Scheduling problem - cost function

[Philippe Jugla]

Hello everyone,

 

I have some difficulties to add a cost parameter that depends on 2 variables to a scheduling model in GLPK. 

 

The problem is as follows : 

 

If the unit has started up and been active for less than k hours than the cost follows a certain cost function, if it has been more than k hours then the cost follows another function. 

 

I have tried the following example but doesn’t seem to work : 

 

#set

set TIME:=0...T

#binary variables (already defined and working) 

var start_up {TIME} binary; 

var unit_on {TIME} binary; 

#parameters

param T:=10;

param price {TIME};

param k:=2;

#this is what I’ve tried :

param cost {t in TIME} := 

              if sum { s in TIME : s = t - k and s >= 0 } start_up[s] + unit_on[s] < k+1 then 2.5*price[t] + 5 else 3.0*price[t] + 10; 

 

The following error is thrown : « operand preceding < has invalid type ». I guess it is because of the variables ? I tried to define cost as a variable but with no success as well..

I am also trying to workaround things by defining another binary variable X {TIME} that I would constrain, and then define the cost with something like cost[t] = (1-X)*(cost_function_1) + X*cost_function_2 but it seems quite complicated for this type of problem.

Does anyone know what is the issue ? How could I work things out ?

Any help or advice would be greatly appreciated !

Best regards 

 

Philippe