prodsp.gms : Stochastic Programming Example
The problem consists of determining the product mix for a furniture shop with two
workstations: carpentry and finishing. The availability of labor in man-hours at
the two stations is limited. There are four product classes, each consuming a
certain number of man-hours at the two stations. Each product earns a certain
profit and the shop has the option to purchase labor from outside. The objective
is to maximize the profit.
Reference:
- King, A J, Stochastic Programming Problems: Examples from the Literature. In Ermoliev, Y, and Wets, R J, Eds, Numerical Techniques for Stochastic Optimization Problems. Springer Verlag, 1988, pp. 543-567.
Large Model of Types: OSLSE lp
<![CDATA[
$title Stochastic Programming Example (PRODSP,SEQ=186)
$ontext
The problem consists of determining the product mix for a furniture shop with two
workstations: carpentry and finishing. The availability of labor in man-hours at
the two stations is limited. There are four product classes, each consuming a
certain number of man-hours at the two stations. Each product earns a certain
profit and the shop has the option to purchase labor from outside. The objective
is to maximize the profit.
King, A J, Stochastic Programming Problems: Examples from the
Literature. In Ermoliev, Y, and Wets, R J, Eds, Numerical
Techniques for Stochastic Optimization Problems. Springer Verlag,
1988, pp. 543-567.
$offtext
Sets i product class / class-1*class-4 /
j workstation / work-1 *work-2 /
s Nodes / s1*s300 /
Parameters c(i) profit / class-1 12,class-2 20, class-3 18, class-4 40 /
q(j) cost / work-1 5, work-2 10 /
h(j,s) available labor
t(j,i,s) labor required
table trand(j,*,i) min and max values
class-1 class-2 class-3 class-4
work-1.min 3.5 8 6 9
work-1.max 4.5 10 8 11
work-2.min .8 .8 2.5 36
work-2.max 1.2 1.2 3.5 44 ;
t(j,i,s) = uniform(trand(j,'min',i),trand(j,'max',i));
h('work-1',s) = normal(6000,100);
h('work-2',s) = normal(4000, 50);
Variables EProfit expected profit
x(i) products sold
v(j,s) labor purchased
positive variable x,v
Equations obj expected cost definition
lbal(j,s) labor balance;
obj.. EProfit =e= sum(i, c(i)*x(i)) - 1/card(s)*sum((j,s), q(j)*v(j,s));
Equation foo(i) dummy stage 0 constraint for OSLSE;
foo(i).. x(i) =g= 0;
lbal(j,s).. sum(i, t(j,i,s)*x(i)) =l= h(j,s) + v(j,s);
model mix / all /;
mix.solprint$(card(s) > 10) = %solprint.Quiet%;
solve mix using lp maximizing eprofit;
display eprofit.l,x.l;
]]></plaintext></body></div>