```! 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, Quasi-random ; SETS: scene: u, v, x, cost, d, unif; ! Set of scenarios; ENDSETSDATA: 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 quasi-random 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 ```