如何使用 CPLEX opl 添加这样的约束？

Question

S[i][j][k] is the starting time of operation O[i][j] on machine[k].

C[i][j][k] completion time of operation O[i][j] on machine[k].

v[i][j][k] equals 1 if operation O[i][j] performs on machine[k], otherwise 0.

I want to add constraint that S[i][j][k]+C[i][j][k]<=v[i][j][k]*Big-M, where k belongs to MC[i][j]

MC[i][j] is the candidate machine set that can process operation O[i][j].

Can anyone help to formulate this problem?

I am new to CPLEX, and I don't know how to add a constraint like this(because k has some constraint that k should belongs to MC[i][j])

Answer 1

In OPL you can write this sort of constraint almost as if it were natural language:

float bigM = ...; // Put some value for bigM
forall (i in I)
  forall (j in J)
    forall (k in MC[i][j])
      S[i][j][k] + S[i][j][k] <= v[i][j][k] * bigM;

Note that there seems to be a problem in your description: S[i][j][k] specifies both the starting and completion time of a job. That is most likely not what you want.