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Formulation MCF F comprises O (ˈ A S ˈ ˈ F ˈ + ˈ A R ˈ ) constraints, O (ˈ A S ˈ ˈ F ˈ ) continuous and O (ˈ A ˈ ) binary variables.
Formulation CF R comprises O (ˈ A ˈ ˈ R ˈ 2 ) constraints, O (ˈ A ˈ ˈ R ˈ 2 ) continuous and O (ˈ A ˈ ) binary variables.
Formulation MTZ comprises O (ˈ A ˈ ) constraints, O (ˈ S ˈ ) continuous and O (ˈ A ˈ ) binary variables.
There are 6 classes of problems, and for each problem ˈ F ˈ = ˈ R ˈ.
Formulation CF F comprises O (ˈ A S ˈ ˈ F ˈ 2 ) constraints, O (ˈ A S ˈ ˈ F ˈ 2 ) continuous and O (ˈ A ˈ ) binary variables.
Models SCF R and SCF R + comprise O (ˈ A ˈ ) constraints and O (ˈ A ˈ ) binary variables.
Model SCF F comprises O (ˈ A ˈ ) constraints and O (ˈ A ˈ ) binary and continuous variables.
In this example n ≔ ˈ F ˈ − 1.
Thus, the worst-case running time of the whole peeling method is O (ˈ F ˈ ˈ R ˈ ).
Thus, the total computational complexity for finding the cheapest assignment in the worst case is O (ˈ F ˈ ˈ R ˈ ).
Using one commodity per customer, ConFL can be stated as (15) (MCF R ) min ∑ ij ∈ A x ij c ij + ∑ i ∈ F z i f i s. t. ∑ ji ∈ A f ji k − ∑ ij ∈ A f ij k = 1 i = k − 1 i = r 0 i ≠ k, r ∀ i ∈ V, ∀ k ∈ R (16) 0 ≤ f ij k ≤ x ij ∀ ij ∈ A, ∀ k ∈ R (3 ) – (6 ) Formulation MCF R comprises O (ˈ A ˈ ˈ R ˈ ) constraints, O (ˈ A ˈ ˈ R ˈ ) continuous and O (ˈ A ˈ ) binary variables.
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