[Help-glpk] Newbie Question

[Mark Dyer]

I am trying to write a model to maximize overall output when selecting personnel
given a budget, the salary of each potential person and their output ability.
 
The problem I have is writing a rule where one person will be choosen as team 
leader and their output will be calculated as double.
 
Please, could someone help me with this?
 
Thanks.
 
/* sets */
set PERSON;
set POSITIONS;
/* parameters */
param num_of_positions {i in POSITIONS};
param salary {i in PERSON};
param output {i in PERSON};
param position {i in PERSON, j in POSITIONS};
/* decision variables: yi, i in {1,..,7}. yi = 1 -> person i is hired */
var y {i in PERSON} binary >=0;
/* objective function */
maximize z: sum{i in PERSON} output[i]*y[i];
/* Constraints */
s.t. pos{j in POSITIONS}: sum{i in PERSON} 
      position[i,j]*y[i] = num_of_positions[j];
s.t. people: sum{i in PERSON} y[i] = 12;
s.t. budget: sum{i in PERSON} salary[i]*y[i] <= 1150000;

data;
set PERSON := 1 2 3 ... 100;
set POSITIONS := A B C D E;
 
param num_of_positions :=
A     1
B     5
C     3
D     2
E     1;
 
param salary:=
1   90000
2   90000
3   70000
.
.
98  61000
99  58000
100 67000;
 
param output:=
1   22
2   93
3   14
.
.
98  41
99  10
100 16;

param position: A B C D E:=
1               1 0 0 0 0
2               0 0 1 0 0
3               0 1 0 0 0
.
.
98              0 1 0 0 0
99              0 0 0 0 1
100             1 0 0 0 0;




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I am trying to write a model to maximize overall output when selecting personnel
given a budget, the salary of each potential person and their output ability.
 
The problem I have is writing a rule where one person will be choosen as team leader and their output will be calculated as double.
 
Please, could someone help me with this?
 
Thanks.
 
/* sets */
set PERSON;
set POSITIONS;
/* parameters */
param num_of_positions {i in POSITIONS};
param salary {i in PERSON};
param output {i in PERSON};
param position {i in PERSON, j in POSITIONS};
/* decision variables: yi, i in {1,..,7}. yi = 1 -> person i is hired */
var y {i in PERSON} binary >=0;
/* objective function */
maximize z: sum{i in PERSON} output[i]*y[i];
/* Constraints */
s.t. pos{j in POSITIONS}: sum{i in PERSON}
      position[i,j]*y[i] = num_of_positions[j];
s.t. people: sum{i in PERSON} y[i] = 12;
s.t. budget: sum{i in PERSON} salary[i]*y[i] <= 1150000;

data;
set PERSON := 1 2 3 ... 100;
set POSITIONS := A B C D E;
 
param num_of_positions :=
A     1
B     5
C     3
D     2
E     1;
 
param salary:=
1   90000
2   90000
3   70000
.
.
98  61000
99  58000
100 67000;
 
param output:=
1   22
2   93
3   14
.
.
98  41
99  10
100 16;

param position: A B C D E:=
1               1 0 0 0 0
2               0 0 1 0 0
3               0 1 0 0 0
.
.
98              0 1 0 0 0
99              0 0 0 0 1
100             1 0 0 0 0;

---

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