Hi all,
I am working in pharma and here I need you help for a problem related to a pharmacokinetic equation.
I would like to have the (X,Y,S, T, U, V, W) possible values that will lead to a value of Z=5.7.
Z= 1/X*1/(Y/(1+(U×V)/(W×(U+S)))+(1-Y)) )
knwing that:
0.57<X<0.79
0.00016<W<0.00032
0.89<Y<0.94
0.0936<U<0.967
V =0.05 ou 0.072
S = 29 ou 5.3
This GAMS model calculates some solutions:
variables z,x,y,u,v,w,s;
equation e;e.. z =e= (1/X)*1/(Y/(1+(U*V)/(W*(U+S)))+(1-Y));
x.lo = 0.57; x.up = 0.79;
w.lo = 0.00016; w.up = 0.00032;
y.lo = 0.89; y.up = 0.94;
u.lo = 0.0936; u.up = 0.0967;binary variable b1,b2;
equation e1,e2;
e1.. v =e= 0.05*b1 + 0.072*(1-b1);
e2.. s =e= 29*b2 + 5.3*(1-b2);z.fx = 5.7;
model m /all/;
b1.fx=0; b2.fx=0; solve m minimizing z using rminlp;
b1.fx=0; b2.fx=1; solve m minimizing z using rminlp;
b1.fx=1; b2.fx=0; solve m minimizing z using rminlp;
b1.fx=1; b2.fx=1; solve m minimizing z using rminlp;
I could only find feasible solutions for b2=0 (i.e. s=5.3). This was confirmed by the global solver Baron. Here they are:
LOWER LEVEL UPPER MARGINAL ---- VAR z 5.7000 5.7000 5.7000 1.0000 |
LOWER LEVEL UPPER MARGINAL ---- VAR z 5.7000 5.7000 5.7000 1.0000 |
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