How is a conditional summation possible in Cplex? like sumifs in Excel?

Question

I want to sum all used resources among times in my model (it\'s rcpsp model) how can I do it in CPLEX? at first I wrote this:

forall(k in K)
  forall(t in 1..f[n         


        

Answer 1

There are several ways to put your problem into an integer programming framework. There are books written on this subject. I think this is the simplest formulation.

I assume that in your problem, r[i,k] and d[i] are known and that the time horizon is broken into discrete time periods.

• on[i,t] indicator that activity i is active at time t
• start[i,t] indicator that activity i starts at the start of period t
• end[i,t] indicator that activity i finishes at the end of period t

So in[i,t] replaces the condition f[i]-d[i]<=t-1 && t<=f[i])*r[i,k] Your constraint becomes

forall(k in K)
   forall(t in 1..f[nAct])
      sum(i in I : r[i,k] = 1) on[i,t] <= aR[k]; 

You also need to add constraints to enforce the definition of on, start and off.

   forall(t in 2..f[nAct])
      forall(i in I)
         on[i,t-1] - on[i,t] = end[i,t-1] - start[i,t];

   forall(i in I)
      on[i,0] = start[i,0];

   forall(i in I)
      sum(t in 1..f[nAct]) start[i,t] = 1;
   forall(i in I)
      sum(t in 1..f[nAct]) end[i,t] = 1;
   forall(i in I)
      sum(t in 1..f[nAct]) on[i,t] = d[i];