set dienst := 1..16;
set arzt := 1..10;
set tag := 1..14;

param eignung{arzt, dienst}, binary;
param tagAbw{arzt, tag}, binary;
param nachfrage{dienst,tag}, binary;
set abwesend := { (j,t) in {arzt,tag}: tagAbw[j,t] != 0 }; 
set anwesend := { (j,t) in {arzt,tag}: (j,t) not in abwesend };
set geeignet := { (j,i) in {arzt, dienst}: eignung[j,i] != 0 };

var xUD{i in dienst, t in tag};
var x{i in dienst,j in arzt, t in tag}, binary;

maximize cost:
	sum{i in dienst,j in arzt, t in tag} x[i,j,t];
	
s.t. f2{i in dienst, (j,t) in anwesend }: 
	sum{(j,p) in geeignet}x[i,j,t] + xUD[i,t] == nachfrage[i,t];
		
solve;

# Data block

data;

param nachfrage :  
1 2 3 4 5 6 7 8 9 10 11 12 13 14 
:=
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
3 1 1 1 1 1 1 1 1 1 1 1 1 1 1
4 1 1 1 1 1 1 1 1 1 1 1 1 1 1
5 1 1 1 1 1 1 1 1 1 1 1 1 1 1
6 1 1 1 1 0 0 1 1 1 1 1 0 0 1
7 0 1 1 1 1 0 0 0 1 1 1 1 0 0
8 0 1 1 1 1 0 0 0 1 1 1 1 0 0
9 1 0 1 1 1 0 0 1 0 1 1 1 0 0
10 1 1 0 1 1 0 0 1 1 0 1 1 0 0
11 1 1 1 0 1 0 0 1 1 1 0 1 0 0
12 1 1 1 1 0 0 0 1 1 1 1 0 0 0
13 1 1 1 1 1 0 0 1 1 1 1 1 0 0
14 1 1 1 1 1 0 0 1 1 1 1 1 0 0
15 1 1 1 1 1 0 0 1 1 1 1 1 0 0
16 1 1 1 1 1 0 0 1 1 1 1 1 0 0;

param tagAbw : 
1 2 3 4 5 6 7 8 9 10 11 12 13 14 
:=
1 0 1 0 0 0 0 0 0 0 0 0 1 0 0  
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0  
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0  
4 0 0 0 0 0 1 0 0 0 0 1 0 0 0  
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0  
6 0 0 0 0 0 0 0 0 0 0 0 0 0 0  
7 0 1 0 0 0 0 0 0 0 1 0 1 0 1  
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0  
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0  
10 0 0 0 1 0 0 0 0 0 0 0 1 0 0 ;


param eignung : 
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 
:=
1 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 1 
2 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 1 
3 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 1 
4 1 0 0 0 0 0 1 1 0 0 0 1 0 0 1 1 
5 1 0 0 0 0 0 1 1 0 0 0 1 0 0 1 1 
6 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 1 
7 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 
8 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 
9 0 1 0 0 0 1 1 1 0 0 0 1 0 0 1 1 
10 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1; 

end;