SAS syntax "for all" i in SET

[norachanisara]

Hi,

I am new to SAS and wondering what should be the right SAS syntax for the following

/* Time constraints */
con time_constraints_A:
   sum{i in LOCATIONS, j in LOCATIONS} t_A[i, j] * x[i, j, k]
   + sum{i in LOCATIONS} s_A[i] * y[i, k] <= max_time[k], 
   for all k in VEHICLES where z[k] = 1;

I don't think the last line is correct but that is the logic in plain english I want to do. I want the sum + sum for all k in set VEHICLE where z[k] = 1

Same for this constraint

con type_link:
      v_A[i] * z[k] + v_B[i] * (1 - z[k]) >= x[i, j, k], 
      for all i in LOCATIONS, j in LOCATIONS, k in VEHICLES;

Thanks a lot

[Ksharp]

Post it at SAS/OR forum:
https://communities.sas.com/t5/Mathematical-Optimization/bd-p/operations_research
And calling @RobPratt

[RobPratt]

Assuming that you also want z[k] = 0 to imply that x[i,j,k] = 0 and y[i,k] = 0, you can impose the following:

con time_constraints_A {k in VEHICLES}:
   sum{i in LOCATIONS, j in LOCATIONS} t_A[i, j] * x[i, j, k]
   + sum{i in LOCATIONS} s_A[i] * y[i, k] <= max_time[k] * z[k];

For the second constraint, here is correct syntax:

con type_link {i in LOCATIONS, j in LOCATIONS, k in VEHICLES}:
      v_A[i] * z[k] + v_B[i] * (1 - z[k]) >= x[i, j, k];