transsp.gms : A Stochastic Transportation Problem

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;
``````