$title Simple chance constraint model (SIMPLECHANCE,SEQ=82)

$onText

Simple chance constraint model from Lindo manual

Reference: LINDO API 7.0 User Manual

$set JorI I -> individual chance constraints
$set JorI J -> joint      chance constraints

$offText

$if not set JorI $set JorI I

Scalar
*       Random parameters
        om1  / 1 /
        om2  / 1 /;

Variable           Z     Objective;
Positive Variables X1,X2;

Equations OBJ, E1, E2;

OBJ.. Z =e= X1 + X2;
E1..  om1*X1 +   X2 =g=  7;
E2..  om2*X1 + 3*X2 =g= 12;

Model sc / all /;

file emp / '%emp.info%' /; put emp '* problem %gams.i%'/;
* chance <prob> <equ1> [equ2 ... equn]
$ifThenI %JorI% == I
$onPut
randvar om1 discrete 0.25 1
                     0.25 2
                     0.25 3
                     0.25 4
randvar om2 discrete 0.3333 1
                     0.3334 2
                     0.3333 3
chance E1 0.6
chance E2 0.6
$offPut
$else
$onPut
randvar om1 discrete 0.25 1
                     0.25 2
                     0.25 3
                     0.25 4
randvar om2 discrete 0.3333 1
                     0.3334 2
                     0.3333 3
chance E1 E2 0.6
$offPut
$endIf
putclose emp;

Set scen        scenarios / s1*s12 /;
Parameter
    s_om1(scen)
    s_om2(scen)
    x1_l (scen)
    x2_l (scen)
    x1_m (scen)
    e1_l (scen)
    e2_l (scen)
;

Set dict / scen .scenario.''
           om1  .randvar .s_om1
           om2  .randvar .s_om2
           x1   .level   .x1_l
           x2   .level   .x2_l
           x1   .marginal.x1_m
           e1   .level   .e1_l
           e2   .level   .e2_l
/;
solve sc min z use emp scenario dict;

display s_om1, x1_l, x2_l, x1_m, e1_l, e1_l;