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Scheduling problem - cost function

From: Philippe Jugla
Subject: Scheduling problem - cost function
Date: Thu, 1 Apr 2021 15:07:25 +0000

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 TIME:=0...T

#binary variables (already defined and working) 

var start_up {TIME} binary; 

var unit_on {TIME} binary; 


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 



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