This is modeled with a
random variable df (demand factor) which gets multiplied with the demand. It has
a discrete distribution. A recourse variable u (unsatisfied demand) was added.

Contributor: Lutz Westermann

Small Model of Type : SP

Category : GAMS EMP library

Main file : transsp.gms

$title  A Stochastic Transportation Problem (TRANSSP,SEQ=94)
$onText

This model is a stochastic extension of the TRNSPORT model from the GAMS model
library. Here the demand at each market is uncertain. This is modeled with a
random variable df (demand factor) which gets multiplied with the demand. It has
a discrete distribution. A recourse variable u (unsatisfied demand) was added.

Contributor: Lutz Westermann

$offText


  Sets
       i   canning plants   / seattle, san-diego /
       j   markets          / new-york, chicago, topeka / ;

  Parameters

       a(i)  capacity of plant i in cases
         /    seattle     350
              san-diego   600  /

       b(j)  demand at market j in cases
         /    new-york    325
              chicago     300
              topeka      275  / ;

  Table d(i,j)  distance in thousands of miles
                    new-york       chicago      topeka
      seattle          2.5           1.7          1.8
      san-diego        2.5           1.8          1.4  ;

  Scalar f  freight in dollars per case per thousand miles  /90 /
         p  penalty for unsatisfied demand                  / 1 /
         bf demand factor                                   / 1 /;

  Parameter c(i,j)  transport cost in thousands of dollars per case ;

            c(i,j) = f * d(i,j) / 1000 ;

 display c;

  Variables
       x(i,j)  shipment quantities in cases
       u(j)    unsatisfied demand (recourse variable)
       z       total transportation costs in thousands of dollars ;

  Positive Variable x,u ;

  Equations
       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)) + p*sum(j,u(j));

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

  demand(j) ..   sum(i, x(i,j))  =g=  bf*b(j) - u(j) ;

Model transport /all/ ;

file emp / '%emp.info%' /; put emp '* problem %gams.i%'/;
$onPut
randvar bf discrete 0.3 0.95
                    0.5 1.00
                    0.2 1.05
stage 2 bf u demand
$offPut
putclose emp;

Set scen        scenarios / l,m,h /;
Parameter
    s_bf(scen)    demand factor realization by scenario
    s_u(scen,j)
    s_x(scen,i,j) shipment per scenario
    s_s(scen) ;

Set dict / scen .scenario.''
           bf   .randvar .s_bf
           u    .level   .s_u
           x    .level   .s_x /;

Solve transport using emp minimizing z scenario dict;

Display s_bf, s_x, s_u;