How to add an additional binary variable with CPLEX and Python?

Question

I have an integer programming problem with a decision variable X_i_j_k_t that is 1 if job i was assigned to worker j for day k and shift t. I am maximizing the benefit of assigning orders to my workers. I have an additional binary variable Y_i_k_t that is 1 if the job was executed and a given day and shift (jobs might require more than one worker). How can I add this variable in CPLEX? So as to form, for example, sum(i, k, t)(Y_i_k_t) <= 1 (the order can´t be done more than once).

Thank you in advance

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– Kevin, Commented Nov 25, 2019 at 3:35

Daniel Junglas · Accepted Answer · 2019-11-21 07:37:02Z

1

You did not say whether you use the CPLEX Python API or docplex. But in either case, you can call the functions that create variables multiple times.

So in the CPLEX Python API call Cplex.variables.add() again to add another set of variables.

In docplex just call Model.binary_var_dict() (or whatever method you used to create X) again for the Y variables.

answered Nov 21, 2019 at 7:37

Daniel Junglas

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6 Comments

Phylosofazo M Over a year ago

I am sorry. I am using the CPLEX Python API. So, with cplex.variables.add() I can add that binary variable? I'm not sure how exactly to do it.

Daniel Junglas Over a year ago

Can you augment your question with the code that creates the X variable? Then I can show you how to analogously create the Y variables.

Phylosofazo M Over a year ago

my_problem.variables.add(obj = coeficientes_funcion_objetivo, lb = [0]*data.n, ub = [1]*data.n, types=['B']*data.n). Where "coeficientes_funcion_objetivo" is my list with the benefit of each order per needed worker.

Daniel Junglas Over a year ago

The functions returns the indices of the X variables. Now do the same to create Y variables and get their indices. Maybe take a look at the examples that ship with CPLEX. There are several examples that create multiple types of variables. For example, admipex8.py which creates variables called supply and cost.

Phylosofazo M Over a year ago

Ok, I think I got it, thanks! The objective function of this problem is maximize the benefit minus the cost. These are two different sums. How can I do thiis with CPLEX Python API?

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