$title Kilosa farm problem (KILOSAFARM,SEQ=74)

$onText

Kilosa farm problem using chance constraints from Lindo manual

Reference: LINDO API 7.0 User Manual

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Scalar
*       Random parameters
        ksi_r  'random rainfall during the growing season (mm) [~ Normal(515.5,137.0)]' / 515 /
        eps_m  'white noise in the yield of maize              [~ Normal(  0.0, 10.0)]' /   0 /
        eps_s  'white noise in the yield of sorghum            [~ Normal(  0.0, 10.0)]' /   0 /;

Variable Z Objective;
Positive Variables
         XM acreage of maize in hectares
         XS acreage of sorghum in hectares;

Equations OBJ, CALORIES, PROTEIN;

OBJ..      Z =e= XM + XS;
CALORIES.. 2.8*(0.020*ksi_r - 1.65 + eps_m)*XM + 2.8*(0.008*ksi_r + 5.92 + eps_s)*XS =g= 44;
PROTEIN..  6.4*(0.020*ksi_r - 1.65 + eps_m)*XM + 8.0*(0.008*ksi_r + 5.92 + eps_s)*XS =g= 89;

Model kf / all /;

$ifI %gams.emp%==de $set doDisc 1
$if not set doDisc $set doDisc 0

file emp / '%emp.info%' /; put emp '* problem %gams.i%'/;
* chance <prob> <equ1> [equ2 ... equn]
$ifThen %doDisc%==0
$onPut
randvar ksi_r normal 515.5 137
randvar eps_m normal     0  10
randvar eps_s normal     0  10
chance calories 0.9
chance protein  0.9
$offPut
$else
scalar r;
$if not set samplesize $set samplesize 5
put   'randvar ksi_r discrete '; for (r=1 to %samplesize%, put (1/%samplesize%):8:6 ' ' normal(515.5,137):7:3);
put / 'randvar eps_m discrete '; for (r=1 to %samplesize%, put (1/%samplesize%):8:6 ' ' normal(0,10):7:3);
put / 'randvar eps_s discrete '; for (r=1 to %samplesize%, put (1/%samplesize%):8:6 ' ' normal(0,10):7:3);
put / 'chance calories 0.9'
    / 'chance protein  0.9';
$endIf
putclose emp;

Set scen        scenarios / s1*s100 /;
Parameter
    s_ksi_r(scen)
    s_eps_m(scen)
    s_eps_s(scen)
    s_xm(scen)
    s_xs(scen);

Set dict / scen .scenario.''
           ksi_r.randvar .s_ksi_r
           eps_m.randvar .s_eps_m
           eps_s.randvar .s_eps_s
           xm   .level   .s_xm
           xs   .level   .s_xs    /;

solve kf min z use emp scenario dict;

display s_ksi_r, s_eps_m, s_eps_s, s_xm, s_xs;