$title Newsboy problem, discrete and joint distribution (NBDISCJOINT,SEQ=79)

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Newsboy problem from Lindo manual
Random paramters D and R are discrete and jointly distributed

Reference: LINDO API 7.0 User Manual

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Scalar  c       Purchase costs per unit                                 / 30 /
        p       Penalty shortage cost per unit unsatisfied demand       /  5 /
        h       Holding cost per unit leftover                          / 10 /
        v       Revenue per unit sold                                   / 60 /
*       Random parameters
        d       Demand                                                  / 63 /
        r       Refund per unit                                         /  9 /;

Variable Z Profit;
Positive Variables
         X Units bought
         I Inventory
         L Lost sales
         S Units sold
         Y Units returned
         E Units kept;

Equations Row1, Row2, Row3, Row4, Profit;

* Units bought, X, Buy at least 1 (serves as a dummy constraint for stage 1);
Row1.. X =g= 1;

* Inventory (I) and Lost Sales (L);
Row2.. I =e= X + L - d;

* Units sold S, and inventory left over, I;
Row3.. S =e= X - I;

* Y units returned to vendor for a possible refund, and E kept;
Row4.. Y + E =e= I;

* Profit, to be maximized;
Profit..  Z =e= v*S - c*X - h*I - p*L + r*Y - h*E;

Model nb / all /;

file emp / '%emp.info%' /; put emp '* problem %gams.i%'/;
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jrandvar d r 0.12 90 9 0.28 90 -15 0.15 60 9 0.15 60 -15 0.27 30 9 0.03 30 -15
stage 2 d r
stage 2 I L S Y E Z
stage 2 Row2 Row3 Row4 Profit
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putclose emp;

Set scen        scenarios / s1*s36 /;
Parameter
    s_d(scen)   demand realization by scenario
    s_r(scen)   refund realization by scenario
    s_x(scen)
    s_s(scen) ;

Set dict / scen .scenario.''
           d    .randvar .s_d
           r    .randvar .s_r
           s    .level   .s_s
           x    .level   .s_x /;

solve nb max z use emp scenario dict;

display s_d, s_r, s_s, s_x;