CPM Cost modelation

Question

I need to make a CPM model with costs using AMPL.

My .mod:

set TASKS;

set ARCS within {TASKS cross TASKS};

param duration{TASKS} >= 0;

param cost{TASKS} >=0; 
param description{TASKS} symbolic;

var
TASKS_ES{TASKS} >= 0;     #Earliest Start 
var 
TASKS_EF{TASKS} >= 0;     # Earliest Finish 
var 
TASKS_LS{TASKS} >= 0;     # Latest Start 
var 
TASKS_LF{TASKS} >= 0;     # Latest Finish 
var 
TASKS_SLACK{TASKS} >= 0;  # Slacks 

#Final time (global) 

var TF >= 0;

minimize CPM: card(TASKS)*TF - sum {j in TASKS} TASKS_SLACK[j];

.. #constraints

My .dat:

param : TASKS : duration cost description :=
   T01   5 5 'A'
   T02   1 1 'B'
   T03   2 2 'C'
   T04   3 3 'D'
   T05   2 2 'E'
   T06   3 3 'F'
   T07   4 4 'G'
   T08   2 2 'H'
   T09   1 1 'I'
   T10   1 1 'J'
;

set ARCS := 
   T01  T02
   T01  T03
   T02  T03
   T02  T05
   T03  T04
   T05  T07
   T04  T07
   T03  T06
   T06  T07
   T07  T08
;

Works perfectly, but i need to add this constraint for calculate the cost of all tasks (I can minimize the duration of all tasks, but i need the optimal time of each task):

cost(duration_task(i,j)) = k(i,j) - cost(i,j) * duration_task(i,j)

duration_task is the time that minimizes my objective function with all the constraints.

This will be like:

subject to cost {(i,j) in ARCS} : max_cost + (min_cost - max-cost / max_time - min_time)*(time_task(i,j) - min_time)

Example:

Need some help, thanks.

• EDITED!