! A very simple stochastic programming problem (NewsVendScen);
! The newsvendor problem. Decide how much to stock when we
have uncertain demand;
! Keywords: Charthisto, Newsboy problem, Normal distribution,
Stochastic optimization, QRAND function, Quasirandom ;
SETS:
scene: u, v, x, cost, d, unif; ! Set of scenarios;
ENDSETS DATA:
p = .6; ! Penalty cost/unit for stocking too little;
h = .3; ! Cost/unit of holding too much;
mu = 90; ! Mean demand;
sd = 20; ! Standard deviation. To avoid negative demand,
should have mu >> 3*sd;
scene = 1..250; ! Number of scenarios;
! Generate a vector of quasirandom uniforms with arbitrary seed;
unif = @QRAND(1923436);
nbins = 15; ! Number of bins to use in the histogram,
0 means solver decides;
ENDDATA
SUBMODEL findopt:
! Random parameters:
unif( s) = uniform r.v, used to generate..
d(s) = demand in scenario s,
Decision variables,
stage 0:
x0 = amount to stock,
stage 1:
u(s) = amount under ~ short,
v(s) = amount over;
! minimize average cost of under + over;
min = obj;
obj = @SUM(scene(s): cost(s))/ns;
! For each demand scenario, compute Over and Under;
@FOR(scene(s):
cost(s) = (p*u(s) + h*v(s));
! Under  Over = demand  amount stocked;
u(s)  v(s) = d(s)  x0;
);
ENDSUBMODEL
CALC:
@SET( 'TERSEO',2); ! Output level (0:verb, 1:terse, 2:only errors, 3:none);
ns = @size( scene); ! Number of scenarios;
! Generate a vector of random variables with expected mean and sd;
! Click on: Edit  Paste Function  Distributions to
see all available distributions;
@FOR( scene(s):
d( s) = @PNORMINV( mu, sd, unif( s));
);
@SOLVE( findopt);
@WRITE( 'Recommended amount to stock= ', @FORMAT( x0, '8.2f'),
' (Based on mean demand of: ', @FORMAT( mu, '8.2f'),')', @NEWLINE(1));
@WRITE( 'Expected shortage + overage cost= ', @FORMAT( obj, '8.2f'), @NEWLINE(1));
! Create a histogram with a specified number of bins. To see all available chart types
click on: Edit  Paste Function  Charting;
@CHARTHISTO( 'Histogram of objective', 'Objective value', 'Frequency', 'legend', nbins, cost);
ENDCALC
