Laguna, M, Applying Robust Optimization to Capacity Expansion of One Location in Telecommunications with Demand Uncertainty. Management Science 44, 11 (1998), 101-110.
Large Model of Type: MIP
$title Robust Optimization (ROTDK,SEQ=185)
$Ontext
Robust Optimization
Laguna, M, Applying Robust Optimization to Capacity Expansion of
One Location in Telecommunications with Demand Uncertainty.
Management Science 44, 11 (1998), 101-110.
$Offtext
SETS s scenarios / 1*1000/
t time periods / t1*t12 /
j components / C001*C010 /
alias(t,tt);
PARAMETERS
di(s,t) increment
D(t,s) demand
c(j) capacity size
p(j) capacity cost
mu mean capacity parameter
sigma std capacity parameter;
mu = 100; sigma = 10;
c(j) = round(uniform(1,mu));
p(j) = round(mu + c(j) + uniform(-sigma,sigma));
di(s,t)$(ord(s) <= 0.25*card(s)) = round(normal( 50,10));
di(s,t)$(ord(s) > 0.25*card(s) and ord(s) <= 0.75*card(s)) = round(normal(100,20));
di(s,t)$(ord(s) > 0.75*card(s)) = round(normal(150,40));
d(t,s) = sum(tt$(ord(tt) <= ord(t)), di(s,tt));
*display c,p,di,d;
parameters dis(t) discount factor
w shortage penalty;
dis(t) = power(.86,ord(t)-1);
w = 5;
variables x(j,t) expansion
z(s) max capacity shortage
cap(t) installed capacity
obj;
integer variable x; positive variable z;
equations capbal(t) capacity balance
dembal(t,s) demand balance
objdef;
objdef.. obj =e= sum((j,t), dis(t)*p(j)*x(j,t))
+ w/card(s)*sum(s, z(s));
capbal(t).. cap(t) =e= cap(t-1) + sum(j, c(j)*x(j,t));
dembal(t,s).. cap(t) + z(s) =g= d(t,s);
model rotdk / all /;
option limcol=0,limrow=0;
* do not reset optcr if already set to a nondefault value
if {(.1 = %gams.optcr%), option optcr = 0.05; };
solve rotdk min obj us mip;
