[SCIP] Complexity of Milp formulation

[Faten]

Hello,
Please, can someone help me the complexity of my MILP formualtion that can
determine the assignment of resources to tasks.




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Here are the details

My assignment problem is modeled as a mixed integer linear program (MILP)
and solved by CPLEX in order to determine the VM type of each task.
X(i,t) i = 1 means that the task Ti is assigned to VM of type t, otherwise
X(i,t) = 0.
fi denotes the finish time of task Ti. Our MILP problem can be formally
described as follows (an objective function (1)
and some constraints (2 to 7)):
The goal of the objective function (1) is to minimize the total execution
cost of the workflow.
 Each task is assigned to one and only one VM type according to constraint
(2).
Constraints (3) and (4) guarantee the precedence constraints.
Constraint (5) denotes a binary decision variable. According
to constraint (6), the execution times of tasks are integers (in minutes).
Finally, the deadline is met according to the constraint (7).

Thanks

Best Regards,
Faten

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